Page 1 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 1, Electric Charges and Fields, Electrostatics, Electrostatics deals with the study of forces, fields and potentials arising, from static charges., , Frictional electricity, The electricity produced by rubbing suitable bodies is called frictional, electricity., On rubbing electrons are transferred from one body to the other. The body,, which loses electrons, will become positively charged and which gains, electrons becomes negatively charged., , Electric Charge, From simple experiments on frictional electricity, it is inferred that there, are two types of charges in nature-Positive and Negative ., Like charges repel and unlike charges attract., • When a glass rod is rubbed with silk, glass rod becomes positively, charged and silk negaitive., • When a plastic rod is rubbed with fur, plastic rod becomes negatively, charged and fur positive., 1. Good conductors like copper cannot be charged by friction because any, charge produced on it can easily flow through the rod through our body and, to the ground., 2. Insulators like plastic, ebonite, glass etc can be easily charged by friction, because the charges will stay on them., 3. Electrostatic experiments cannot be performed in moist climate because, moist air is slightly conducting. So the static charges will get conducted away, from the charged body., , How is frictional electrification caused?, The number of protons inside the nucleus of an atom is equal to the number, of electrons outside the nucleus. When a body is rubbed with another, due to, friction, some electrons from one body gets transferred to the other body., The body, which loses electrons, will become positively charged and which, gains electrons becomes negatively charged. The two bodies thus acquire, opposite charges and they are equal in magnitude. This is the reason for, frictional electricity., , Gold Leaf Electroscope, A simple apparatus to detect charge on a body is called a gold-leaf, electroscope.

Page 2 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Apparatus It consists of a vertical metal rod placed in a box. Two thin gold, leaves are attached to its bottom end as shown in figure., , Working, When a charged object touches the metal knob at the top of the rod, charge, flows on to the leaves and they diverge. The degree of divergence is an, indicator of the amount of charge., , Conductors and Insulators, Conductors, Conductors are those substances which allow passage of electricity through, them., Eg. Metals, human and animal bodies and earth are conductors., • They have electric charges (electrons) that are comparatively free to, move inside the material., • When some charge is transferred to a conductor, it readily gets, distributed over the entire surface of the conductor., ▪ Metals cannot be charged by friction,because the charges transferred, to the metal leak through our body to the ground as both are, conductors of electricity., , Insulators, The substances which offer high resistance to the passage of electricity, through them are called Insulators ., Eg. glass, porcelain, plastic, nylon, wood, ▪ If some charge is put on an insulator, it stays at the same place. So, insulators gets electrified on combing dry hair or on rubbing,, , Earthing (or) Grounding, When a charged body is brought in contact with, earth, all the excess charge pass to the earth, through the connecting conductor. This process of, sharing the charges with the earth is called, grounding or earthing. Earthing provides, protection to electrical circuits and appliances.

Page 3 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Methods of Charging, A body can be charged in different ways, 1)Charging by friction, 2)Charging by conduction, 3)Charging by induction, , 1) Charging by friction, When two bodies are rubbed each other, electrons in one body (in which, electrons are held less tightly) transferred to second body (in which, electrons are held more tightly), When a glass rod is rubbed with silk, some of the electrons from the glass, are transferred to silk. Hence glass rod gets +ve charge and silk gets -ve, charge., , 2) Charging by conduction, Charging a body with actual contact of another body is called charging by, conduction. If a neutral conducting body (A) is brought in contact with, positively charged conducting body (B), the neutral body gets positively, charged., , 3)Charging by induction, When a charged body is brought near to an uncharged conductor (without, touching), that end of the uncharged conductor which is near to the charged, body gets oppositely charged and the farther end is charged with the same, type of charge.

Page 4 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Charging a metal sphere positively without touching it, , Properties of electric charges, 1.Electric charges are of two kinds – positive and negative., 2.Like charges repel and unlike charges attract each other., 3. Quantization of charge : According to quantisation of electric charge,, charge of a body is an integral multiple of a basic charge, which is the, electronic charge., Charge on a body, q=± ne ;, , where, n=1,2,3........., , e is the electronic charge. e=1.602 x 10−19 C, 4. Charge is conserved: It means that total charge of an isolated system, remains constant. It also implies that electric charges can neither be created, nor destroyed. If an object loses some charge, an equal amount of charge, appears somewhere else., 5.Charge is a scalar quantity., 6. Additivity of charge: The total charge on a surface is the algebraic sum of, individual charges present on that surface., If q1 , q 2 , q 3 ....................., q n are the charges on a surface, then total or net, charge,, 𝒒 = 𝒒𝟏 + 𝒒𝟐 + 𝒒𝟑 +.................. + 𝒒𝒏, , Example 1, How many electronic charges form 1 C of charge?, q=±ne,, 𝑞, n=, 𝑒, , n=, , 1, , 1.602 x 10−19, , =6.25 x1018

Page 5 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example 2, A comb drawn through person’s hair causes 1022 electrons to leave the, person’s hair and stick to the comb. Calculate the charge carried by the, comb., q= ne,, q = 1022 x 1.602 x 10−19 C, = −1.602 x 103 C, As the comb gains electrons it gets negatively charged., , Coulomb’s Law, , Definition of coulomb, 𝟏, , 𝐅 = 𝟒𝛑𝛆, , 𝟎, , 𝐪𝟏 𝐪𝟐, 𝐫𝟐, , Coulomb’s Law in vector form

Page 6 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Super position principle, Force on a charge due to a number of charges is the vector sum of forces, due to individual charges.For a system of n charges., , Electric Field, Electric field is the region around a charge where its effect can be felt., Intensity of electric field at a point is the force per unit charge., , 𝐄=, , 𝐅, 𝐪, , Electric field due to a point charge, , 𝟏, 𝐄 = 𝟒𝛑𝛆, , 𝐪, 𝟐, 𝟎𝐫, , Electric field due to a system of charges, Electric field at a point due to a system of charges is the vector sum of the, electric fields at the point due to individual charges.

Page 7 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Electric Field Lines, An electric field line is a curve drawn in such a way that the tangent to it at, each point is in the direction of the net field at that point., ▪ Electric Field lines tart from positive charge, end at negative charge., ▪ Electric field lines of a positive charge are radially outwards and, that of a negative charge is radially inwards, ▪ Electric field lines do not form closed loops., ▪ In a charge free region field lines are continuous., ▪ Two field lines never intersect.( Two directions for electric field is, not possible at a point), ▪ Field lines are parallel ,equidistant and in same direction in, uniform electric field., Positive Charge, , Negative Charge, , Two positive Charges, , Dipole - Positive and Negative charge

Page 11 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Dipole in a Uniform External field, In a uniform electric field there will be a net torque on the dipole, but the net, force will be zero. Due to the torque ,the dipole rotates. There will be no, translatory motion as the net force is zero., , Torque on a Dipole in a Uniform External field, , Torque,, , τ = one of the forces x perpendicular distance between them., τ = qE x 2a sinθ, τ =pE sinθ, , ⃗ ×𝐄, ⃗, 𝛕=𝐏, • When p and E are in the same direction or opposite direction( θ=0 or180 ), τ =pE sin0 =0, • Torque is maximum , when p and E are perpendicular. (θ=90), τ =pE sin90 =pE, , Dipole in a non uniform electric field, In a non uniform electric field the dipole experiences a net force as well as a, net torque in general ., Case 1 -when p is parallel to E, , when p is parallel to E, the dipole has a net force in the direction of, increasing field., But the net torque will be zero τ =pE sin0 =0

Page 16 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example, Find the electric field due two plane sheets of charge in regions I ,II and III

Page 17 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 2, Electrostatic Potential and Capacitance, Electrostatic Potential Energy, Electrostatic potential energy difference between two points, Electric potential energy difference between two points in an electric field ,, can be defined as the work done by an external force in moving (without, accelerating) charge q from one point to another in the electric field ., P, , ∆U = UP − UR = − ∫R F . dr, , • The work done by an electrostatic field in moving a charge from one, point to another depends only on the initial and the final points and is, independent of the path taken to go from one point to the other., , Electrostatic Potential Energy at a point, Electric potential energy at a point P in an electric field is defined as the, work done by the external force in bringing the charge q from infinity to, that point., UP∞ = UP − U∞ = UP − 0 = UP, 𝐏, , 𝐔𝐏 =− ∫∞ 𝐅 . ⅆ𝐫, , Electrostatic Potential (V), V=, , W, q, , W=qV, Unit of potential is J/C or volt (V)

Page 18 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Electrostatic Potential difference between two points, Electrostatic Potential difference between two points in an electric field is, the work done by an external force in bringing a unit positive charge from, one point to other in that field., W, VP − VR = RP, q, , P, , VP − VR =, , − ∫R F .dr, q, , F=qE, P, , VP − VR =, , 𝐕𝐏 − 𝐕𝐑 =, , 𝐏, − ∫𝐑 𝐄, , − ∫R qE .dr, q, , . ⅆ𝐫, , Electrostatic Potential at a point P, Electrostatic Potential at a point P in an electric field is the work done by an, external force in bringing a unit positive charge from infinity to that point., 𝐏, , 𝐕𝐏 = − ∫∞ 𝐄 . ⅆ𝐫, Potential due to a Point Charge

Page 19 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Variation of potential V with r and Electric field with r for a point charge Q, , Example, (a) Calculate the potential at a point P due to a charge of 4 × 10−7 C,located, 9 cm away, (b) Hence obtain the work done in bringing a charge of 2 × 10−9 C from, infinity to the point P. Does the answer depend on the path along which, the charge is brought?, 1 𝑄, (a) V =, 4πε0 𝑟, , 9, , = 9 × 10 x, 𝟒, , 4 𝑥 10−7, 0.09, , V = 𝟒 𝒙 𝟏𝟎 V, (b) W= qV, = 2 𝑥 10−9 x 4 𝑥 104, W = 𝟖 𝒙 𝟏𝟎−𝟓 J, No, work done will be path independent. Any arbitrary infinitesimal path, can be resolved into two perpendicular displacements: One along r and, another perpendicular to r. The work done corresponding to the later will be, zero., , Potential due to an Electric Dipole

Page 21 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Potential due to a System of Charges, By the superposition principle, the potential at a point due to a system of, charges is the algebraic sum of the potentials due to the individual charges., , V = V1 + V2 + ⋯, V =, , 𝐕 =, , 1, , q1, , 4πε0 r1, , 𝟏, , +, , + Vn, , 1, , q2, , 4πε0 r2, , 𝐪, , 𝟒𝛑𝛆𝟎, , + ……………+, , 𝐪𝟐, , (𝐫𝟏 +, , 𝐫𝟐, , 𝟏, , 1, , qn, , 4πε0 rn, , + ……………+, , 𝐪𝐧, 𝐫𝐧, , ), , Potential due to a uniformly charged spherical shell, , a)The potential at a distance r, from the shell ,where r≥ R, (R-radius of sphere), For a uniformly charged spherical shell, the electric field outside the shell is, as if the entire charge is concentrated at the centre, 𝟏, , 𝐪, , V= 𝟒𝛑𝛆, , 𝟎, , 𝐫, , (r≥ R), , b) Inside the shell, Inside the shell the electric field is zero. This implies that the potential is, constant inside the shell ,which is equal to the value of potential at the, surface, 𝟏, , V= 𝟒𝛑𝛆, , 𝟎, , 𝐪, 𝐑, , Example, Two charges 3 𝑥 10−8 C and –2 𝑥 10−8 C are located 15 cm apart. At what, point on the line joining the two charges is the electric potential zero? Take, the potential at infinity to be zero.

Page 23 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Equipotential Surfaces, An equipotential surface is a surface with a constant value of potential at all, points on the surface., • As there is no potential difference between any two points on an, equipotential surface, no work is required to move a test charge on the, surface., • For any charge configuration, equipotential surface through a point is, normal to the electric field at that point, , Equipotential surfaces for a single point charge, For a single charge q, the potential is, 1 q, V=, 4πε0 r, , V is a constant if r is constant ., Thus, equipotential surfaces of a single point charge are concentric spherical, surfaces centred at the charge., , Equipotential surfaces for a uniform electric field., , Equipotential surfaces for a dipole, , Equipotential surfaces for two identical positive charges.

Page 26 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Potential energy of a dipole in an external field, , Electrostatics of conductors, 1.Inside a conductor, electrostatic field is zero, A conductor has free electrons. In the static situation, the free charges have, so distributed themselves that the electric field is zero everywhere inside., 2. At the surface of a charged conductor, electrostatic field must be normal, to the surface at every point., 3. The interior of a conductor can have no excess charge in the static, situation., 4. Electrostatic potential is constant throughout the volume of the, conductor and has the same value (as inside) on its surface.

Page 27 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , 5.Electric field at the surface of a charged conductor E =, , σ, , ε0, , 6.Electrostatic shielding, The electric field inside a cavity of any conductor is zero. This is known as, electrostatic shielding. All charges reside only on the outer surface of a, conductor with cavity., The effect can be made use of in protecting sensitive instruments from, outside electrical influence., Why it is safer to be inside a car during lightning?, Due to Electrostatic shielding, electricfield E=0 inside the car., So it is safer to sit inside a car than standing outside during lightening., , Dielectrics and polarisation, Dielectrics, Dielectrics are non-conducting substances. In contrast to conductors, the, Dielectric substances may be made of polar or non polar molecules., , Non polar molecules, , In a non-polar molecule, the centres of positive and negative charges, coincide. The molecule then has no permanent (or intrinsic) dipole moment., Eg: oxygen (O2 ) , hydrogen (H2 )

Page 28 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , In an external electric field, the positive and negative charges of a nonpolar, molecule are displaced in opposite directions. The non-polar molecule thus, develops an induced dipole moment. The dielectric is said to be polarised by, the external field, , Polar molecules, , In polar molecules, the centres of positive and negative charges are, separated (even when there is no external field). Such molecules have a, permanent dipole moment., Eg: HCl , H2 O, In the absence of any external field, the different permanent dipoles are, oriented randomly ; so the total dipole moment is zero. When an external, field is applied, the individual dipole moments tend to align with the field. A, dielectric with polar molecules also develops a net dipole moment in an, external field., , Polarisation(P), The dipole moment per unit volume is called polarisation ., For linear isotropic dielectrics,, , 𝐏 = 𝛘𝐞 𝐄, where χe is the electric susceptibility of the dielectric medium., , Capacitor, A capacitor is a system of two conductors separated by an insulator., Capacitor is a charge storing device.

Page 29 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Capacitance, The potential difference, V ( V = V1 - V2 ) between the two is proportional to, the charge , Q., Q∝V, Q=CV, , 𝐂=, , 𝐐, 𝐕, , The constant C is called the capacitance of the capacitor., C is independent of Q or V., The capacitance C depends only on the geometrical configuration (shape,, size, separation) of the system of two conductors ., SI unit of capacitance is farad., 1 farad =1 coulomb volt −1, 1 F = 1 C V −1, Other units are,, 1 μF = 10 -6 F , 1 nF = 10 -9 F , 1 pF = 10-12 F, etc., , Symbol of capacitor, Fixed capacitance, , • C=, , Q, V, , Variable capacitance, , . For large C, V is small for a given Q. This means a capacitor, , with large capacitance can hold large amount of charge Q at a relatively, small V, • High potential difference implies strong electric field around the, conductors. A strong electric field can ionise the surrounding air and, accelerate the charges so produced to the oppositely charged plates,, thereby neutralising the charge on the capacitor plates, at least partly., • The maximum electric field that a dielectric medium can withstand, without break-down (of its insulating property) is called its dielectric, strength; for air it is about 3 × 106 V𝑚−1, , The parallel plate capacitor, A parallel plate capacitor consists of two large plane parallel conducting, plates separated by a small distance.

Page 30 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Capacitance of a parallel plate capacitor, , Capacitance can be increased,, • By increasing the area of the plates., • By decreasing the distance between the plates., • By introducing a dielectric medium between the plates., , Effect of dielectric on capacitance, The capacitance of a parallel plate capacitor when the medium between the, plates is air,, Cair =, , ε0 A, d, , When dielectric medium of dielectric constant K is placed between the, plates, the capacitance ,, Kε0 A, , Cmed =, , d, , The capacitance increases K times, where K is the dielectric constant., , 𝐂𝐦𝐞ⅆ =K 𝐂𝐚𝐢𝐫, Definition of dielectric constant in terms of capacitance, Cmed, Cair, , K=, , Kε0 A, d, ε0 A, d, 𝐂𝐦𝐞ⅆ, , =, , =K, , 𝐂𝐚𝐢𝐫, , The dielectric constant of a substance is the factor by which the capacitance, increases from its vacuum value, when a dielectric is inserted between the, plates.

Page 33 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The effective capacitance increases when capacitors are connected in, parallel. In parallel combination the effective capacitance will be greater, than the greatest among individual capacitors., , Example, Find the effective capacitance of the combination., , C = C1 + C2 + C3, C =0.1 μF + 0.2 μF + 0.3 μF, C =0.6 μF

Page 35 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Energy Stored in a Capacitor, 1, , 2, , This work is stored as potential energy in the electric field between the, plates., , Energy 𝐔 =, , 𝐐𝟐, 𝟐𝐂

Page 36 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Energy stored in a capacitor can also be expressed as, , u=, , U, Ad

Page 37 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 3, Current Electricity, Charges in motion constitute an electric current. Such currents occur, naturally in many situations. Lightning is one such phenomenon in which, charges flow from the clouds to the earth through the atmosphere. The flow, of charges in lightning is not steady, but in our everyday life we see many, devices where charges flow in a steady manner. A torch and a cell-driven, clock are examples of such devices., , Electric Current, When current steady ,, The rate of flow of charge through any cross-section of a conductor is, called electric current flowing through it., , 𝐈=, Unit of electric current =, , 𝐪, 𝐭, , coulomb, second, , =C/s =ampere (A), , When current is not steady,, The current at time t across the cross-section of the conductor is defined as, the ratio of ∆Q to ∆t in the limit of ∆t tending to zero,, 𝚫𝐐, ⅆ𝐐, I= 𝐥𝐢𝐦, =, 𝚫𝐭→𝟎 𝚫𝐭, , ⅆ𝐭, , Electric Currents in Conductors, When no electric field is present:The electrons will be moving due to thermal motion . During motion, electrons collide with the fixed ions. The direction of its velocity after the, collision is completely random. The average velocity of electrons will be, zero. So, there will be no net electric current., When an electric field is present:-, , The electrons will be accelerated due to this field towards +Q. They will thus, move to neutralise the charges and constitute an electric current. Hence, there will be a current for a very short while and no current thereafter., To maintain a steady electric field in the body of the conductor we use cells, or batteries.

Page 38 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Ohm’s Law, A basic law regarding flow of currents was discovered by G.S. Ohm in 1828., At constant temperature ,the current flowing through a conductor is directly, proportional to the potential difference between the ends of the conductor., V∝I, V = RI, 𝐕, 𝐑=, 𝐈, The constant of proportionality R is called the resistance of the conductor, The SI units of resistance is ohm and is denoted by the symbol Ω., , Conductance, The reciprocal of resistance is called Conductance., 𝟏, 𝐂=, 𝐑, 𝐈, , 𝐂=, 𝐕, −1, −1, Unit of conductance is ohm (Ω or mho) or =siemens, Ohm’s Law : Experimental verification, , Voltage –Current Graph (V-I Graph), AB, Slope =, BC, 𝐕, , Slope = = R, 𝐈, Slope of V-I graph gives Resistance., Its reciprocal gives conductance., Which material has more resistance?, , Slope of V-I graph gives Resistance. Slope of A is greater than that of B., So material A has more resistance than B.

Page 39 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Factors on which the Resistance of a Conductor Depends:1)The material of the conductor, 2)The dimensions of the conductor, a)Length of the conductor, The resistance of a conductor is directly proportional to, length l of the conductor., 𝐑∝𝒍, b) The area of cross section of the conductor, The resistance of a conductor is inversely proportional to the crosssectional area, A., 𝟏, 𝐑∝, 𝐀, , Resistivity of a Conductor, The resistance of a conductor is directly proportional to length 𝑙 of the, conductor and inversely proportional to the cross-sectional area, A., 𝑙, R∝, A, , 𝐑=, , 𝛒𝒍, 𝐀, , where the constant of proportionality ρ is called resistivity., Resistivity depends on the material of the conductor but not on its, dimensions., , 𝛒=, Unit of resistivity =, , 𝐑𝐀, 𝒍, , Ωm2, m, , Ohm’s Law in Vector Form, , = Ωm

Page 41 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Conductivity, Comparing with, j = σE, , 𝛔=, , 𝐧𝐞𝟐 𝛕, 𝐦, , Mobility, Conductivity arises from mobile charge carriers., In metals, these mobile charge carriers are electrons., In an ionised gas, they are electrons and positive charged ions., In an electrolyte, these can be both positive and negative ions., Mobility µ defined as the magnitude of the drift velocity per unit electric, field., 𝛍=, 𝛍=, , 𝐯ⅆ, 𝐄, , =, , 𝐞𝐄, 𝛕, 𝐦, , eE, τ, m, , E, , Limitations of Ohm’s Law, Ohmic Conductors, Conductors which obey Ohm’s law are called Ohmic, conductors.The Voltage – Current graph of such, conductors will be linear ., Eg:- metals ,Nichrome, Non - Ohmic Conductors, The materials and devices used in electric circuits which do not obey Ohm’s, law are called Non – Ohmic conductors. So V-I grapis not linear., Eg:- Semi conductors, Diodes , Transistors., The deviations broadly are one or more of the following types:, a) The value of V stops to be proportional to I., b) The value of current changes when we reverse the direction of V., c) The relation between V and I is not unique, i.e., there is more than one value of V, for the same current I., , Resistivity of Various Materials, The materials are classified as conductors, semiconductors and insulators, depending on their resistivities, in an increasing order of their values.

Page 43 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Resistors, Commercially produced resistors for domestic use or in laboratories are of, two major types: wire bound resistors and carbon resistors., ▪ Wire bound resistors are made by winding the wires of an alloy, viz.,, manganin, constantan, nichrome or similar ones., ▪ Resistors in the higher range are made mostly from carbon. Carbon, resistors are compact, inexpensive and thus find extensive use in, electronic circuits. Carbon resistors are small in size and hence their, values are given using a colour code., , Colour Code of Resistors, , ▪ The first two bands from the end indicate the first two significant figures of the, resistance in ohms., ▪ The third band indicates the decimal multiplier ., ▪ The last band stands for tolerance .Sometimes, this last band is absent and that, indicates a tolerance of 20%., - 10x 101 ± 5%, - 22x 102 ± 5%

Page 45 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Power, , Cells, Emf, Internal Resistance, Cell, , A simple device which maintain a steady current in an electric circuit is the, electrolytic cell., Basically a cell has two electrodes, called the positive (P) and the, negative(N) .They are immersed in an electrolytic solution. The electrodes, exchange charges with the electrolyte., , Internal resistance of a cell (r), Resistance offered by the electrolytes to the flow of current through it is, called internal resistance of the cell

Page 50 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Meter Bridge, Meter Bridge is an electrical device to measure an unknown resistance., It works on the principle of balanced Wheatstone Bridge., , By Wheatstone’s principle, when the bridge is balanced,, R2, R1, , R, , = R4, 3, , The resistivity of the wire, ρ=, 𝛒=, , RA, L, 𝐑𝛑𝐫 𝟐, 𝐋, , R= resistance of the wire, r= radius of the wire, L= length of the wire, Example, In a metre bridge the null point is found at a distance of 33.7 cm from A. If, now a resistance of 12Ω is connected in parallel with S, the null point occurs, at 51.9 cm. Determine the values of R and S., From the first balance point, we get, 33.7, 𝑅, = ---------(1), 66.3, 𝑆, After S is connected in parallel with a resistance of 12Ω , the resistance, across the gap changes from S to 𝑆𝑒𝑞, 𝑆𝑒𝑞 =, 51.9, 48.1, 51.9, 48.1, , =, =, , 𝑅, 𝑆𝑒𝑞, , =, , 𝑅, 12 𝑆, 12+𝑆, , (12+𝑆)𝑅, 12 𝑆, , Substituting from eq(1), 51.9, , (12+𝑆), , 33.7, , =, x, 48.1, 12, 66.3, S = 13.5Ω., Using eq(1),, R = 6.86 Ω., , 12 𝑆, 12+𝑆

Page 51 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Potentiometer, A potentiometer is a long piece of uniform wire of few meters in length, across which a standard cell is connected., , Principle of Potentiometer, The potential difference between two points of a current carrying conductor, of uniform thickness is directly proportional to the length of the wire, between the points, , 𝛆∝𝒍, , Potentiometer is used,, 1. to compare the emf of two cells, 2. to measure the internal resistance of a cell, , 1.Comparison of emf ’s of two cells, , The primary key is closed., Let l1 be the balancing length for for cell ε1 ., ε1 ∝ 𝑙1, Let l2 be the balancing length for for cell ε2 ., ε2 ∝ 𝑙2, 𝛆𝟏, 𝛆𝟐, , 𝒍, , = 𝒍𝟏, 𝟐

Page 53 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 4, Moving Charges and Magnetism, Introduction, Christian Oersted discovered that moving charges or currents produce a, magnetic field in the surrounding space. The direction of the magnetic field, depends on the direction of current., , The magnetic field due to a straight long current-carrying wire. The wire is, perpendicular to the plane of the paper. A ring of compass needles surrounds the wire., The orientation of the needles is shown when, (a) the current emerges out of the plane of the paper,, (b) the current moves into the plane of the paper., (c) The arrangement of iron filings around the wire., *The darkened ends of the needle represent north poles., *A current or a field (electric or magnetic) emerging out of the plane of the, paper is depicted by a dot (.), *A current or a field going into the plane of the paper is depicted by a cross (⊗ )., , Magnetic Force, Sources and fields, A static charge q is the source of electric field(E) ., Moving charges or currents produces a magnetic field (B), in addition to, electric field(B)., ▪ Magnetic field is a vector field., ▪ It obeys the principle of superposition: the magnetic field of several, sources is the vector addition of magnetic field of each individual, source., , Lorentz Force, The total force acting on a charge q moving with a velocity v in presence of, both the electric field E and the magnetic field B is called Lorentz force., F = Felectric + Fmagnetic, ⃗ + 𝐪(𝐯⃗ × ⃗𝐁, ⃗), 𝐅 = 𝐪𝐄, , ⃗ + (𝐯⃗ × 𝐁, ⃗⃗ )], 𝐅=𝐪[𝐄, Electric Lorentz force, ⃗, 𝐅 = 𝐪𝐄

Page 55 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Fleming’s left hand rule, Stretch the fore finger , middle finger and thumb of left hand in three, mutually perpendicular directions, such that fore finger in the direction of, magnetic fileld, the middle finger in the direction of current ,then the thumb, gives the direction of force., , Example, 1 A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is, suspended in mid-air by a uniform horizontal magnetic field B . What is the, magnitude of the magnetic field?, , There is an upward force F, of magnitude I 𝑙 B,. For mid-air suspension,, this must be balanced by the force due to gravity:, m g = I 𝑙B, mg 2 x 9.8, B=, =, = 0.65 T, I𝑙, , 2 x1.5, , Example, The magnetic field is parallel to the positive y-axis and the charged particle, is moving along the positive x-axis ( which way would the Lorentz force be, for (a) an electron (negative charge),, (b) a proton (positive charge)., , The velocity v of particle is along the x-axis, while B, the magnetic field is, ⃗⃗ is along the z-axis (screw rule or right-hand, along the y-axis, so 𝐯⃗ × 𝐁, thumb rule)., (a) for electron it will be along –z axis., (b) for a positive charge (proton) the force is along +z axis.

Page 57 : Join Telegram Channel: https://t.me/hsslive, , 00, , Downloaded from www.Hsslive.in ®, , 900, , Case 3- When θ between and, i.e. when the charged particle moves at an arbitrary angle 𝜃, with the field direction, it undergoes helical path., Here velocity has one component along B, and the other perpendicular to B., The motion in the direction of field is unaffected by magnetic field, as the, magnetic force is zero. The motion in a plane perpendicular to B is circular ,, thereby producing a helical motion., , The distance moved along the magnetic field in one rotation is called pitch p., p =vparallel x T, P=, , 𝐪𝐁, , 𝐯, 𝟐𝛑𝐦 𝐩𝐚𝐫𝐚𝐥𝐥𝐞𝐥, , Motion Fields in Combined Electric and Magnetic Fields, Velocity Selector, , A charge q moving with velocity v in presence of both electric and magnetic, fields experiences a force., ⃗ + (𝐯⃗ × ⃗𝐁, ⃗ )], 𝐅=𝐪[𝐄, Let the charge is moving in x-direction , electric field along y-direction and, magnetic field along z-direction. Then electric and magnetic forces will be in, opposite directions., F = q E – qvB, Now adjust the value of E and B such that magnitude of the two forces are, equal. Then, total force on the charge is zero and the charge will move in the, fields undeflected., q E = qvB, , v=, , 𝐄, 𝐁, , The crossed E and B fields serve as a velocity selector. Only particles with, E, speed pass undeflected through the region of crossed fields., B

Page 58 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , This method was employed by J J Thomson to measure e/m ratio of an electron.This, principle is also employed in Mass Spectrometer-a a device that separates charged, particles., , Cyclotron, The cyclotron is a machine to accelerate charged particles or ions to high, energies. It was invented by E.O. Lawrence and M.S. Livingston in 1934 to, investigate nuclear structure., The cyclotron uses crossed(perpendicular) electric and magnetic fields in, combination to increase the energy of charged particles. Cyclotron uses the, fact that the frequency of revolution of the charged particle in a magnetic, field is independent of its energy., , Costruction and working, , Cyclotron consists of two semicircular disc-like metal containers, D1 and D2 ,, which are called dees . A high frequency alternating voltage is applied to the, dees. Inside the dees there is no electric field, but the magnetic field inside, the dees is perpendicular .There is a source of positive ions at P . A positive, ion is emited at an instant D1 is positive and D2 negative . Then the ion is, accelerated towards D2 and moves in a semi circular path inside D2 on, account of a uniform perpendicular magnetic field B. The frequency νa of the, applied voltage is adjusted so that the polarity of the dees is reversed in the, same time that it takes the ions to complete one half of the revolution. When, the positive ions arrive at the edge of D2 , D1 is at negative polarity. Then the, ions are accelerated towards D1 and moves in a semicircular path inside D1 ., Each time the ion accelerates, the radius of their path increases and each, time their kinetic energy increases. When they attain the required energy,, they are then deflected by a magnetic field and leave the system via exit port, The whole assembly is evacuated to minimise collisions between the ions, and the air molecules.

Page 62 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Magnetic field at the centre of the loop, At the centre x=0, B=, , B=, , μ0 IR2, 2R3, , 𝛍𝟎 𝐈, 𝟐𝐑, , The direction of the magnetic field is given by right-hand thumb rule ., Curl the palm of your right hand around the circular wire with the fingers, pointing in the direction of the current. The right-hand thumb gives the, direction of the magnetic field., , The upper side of the loop(current is anticlockwise) may be thought of as, the north pole and the lower side(current is clockwise) as the south pole of, a magnet., , Ampere's Circuital Law, , The line integral of magnetic field over a closed loop is equal to μ0 times the, total current passing through the surface., The closed loop is called Amperian Loop., , ∮ ⃗⃗⃗, 𝐁. ⅆ𝒍 = 𝛍𝟎 𝐈

Page 63 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Applications of Ampere's Circuital Law, 1.Magnetic field due to a straight infinite current-carrying wire, , By Ampere's Circuital Law, ∮ ⃗⃗⃗, B. 𝑑𝑙 = μ0 I, ∮ Bd𝑙 cos 0 = μ0 I, B∮ d𝑙 = μ0 I, B x 2πr = μ0 I, , 𝐁=, , 𝛍𝟎 𝐈, , 𝟐𝛑𝐫, , A plot of the magnitude of B with distance r from the centre of the wire having radius a, , Right-hand rule, There exists a simple rule to determine the direction of the magnetic field, due to a long wire ,called the right-hand rule. Grasp the wire in your right, hand with your extended thumb pointing in the direction of the current., Your fingers will curl around in the direction of the magnetic field.

Page 65 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , (3)Magnetic field due to a Toroid, A Toroid is a long solenoid bend in the form of a circle. Or A Toroid is a, hollow circular ring on which a large number of turns of a wire are closely, wound. The magnetic field is present only within the toroid, , By Ampere's Circuital Law for N turns,, ∮ ⃗⃗⃗, B. 𝑑𝑙 = μ0 NI, ∮ B d𝑙 cos 0 = μ0 NI, B∮ d𝑙 = μ0 NI, B x 2πr = μ0 NI, μ NI, B= 0, 2πr, , 𝐍, , 𝐁 = 𝛍𝟎 𝐧𝐈, , where 𝐧 = 𝟐𝛑𝐫, , Example, A solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns., It carries a current of 5 A. What is the magnitude of the magnetic field inside, the solenoid?, The number of turns per unit length , n=, =, , N, 𝑙, 500, 0.5, , = 1000, , B = μ0 nI, = 4π × 10−7 x1000x5, =6.28 ×10−3 T

Page 67 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The ampere is that current which, when flaws through two very long,, straight, parallel conductors placed one metre apart in vacuum, would, produce a force equal to𝟐 𝐱 𝟏𝟎−𝟕 N/m on each other., , Torque on Current Loop, Magnetic Dipole, Torque on a rectangular current loop in a uniform magnetic field, , A rectangular loop carrying a steady current I is placed in a uniform, magnetic field B,which is applied in the plane of the loop., Force on AD and BC is zero, Force on BC , F=IaBsin0=0, Force on AD , F=IaBsin 180=0, , Force on AB =Force on CD = IbB sin 90=IbB, Forces on AB and CD are equal and oppsite. So the coil does not experience a, net force, but it experiences a torque., Torque , τ =Force x perpendicular distance, τ =IbB x a =IabB, τ = IAB, where A = ab is the area of the rectangle., When the plane of the loop, makes an angle with the magnetic field. We take, the angle between the field and the normal to the coil to be angle θ., , τ = IbB x asin θ, τ = IAB sinθ, For N turns of the coil, τ = NIAB sinθ

Page 69 : Join Telegram Channel: https://t.me/hsslive, , μ𝑙 =, , e, , 2m, , 𝛍𝒍 =, , Downloaded from www.Hsslive.in ®, , (mvr), , 𝐞, , 𝟐𝐦, , 𝒍, , 𝑙=orbital angular momentum of the electron about the central nucleus., 𝛍𝒍, 𝒍, , 𝐞, , = 𝟐𝐦, , This ratio is called the gyromagnetic ratio and is a constant., Its value is 8.8 × 1010 C /kg for an electron., Bohr Magneton, By Bohr’s postulates,the angular momentum,, nh, 𝑙=, where n=1,2,3……, 2π, For first orbit ,n=1, e h, μ𝑙 =, μ𝑙 =, , 2m 2π, eh, 4πm, , This value is called the Bohr magneton., , The Moving Coil Galvanometer, , The moving coil galvanometer(MCG) consists of a coil, with many turns, free, to rotate about a fixed axis , in a uniform radial magnetic field. There is a, cylindrical soft iron core which not only makes the field radial but also, increases the strength of the magnetic field., When a current flows through the coil, a torque acts on it., τ = NI AB--------------(1)

Page 70 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The magnetic torque NIAB tends to rotate the coil. A spring Sp provides a, counter torque., τ = kϕ -----------------(2), where k is the torsional constant of the spring; i.e. the restoring torque per, unit twist., ϕ is the deflection is indicated on the scale by a pointer attached to the, spring., In equilibrium,, kϕ = NI AB -------------(3), , 𝛟=(, , 𝐍 𝐀𝐁, 𝐤, , )𝐈, , The quantity in brackets is a constant for a given galvanometer., , 𝛟 ∝I, Thus the deflection produced in the coil is directly proportional to the, current through the coil., , Current Sensitivity of the Galvanometer, Current sensitivity of the galvanometer is defined as the deflection per unit, current., 𝛟, 𝐈, , =(, , 𝐍 𝐀𝐁, 𝐤, , ), , A convenient way for the manufacturer to increase the sensitivity is to, increase the number of turns N., , Voltage sensitivity of the galvanometer, Voltage sensitivity of the galvanometer is defined as the deflection per unit, voltage., ϕ, N AB I, N AB 1, =(, =(, ), )R, V, k, V, k, 𝛟, , =(, 𝐕, , 𝐍 𝐀𝐁 𝟏, , )𝐑, , 𝐤, , Increasing the current sensitivity may not necessarily increase the voltage, sensitivity., If N → 2N, i.e., we double the number of turns, then current sensitivity,, ϕ, 2N AB, ϕ, =(, ) →2, I, , k, , I, , Thus, the current sensitivity doubles., If N → 2N, then R → 2R then the voltage sensitivity,, ϕ, 2N AB 1, N AB 1, ϕ, =(, =(, =, ), ), V, k, 2R, k, R, V, Thus, the voltage sensitivity remains unchanged..

Page 71 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Conversion of Galvanometer to Ammeter, To convert a Galvanometer to an Ammeter a small resistance , called shunt, resistance S ,is connected in parallel with the galvanometer coil., , Ig G = (I − Ig )S, S=, , 𝐈𝐠 𝐆, 𝐈−𝐈𝐠, , Conversion of Galvanometer to Voltmeter, To convert a Galvanometer to a volteter a high resistance , R is connected in, series with the galvanometer coil., , V = Ig (R + G), R+G=, R =, , V, Ig, 𝐕, 𝐈𝐠, , –G, , Example, A galvanometer with coil resistance 12Ω shows full scale deflection for a, current of 2.5mA. How will you convert it into an ammeter of range, 0 – 7.5 A?, S=, , Ig G, I−Ig, 2.5 x 10−3 x 12, , 2.5 x 10−3 x 12, , S=, =, =4 x 10−3 Ω, −3, 7.5−2.5 x 10, 7.5−0.0025, −3, A resistance of 4 x 10 Ω is to be connected in parallel to the galvanometer, coil to convert it into an ammeter., , Example, A galvanometer with coil resistance 12Ω shows full scale deflection for a, current of 3mA. How will you convert it into a voltmeter of range 0 – 18V?, V, R = –G, Ig, , 18, , R =, – 12 =6x 103 -12 =6000-12 =5988 Ω, −3, 3 x 10, A resistance of 5988 Ω is to be connected in seriesl to the galvanometer coil, to convert it into a voltmeter.

Page 72 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 5, Magnetism and Matter, Some of the commonly known ideas regarding magnetism are:, ▪ The earth behaves as a magnet with the magnetic field pointing, approximately from the geographic south to the north., ▪ When a bar magnet is freely suspended, it points in the north-south, direction. The tip which points to the geographic north is called the, north pole and the tip which points to the geographic south is called the, south pole of the magnet., ▪ Similar poles repel and opposite poles attract., ▪ We cannot isolate the north, or south pole of a magnet. If a bar magnet, is broken into two halves, we get two similar bar magnets with, somewhat weaker properties. Unlike electric charges, isolated magnetic, north and south poles known as magnetic monopoles do not exist., ▪ It is possible to make magnets out of iron and its alloys, , The Bar Magnet, The magnet has two poles similar to the positive and negative charge of an, electric dipole -one pole is designated the North pole and the other, the, South pole. When suspended freely, these poles point approximately, towards the geographic north and south poles, respectively., The arrangement of iron filings surrounding a bar, magnet. The pattern mimics magnetic field lines., The pattern suggests that the bar magnet is a, magnetic dipole. A similar pattern of iron filings is, observed around a current carrying solenoid., , The Magnetic Field Lines, ▪ The magnetic field lines of a magnet (or a solenoid) form continuous, closed loops., (This is unlike the electric dipole where these field lines begin from, a positive charge and end on the negative charge or escape to infinity.), , ▪ The tangent to the field line at a given point represents the direction, of the net magnetic field B at that point., ▪ The larger the number of field lines crossing per unit area, the, stronger is the magnitude of the magnetic field B., ▪ The magnetic field lines do not intersect., (If they intersect, there would be more than one direction for, magnetic field at the point of intersection,which is not possible)

Page 73 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The Magnetic field lines of, (a) a bar magnet,, , (b) a current-carrying finite solenoid and, , (c) electric dipole, , Note:-The magnetic field lines can not be called as magnetic lines of force. Unlike, electrostatics (F =qE) the field lines in magnetism do not indicate the direction of the, force on a moving charge(F=q(vxB)), , Bar magnet as an equivalent solenoid, The resemblance of magnetic field lines for a bar magnet and a solenoid, suggest that a bar magnet may be thought of as a large number of circulating, currents in analogy with a solenoid., , The dipole in a uniform magnetic field, , A small compass needle of magnetic moment m and moment of inertia I is, allowed it to oscillate in a magnetic field B., The restoring torque on the needle ,, τ⃗ = m, ⃗⃗⃗ × ⃗B, τ⃗ = mBsinθ-------------(1), The deflecting torque ,, τ⃗= Iα, τ⃗ = I, , d2 θ, dt2, , -------------(2), , In equilibrium,, I, , d2 θ, dt2, , = − mBsinθ

Page 75 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , (b) A magnetised needle in a uniform magnetic field experiences a torque, but no net force. An iron nail near a bar magnet, however, experiences a, force of attraction in addition to a torque. Why?, No force if the field is uniform. The iron nail experiences a non uniform field, due to the bar magnet. There is induced magnetic moment in the nail,, therefore, it experiences both force and torque. The net force is attractive, because the induced south pole (say) in the nail is closer to the north pole of, magnet than induced north pole., (c) Must every magnetic configuration have a north pole and a south pole?, What about the field due to a toroid, Not necessarily. True only if the source of the field has a net non zero, magnetic moment. This is not so for a toroid or even for a straight infinite, conductor., (d) Two identical looking iron bars A and B are given, one of which is, definitely known to be magnetised. (We do not know which one.) How, would one ascertain whether or not both are magnetised? If only one is, magnetised, how does one ascertain which one? [Use nothing else but the, bars A and B.], Try to bring different ends of the bars closer. A repulsive force in some, situation establishes that both are magnetised. If it is always attractive, then, one of them is not magnetised., In a bar magnet the intensity of the magnetic field is the strongest at the two, ends (poles) and weakest at the central region. This fact may be used to, determine whether A or B is the magnet. In this case, to see which one of the, two bars is a magnet, pick up one, (say, A) and lower one of its ends; first on, one of the ends of the other (say, B), and then on the middle of B. If you, notice that in the middle of B, A experiences no force, then B is magnetised., If you do not notice any change from the end to the middle of B, then A is, magnetised., , The electrostatic analog, ⃗E → ⃗B,, , ⃗ →m, p, ⃗⃗⃗ ,, , 1, ε0, , → μ0 ,, , 1, 4πε0, , →, , μ0, 4π, , The magnetic field along the axial line of a bar magnet,, Axial fileld ,𝐁𝐀 =, , 𝛍𝟎 𝟐𝐦, ⃗⃗⃗, 𝟒𝛑 𝐫 𝟑, , The magnetic field along the equatorial l line of a bar magnet,, Equatorial field ,𝐁𝐄 =, , 𝛍𝟎 𝐦, ⃗⃗⃗, 𝟒𝛑 𝐫 𝟑

Page 76 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The Dipole Analogy, , Dipole moment, Axial Field for a short dipole, Equatorial Field for a short, dipole, Torque in an external field, Energy in an external field, , Electrostatics, 1, ε0, ⃗, p, 1 2p, ⃗, 4πε0 r 3, 1 p, ⃗, 4πε0 r 3, τ⃗ = p, ⃗ × ⃗E, ⃗U = −p, ⃗ . ⃗E, , Magnetism, μ0, ⃗m, ⃗⃗, μ0 2m, ⃗⃗⃗, 4π r 3, μ0 m, ⃗⃗⃗, 4π r 3, τ⃗ = m, ⃗⃗⃗ × ⃗B, ⃗U = −m, ⃗⃗⃗ . ⃗B, , Example, What is the magnitude of the equatorial and axial fields due to a bar magnet, of length 5 cm at a distance of 50 cm from its mid-point? The magnetic, moment of the bar magnet is 0.40 A m2 ,, BE =, BA =, , μ0 m, 4π r3, , =, , μ0 2m, , 10 −7 x 0.40, (0.5)3, , =2x, 4π r3, , =3.2 x10 −7 T, , 3.2 x10 −7 =6.4 x10 −7 T, , Magnetism and Gauss’s Law, Gauss’s law for magnetism states that the net magnetic flux through any, closed surface is zero., ⃗⃗ ⋅ ⅆ𝐬 = 𝟎, 𝛟 = ∮𝐁, The difference between the Gauss’s law of magnetism and that for, electrostatics is due to the fact that isolated magnetic poles (also called, monopoles) do not to exist., There are no sources or sinks of B; the simplest magnetic element is a dipole, or a current loop., , For the Gaussian surfaces represented by i or ii , the number of, magnetic field lines leaving the surface is balanced by the number of, lines entering it. The net magnetic flux is zero for both the surfaces.

Page 77 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example, (a) Magnetic field lines show the direction (at every point) along which a, small magnetised needle aligns (at the point). Do the magnetic field lines, also represent the lines of force on a moving charged particle at every point?, No. The magnetic force is always normal to B (remember magnetic force =, qv × B). It is misleading to call magnetic field lines as lines of force., (b) Magnetic field lines can be entirely confined within the core of a toroid,, but not within a straight solenoid. Why?, If field lines were entirely confined between two ends of a straight solenoid,, the flux through the cross-section at each end would be non-zero. But the, flux of field B through any closed surface must always be zero. For a toroid,, this difficulty is absent because it has no ‘ends’., (c) If magnetic monopoles existed, how would the Gauss’s law of magnetism, be modified?, By Gauss’s law for magnetism, ⃗⃗ ⋅ ⅆ𝐬 = 𝟎, 𝛟 = ∮𝐁, If monopoles existed, the right hand side would be equal to the monopole, (magnetic charge) 𝑞𝑚 enclosed by S., , ⃗⃗ ⋅ ⅆ𝐬 = 𝛍𝟎 𝒒𝒎, 𝛟 = ∮𝐁, q, {Analogous to Gauass law in electrostatics , ϕ = ∮ ⃗E ⋅ ds = ε }, 0, , (d) Does a bar magnet exert a torque on itself due to its own field? Does one, element of a current-carrying wire exert a force on another element of the, same wire?, No. There is no force or torque on an element due to the field produced by, that element itself. But there is a force (or torque) on an element of the same, wire. (For the special case of a straight wire, this force is zero.), (e) Magnetic field arises due to charges in motion. Can a system have, magnetic moments even though its net charge is zero, Yes. The average of the charge in the system may be zero. Yet, the mean of, the magnetic moments due to various current loops may not be zero. We, will come across such examples in connection with paramagnetic material, where atoms have net dipole moment through their net charge is zero

Page 78 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The Earth’s Magnetism, Dynamo effect, Earth’s magnetic field arise due to electrical currents produced by, convective motion of metallic fluids (consisting mostly of molten iron and, nickel) in the outer core of the earth. This is known as the dynamo effect., The magnetic field lines of the earth resemble that of a (hypothetical), magnetic dipole located at the centre of the earth. The axis of the dipole does, not coincide with the axis of rotation of the earth but is presently titled by, approximately 11.3º with respect to the later., The location of the north magnetic pole is at a latitude of 79.74º N and a, longitude of 71.8º W, a place somewhere in north Canada. The magnetic, south pole is at 79.74º S, 108.22º E in the Antarctica., , Ng =geographic north pole, Sg =geographic south pole, , Nm =North magnetic pole, Sm =South magnetic pole, , The pole near the geographic north pole of the earth is called the north, magnetic pole. Likewise, the pole near the geographic south pole is called, the south magnetic pole. The magnetic north was the direction to which the, north pole of a magnetic needle pointed; the north pole of a magnet was so, named as it was the north seeking pole. Thus, in reality, the north magnetic, pole behaves like the south pole of a bar magnet inside the earth and vice, versa., , Geographic meridian, Geographic meridian at a place is the vertical plane passing through the, place and the geographic poles., , Magnetic meridian, The magnetic meridian of a place is the vertical plane passing through the, magnetic north and the south poles.

Page 79 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The elements of the earth’s magnetic field., Three quantities are needed to specify the magnetic field of the earth on its, surface ., 1. Magnetic Declination(D), 2. Magnetic Dip or Inclination (I), 3. The horizontal component (HE ), These are known as the elements of the earth’s magnetic field., , Magnetic Declination (D), Declination at a place is the angle between geographic meridian and, magnetic meridian at that place., The declination is greater at higher latitudes and smaller near the equator., , Dip or Inclination (I), Thus Dip or inclination is the angle that the total intensity of earth’s, magneticfield(BE ) at the place makes with the horizontal(HE ))., (Or) Dip is the angle between BE and HE ., , BE - Total magnetic field of earth, HE - horizontal component, ZE - vertical component, , The value of dip is 900 at magnetic poles and 00 at magnetic equator. At all, other places dip angle lies between 00 and 900 ., , Horizontal component ( 𝐇𝐄 ), It is the horizontal component of the total Intensity of Earth’s magnetic field, at the place.

Page 81 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , B0 = μ0 nI, Bm = μ0 M, B = μ0 nI + μ0 M, B = μ0 H + μ0 M, B = μ0 (H + M) ------------(2), Here M is called magnetisation and H is called magnetic intensity, The total magnetic field inside the sample has two parts: one, due to external, factors such as the current in the solenoid. This is represented by H. The, other is due to the specific nature of the magnetic material, namely M., , Magnetic intensity(H), The magnetic intensity can be defined as, 𝐁, , 𝐇=𝛍 −𝐌, 𝟎, , B = μ0 (H + M), B, =H+M, μ0, , H=, , B, μ0, , −M, , H has the same unit and dimensions as M .Its unit is Am−1 ,dimensions AL−1, , Magnetic Susceptibility(𝛘), The magnetisation can be influenced by external factors(H which is equal to, nI). This influence is mathematically expressed as, M = χH, , 𝛘=, , 𝐌, 𝐇, , where χ is a dimensionless quantity called as magnetic susceptibility. It is a, measure of how a magnetic material responds to an external field., ▪ χ is large and positive for ferromagnetic materials., ▪ χ is small and positive for paramagnetic materials., ▪ χ is small and negative for diamagnetic materials. For diamagnetic, materials M and H are opposite in direction., , Relation connecting Susceptibility and permeability, B = μ0 (H + M), B = μ0 (H + χH), B = μ0 (1 + χ)H) --------------(1), B = μ0 μr H -----------------(2), , 𝐁 = 𝛍𝐇

Page 83 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ Susceptibility of a diamagnetic material is independent of temperature., ▪ Relative permeability , μr is positive and less than one for diamagnetic, materials., 0 ≤ μr < 1, ▪ When a diamagnetic material is placed in an external magnetic field, the, field lines are repelled or expelled and the field inside the material is, reduced., , ▪ The resultant magnetic moment of an individual atom of a diamagnetic, substance is zero., ▪ When a magnetic field is applied, the diamagnetic substance develops a, net magnetic moment opposite to the direction of applied field and, hence repulsion., ▪ Some diamagnetic materials are bismuth, copper, diamond, gold, lead,, mercury,silver, silicon, nitrogen (at STP), water and sodium chloride., ▪ Super coductors exhibits perfect diamagnetism. Here the field lines are, completely expelled. χ = –1 and μr = 0., , Super conductors, These are metals, cooled to very low temperatures which exhibits both, perfect conductivity and perfect diamagnetism. Here the field lines are, completely expelled. χ = –1 and μr = 0. The phenomenon of perfect, diamagnetism in superconductors is called the Meissner effect., , Paramagnetism, ▪ Paramagnetic substances are those which get weakly magnetised in the, direction of external magnetic field., ▪ Paramagnetic substances move from a region of weak magnetic field to, strong magnetic field, i.e., they get weakly attracted to a magnet., ▪ Susceptibility 𝛘 is small and positive for paramagnetic materials., 0<χ<ε, ▪ Susceptibility of a paramagnetic material is inversely proportional to the, absolute temperature T., μ, χ=C 0, T, This is known as Curie’s law, after its discoverer Pieree Curie . The, constant C is called Curie’s constant., ▪ Relative permeability is positive and greater than one for diamagnetic, materials., 1< μr < 1+ ε

Page 84 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ When a paramagnetic material placed in an external field , the field lines, gets concentrated inside the material, and the field inside is enhanced., , ▪ The individual atoms of a paramagnetic material possess a permanent, magnetic dipole moment of their own., ▪ When a magnetic field is applied, the individual atomic dipole moments, align in the same direction and a net magnetic moment in the direction, of applied field and hence attraction., ▪ Some paramagnetic materials are aluminium, sodium, calcium,, chromium, lithium , magnesium, oxygen (at STP) ,copper chloride,, platinum, tungsten, niobium., , Ferromagnetism, ▪ Ferromagnetic substances are those which gets strongly magnetised, when placed in an external magnetic field., ▪ Ferromagnetic substances have strong tendency to move from a region, of weak magnetic field to strong magnetic field, i.e., they get strongly, attracted to a magnet., ▪ Susceptibility 𝛘 is large and positive for ferromagnetic materials., χ >> 1, ▪ The ferromagnetic property depends on temperature. At high enough, temperature, a ferromagnet becomes a paramagnet. The temperature of, transition from ferromagnetic to paramagnetic is called the Curie, temperature Tc . Above the Curie temperature, susceptibility,, c, χ=, where T>Tc, T−Tc, , This is known as Curie’s law, after its discoverer Pieree Curie . The, constant C is called Curie’s constant., ▪ Relative permeability is greater than one and large., µr >> 1, ▪ When a ferromagnetic material placed in an external field , the field lines, gets highly concentrated inside the material, and the field inside is, enhanced., , ▪ The individual atoms (or ions or molecules) in a ferromagnetic material, possess a dipole moment as in a paramagnetic material.

Page 85 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ When a magnetic field is applied, the individual atomic dipole moments, align in the same direction and a net magnetic moment in the direction, of applied field and hence attraction., ▪ Some ferromagnetic materials are iron, cobalt, nickel, gadolinium,Fe2 O3 ., Hard ferromagnets and Soft ferromagnets, The ferromagnetic materials in which the magnetisation persists, ,even, when the external field is removed are called hard magnetic materials or, hard ferromagnets. Such materials are used to make permanent magnets., Eg: Alnico(an alloy of iron, aluminium, nickel, cobalt, and copper),lodestone, The ferromagnetic materials in which the magnetisation disappears on the, removal of the external field are called soft ferromagnetic materials., Eg: Soft iron ., , Hysteresis, Ferromagnetic materials have large χ and are characterised by non-linear, relation between B and H. They show the property of hysteresis., The phenomenon of lagging of magnetic field, B behind the magnetic, intensity, H when a ferromagnetic material is subjected to a cycle of, magnetisation is called hysteresis., The magnetic hysteresis loop is the B-H curve for ferromagnetic materials, , ▪ An unmagnetised material is placed in a solenoid and increase the, current through the solenoid. The magnetic field B in the material rises, and saturates . It is represented by the curve Oa., ▪ Now, we decrease H and reduce it to zero. At H = 0, B ≠ 0. This is, represented by the curve ab. The value of B at H = 0 is called retentivity, or remanence(The value of B corresponding to b).

Page 86 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ Next, the current in the solenoid is reversed and slowly increased until, B=0. This is represented by the curve bc. The value of H at B=0 is called, coercivity (The value of H corresponding to c)., ▪ As the reversed current is increased in magnitude, we once again obtain, saturation. This is represented by the curve cd., ▪ Next, the current is reduced (curve de) and reversed (curve ea). The, cycle repeats itself., The curve Oa does not retrace itself as H is reduced. B always lags behind H., This phenomenon is called hysterisis. The word hysterisis means lagging, behind., ▪ The area of hysteresis curve will be equal to the energy dissipation in, one cycle of magnetisation., , Permanent Magnets and Electromagnets, Permanent Magnets, Substances which at room temperature retain their ferromagnetic property, for a long period of time even after the removal of magnetising field are, called permanent magnets., An efficient way to make a permanent magnet is to place a ferromagnetic, rod in a solenoid and pass a current. The magnetic field of the solenoid, magnetises the rod., The material used to make permanent magnets should have, ▪ High retentivity, ▪ Strong and high coercivity, ▪ High permeability., ▪ Wide hysteresis curve, Eg: Steel , alnico, cobalt steel and ticonal., , Electromagnets, Substances which lose their ferromagnetic property immediately on the, removal of magnetising field are called electromagnets., The material used to make electromagnets should have,, ▪ low retentivity, ▪ low coercivity, ▪ high permeability., ▪ Narrow hysteresis curve, Eg: Soft iron, Electromagnets are used in electric bells,transformers, loudspeakers and, telephone diaphragms. Giant electromagnets are used in cranes to lift, machinery, and bulk quantities of iron and steel

Page 87 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 6, Electromagnetic Induction, Introduction, In the early decades of the nineteenth century, experiments on electric, current by Oersted, Ampere and a few others established the fact that, electricity and magnetism are inter-related. They found that moving electric, charges produce magnetic fields., Is the converse effect possible?, The experiments of Michael Faraday in England and Joseph Henry in USA,, demonstrated that electric currents were induced in closed coils when, subjected to changing magnetic fields. The pioneering experiments of, Faraday and Henry have led directly to the development of modern day, generators and transformers., , Electromagnetic Induction, The phenomenon in which electric current is generated by varying magnetic, fields is appropriately called electromagnetic induction., , The Experiments of Faraday and Henry, Experiment 1, A coil 𝐶1 is connected to a galvanometer G.

Page 88 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Observations, ▪ When the North-pole of a bar magnet is pushed towards the coil, the, pointer in the galvanometer deflects, indicating the presence of electric, current in the coil., ▪ The deflection lasts as long as the bar magnet is in motion., ▪ The galvanometer does not show any deflection when the magnet is, held stationary., ▪ When the magnet is pulled away from the coil, the galvanometer shows, deflection in the opposite direction, which indicates reversal of the, current’s direction., ▪ Moreover, when the South-pole of the bar magnet is moved towards or, away from the coil, the deflections in the galvanometer are opposite to, that observed with the North-pole., ▪ Further, the deflection (and hence current) is found to be larger when, the magnet is pushed towards or pulled away from the coil faster., ▪ When the bar magnet is held fixed and the coil C1 is moved towards or, away from the magnet, the same effects are observed., , Conclusion, It shows that it is the relative motion between the magnet and the coil that is, responsible for generation (induction) of electric current in the coil., , Experiment 2, The bar magnet is replaced by a second coil C2 connected to a battery. The, steady current in the coil C2 produces a steady magnetic field., , Observations, ▪ As coil C2 is moved towards the coil C1 , the galvanometer shows a, deflection. This indicates that electric current is induced in coilC2 ., ▪ When C2 is moved away, the galvanometer shows a deflection in the, opposite direction., ▪ The deflection lasts as long as coil C2 is in motion.

Page 89 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ When the coil C2 is held fixed and C1 is moved, the same effects are, observed., Again, it is the relative motion between the coils that induces the electric, current., , Experiment 3, Two coils C1 and C2 are held stationary. Coil C1 is connected to galvanometer, G while the second coil C2 is connected to a battery through a tapping key K., , ▪ The galvanometer shows a momentary deflection when the tapping, key K is pressed. The pointer in the galvanometer returns to zero, immediately., ▪ If the key is held pressed continuously, there is no deflection in the, galvanometer., ▪ When the key is released, a momentory deflection is observed again,, but in the opposite direction., ▪ It is also observed that the deflection increases dramatically when an, iron rod is inserted into the coils along their axis., , Magnetic Flux, , Magnetic flux through a plane of area A placed in a uniform magnetic field B, can be written as, 𝝓𝑩 = B . A = BA cos θ, where θ is angle between B and A., The SI unit of magnetic flux is weber (Wb) or tesla meter squared (T m2 )., Magnetic flux is a scalar quantity., The flux can be varied by changing any one or more of the terms B, A and θ .

Page 90 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Faraday’s law of electromagnetic induction, The magnitude of the induced emf in a circuit is equal to the time rate of, change of magnetic flux through the circuit., , 𝛆=−, , ⅆ𝛟𝐁, ⅆ𝐭, , The negative sign indicates the direction of ε and hence the direction of, current in a closed loop., In the case of a closely wound coil of N turns, the total induced emf ,, ⅆ𝛟, 𝛆 = −𝐍 𝐁, ⅆ𝐭, The induced emf can be increased by increasing the number of turns N of a, closed coil., , Lenz’s Law, German physicist Heinrich Friedrich Lenz deduced a rule, known as Lenz’s, law which gives the polarity of the induced emf ., The statement of the law is: The polarity of induced emf is such that it tends, to produce a current which opposes the change in magnetic flux that, produced it., When North-pole of a bar magnet is moved towards the coil, a, current is induced in the coil in such a direction that it opposes, the increase in flux. That means the face of coil (towards, magnet) should have North-polarity .So current in that face, will be anti clockwise (counter- clockwise) ., , When North-pole of a bar magnet is moved away from the coil,, a current is induced in the coil in such a direction that it, opposes the decrease in flux. That means the face of coil, (towards magnet) should have South-polarity.So current in, that face will be clockwise., , When South-pole of a bar magnet is moved towards the coil,, the face of coil (towards magnet) should have South-polarity., So current in that face will be clockwise., , When South-pole of a bar magnet is moved away from the, coil, the face of coil (towards magnet) should have Northpolarity .So current in that face will be anti clockwise, (counter- clockwise) .

Page 91 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Lenz’s Law and Conservation of Energy, If the induced current was in the same direction changing magnetic flux, the, front face of coil gets South polarity ,when the north pole of bar magnet is, pushed into the coil .The bar magnet will then be attracted towards the coil, at a increasing acceleration and kinetic energy will continuously increase, without expending any energy. This violates the law of conservation of, energy and hence can not happen., The current induced in the coil is opposite to the direction of changing, magnetic flux. Then the bar magnet experiences a repulsive force due to the, induced current. Therefore, a person has to do work in moving the magnet., This energy(work) is dissipated by Joule heating produced by the induced, current.Thus Lenz’s law is in accordance with law of conservation of energy., , Motional Electromotive Force, When a conducting rod is moved through a constant magnetic field, an emf, is developed between the ends of the rod. This emf is known as Motional, Emf., , Consider a straight conductor moving in a uniform and time independent, magnetic field.The magnetic flux Φ enclosed by the loop PQRS,, ϕ= 𝐵𝑙𝑥, Since x is changing with time, the rate of change of flux Φ will induce an emf, given by:, dϕ, d, ε = − B = (𝐵𝑙𝑥), dt, , 𝜀 = −𝐵𝑙, , dt, , 𝑑𝑥, 𝑑𝑡, , v=, , − dx, dt, , is the speed of the conductor, , 𝜺 = 𝑩𝒍𝒗, The induced emf Blv is called motional emf.

Page 92 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Eddy Currents, When bulk pieces of conductors are subjected to changing magnetic flux,, induced currents are produced in them. These currents are called eddy, currents. This effect was discovered by physicist Foucault., , A copper plate is allowed to swing like a simple pendulum between the pole, pieces of a strong magnet. Eddy currents are generated in the copper plate,, while entering and leaving the region of magnetic field. It is found that the, motion is damped and in a little while the plate comes to a halt in the, magnetic field., , Cutting slots in the copper plate reduces the area of plates and hence, reduces the effect of eddy currents. Thus, the pendulum plate with holes or, slots reduces electromagnetic damping and the plate swings more freely., , Disadvantage of Eddy Current, Eddy currents are undesirable in the metallic cores of transformers and, electric motors since they heat up the core and dissipate electrical energy in, the form of heat., Eddy currents are minimised by using laminated, metal sheets to make a metal core. The laminations, are separated by an insulating material like lacquer., The plane of the laminations must be arranged, parallel to the magnetic field, so that they cut across, the eddy current paths. This arrangement reduces, the strength of the eddy currents.

Page 93 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Advantages of Eddy currents, 1. Magnetic breaking in Trains, Strong electromagnets are mounted in trains to induce eddy currents in, the rails. When these electromagnets are activated, the eddy currents, formed on the rails opposes the motion of the train causes the breaking, effect., 2.Electromagnetic Damping, The coil of certain galvanometers is wound on a metallic core. When the, coil oscillates, eddy currents generated in the core oppose the motion of, the coil and it comes to rest quickly., 3.Induction Furnace, Induction furnace can be used to produce high temperatures and, can, be utilised to prepare alloys, by melting the constituent metals. A high, frequency alternating current is passed through a coil which surrounds, the metals to be melted. The eddy currents generated in the metals, produce high temperatures sufficient to melt it, 4.Electric power meters, The shiny metal disc in the electric power meter (analogue type) rotates, due to the eddy currents. Electric currents are induced in the disc by, magnetic fields produced by sinusoidally varying currents in a coil., , Inductance, An electric current can be induced in a coil by flux change produced by the, same coil or a flux change produced by a neighbouring coil .These, phenomenon are respectively called self induction and mutual induction. In, both the cases, the flux through a coil is proportional to the current., 𝜙αI, 𝝓 =L I, The constant of proportionality, in this relation, is called inductance., Inductance is a scalar quantity. It has the dimensions of [M L2 T–2 A–2] ., The SI unit of inductance is henry and is denoted by H, , Self-Inductance, The phenomenon of production of induced emf in an isolated coil by, varying current through the same coil is called self-induction., The flux linked with the coil is proportional to the current through the coil., 𝜙α I, 𝝓=LI, For N turns of the coil, N𝝓 = LI -------------(1)

Page 94 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , where constant of proportionality L is called self-inductance of the coil. It is, also called the coefficient of self-induction of the coil., When the current is varied, the flux linked with the coil also changes and an, emf is induced in the coil., dNϕ, For N turns,, ε=−, ε=−, , dt, dLI, dt, , ⅆ𝐈, , 𝛆 = −𝐋 ⅆ𝐭, , -----------(2), , Thus, the self-induced emf always opposes any change (increase or, decrease) of current in the coil., , Self-Inductance of a Long Solenoid, Consider a solenoid of crosssectional area A and length l, having n turns per, unit length., The total flux linked with the solenoid ,, 𝜙=𝐵𝐴, 𝑵𝜙 = 𝑁𝐵 𝐴, B = 𝜇0 n I, N=n𝑙, 𝑁𝜙 = 𝑛𝑙 (𝜇0 n I ) 𝐴, 𝑁𝜙 = 𝜇0 n2 A𝑙I ------------(1), But, N𝜙 = LI -----------------(2), From eq (1) and (2), LI = 𝜇0 n2 A𝑙I, , L= 𝝁𝟎 𝐧𝟐 𝐀𝒍 -----------(3), , If we fill the inside of the solenoid with a material of relative permeability 𝜇𝑟, (for example soft iron, which has a high value of relative permiability), then,, , L=𝝁𝒓 𝝁𝟎 𝐧𝟐 𝐀𝒍-----------(4), The self-inductance depends on geometry of coil and on the, permeability of the medium., , Back emf, The self-induced emf is also called the back emf as it opposes any change in, the current in a circuit. Physically, the self-inductance plays the role of, inertia. Self inductance is the electromagnetic analogue of mass in, mechanics. So, work needs to be done against the back emf (ε ) in, establishing the current. This work done is stored as magnetic potential, energy.

Page 95 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Energy stored in an inductor, dW, dt, , = |ε|I, But, |ε| = L, , dW, dt, , = LI, , dI, dt, , I, , W = ∫ dW=∫0 LI, , dI, dt, , dI, dt, , 𝟏, , W = 𝐋𝐈𝟐, 𝟐, , 1, , This expression is analogous to mv 2 , kinetic energy of a particle of mass m,, 2, and shows that L is analogus to m (i.e., L is electrical inertia and opposes, growth and decay of current in the circuit)., , Mutual inductance, The phenomenon of production of induced emf in a coil by varying the, current through a neighbouring coil is called mutual-induction., The flux linked with the coil is proportional to the current through the, neighbouring coil., ϕαI, ϕ=MI, For N turns of the coil,, N𝛟 = MI, where constant of proportionality M is called mutual-inductance of the coil., It is also called the coefficient of mutual-induction of the coil., When the current in the nighbouring coil is varied, the flux linked with the, first coil changes and an emf is induced in the coil., ⅆ𝐈, , 𝛆 = −𝐌 ⅆ𝐭, Mutual inductance of two co-axial solenoids

Page 97 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , An ac generator converts mechanical energy into electrical energy. . It, consists of a coil which is mechanically rotated in the uniform magnetic field, by some external means. The rotation of the coil causes the magnetic flux, through it to change, so an emf is induced in the coil., The magnetic flux at any time t is, ϕ = BA cos θ = BA cos ωt, From Faraday’s law, the induced emf for the rotating coil of N turns is, dϕ, ε = −N, dt, , ε = −N, , d, dt, , ε = −NBA, , BA cos ωt, d, dt, , cos ωt, , ε = NBAω sinω t, , ε = 𝛆𝟎 sin𝛚 t, where ε0 =NBAω is the maximum value of the emf., ω = 2πν , ν=frequency of revolution of the generator’s coil, The direction of the current changes periodically and therefore the current, is called alternating current (ac).

Page 98 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 7, Alternating Current, Introduction, The electric mains supply in our homes and offices is a voltage that varies, like a sine function with time. Such a voltage is called alternating voltage (ac, voltage) and the current driven by it in a circuit is called the alternating, current (ac current), , Today, most of the electrical devices we use require ac voltage. This is, mainly because most of the electrical energy sold by power companies is, transmitted and distributed as alternating current. The main reason for, preferring use of ac voltage over dc voltage is that ac voltages can be easily, and efficiently converted from one voltage to the other by means of, transformers. Further, electrical energy can also be transmitted, economically over long distances., , Representation of ac current and voltage by rotating vectors —, phasors, In order to show phase relationship between voltage and current in an AC, circuit, we use the notion of phasors., A phasor is a vector which rotates about the origin in anticlockwise, direction with angular speed ω., , ▪ The length of each phasor represents the amplitude or peak value of, the voltage or current., ▪ The projection of each phasor on the vertical axis gives the, instantaneous value of the quantity that the phasor represents., ▪ The rotation angle of each phasor is equal to the phase of alternating, quantity at that instant t., ▪ The angle between two phasors will give you the phase difference, between the corresponding quantities

Page 99 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , AC Voltage Applied to a Resistor, , Apply Kirchhoff’s Loop rule ,Σε(t) = 0, vm sin ωt- i R = 0, vm sin ωt= iR, v, i = m sin ωt, R, , 𝐢 =𝐢𝐦 𝐬𝐢𝐧 𝛚𝐭, , 𝐯, , where 𝐢𝐦 = 𝐦, 𝐑, im is called amplitude of current, , Graph of voltage and current across a pure resistor versus 𝛚𝐭, , In a pure resistor, the voltage and current are in phase. The minima, zero, and maxima occur at the same., , Phasor diagram for the circuit, , Power Dissipated in the Resistor, The ac current varies sinusoidally and has corresponding positive and, negative values during each cycle. Thus, the sum of the instantaneous, current values over one complete cycle is zero, and the average current is, zero.The fact that the average current is zero, however, does not mean that, the average power consumed is zero and that there is no dissipation of, electrical energy.

Page 105 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ For DC , f=0 and hence X C = infinite i.e., the capacitor blocks DC., ▪ For AC, as the frequency increases, X C decreases and hence capacitor, allows AC to flow through it., , Graph of v and i versus ωt, v = vm sin ωt, π, i = im sin (ωt + ), 2, , Phasor diagram, , Power Dissipated in the Capacitor, P=iv, p= im cos ωt x vm sin ωt, i v, p= m m sin( 2ωt), 2, The average power over a complete cycle, i vm, , p̅ = P = ⟨ m, , 2, , P=, , im vm, 2, , sin( 2ωt )⟩, , ⟨sin( 2ωt )⟩, ⟨sin( 2ωt )⟩ =0, , P=0, The average power supplied to a capacitor over one complete cycle is zero., , Example, A 15.0 μF capacitor is connected to a 220 V, 50 Hz source. Find the, capacitive reactance and the current (rms and peak) in the circuit. If the, frequency is doubled, what happens to the capacitive reactance and the, current?

Page 106 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The capacitive reactance 𝐗 𝐂 =, =, =, The rms current is , 𝐈 =, 𝐈=, , 𝟏, 𝛚𝐂, 𝟏, 𝟐𝛑𝐟𝐂, , 𝟏, , 𝟐𝐱 𝟑.𝟏𝟒𝐱𝟓𝟎𝐱𝟏𝟓𝐱𝟏𝟎−𝟔, , =212Ω, , 𝐕, 𝐗𝐂, 𝟐𝟐𝟎, 𝟐𝟏𝟐, , =1.04A, , The peak current is 𝐢𝐦 = √𝟐 𝐈, = 𝟏. 𝟒𝟏𝟒 x1.04 =1.47A, If the frequency is doubled, the capacitive reactance is halved , and, consequently, the current is doubled., , Example, A light bulb and an open coil inductor are connected to an ac source through, a key as shown in Figure., , The switch is closed and after sometime, an iron rod is inserted into the, interior of the inductor. The glow of the light bulb, (a)increases; (b) decreases; (c) is unchanged, as the iron rod is inserted., Give your answer with reasons., Solution:, As the iron rod is inserted, the magnetic field inside the coil magnetizes the, iron increasing the magnetic field inside it. Hence, the inductance of the coil, increases. Consequently, the inductive reactance of the coil increases. As a, result, a larger fraction of the applied ac voltage appears across the inductor,, leaving less voltage across the bulb. Therefore, the glow of the light bulb, decreases., , Example, An electric bulb B and a parallel plate capacitor C are connected in series as, shown in figure.

Page 109 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , a) R = 200Ω , C =15.0 μF =15x 𝟏𝟎, , −𝟔, , F,, , V = 220 V,, , 𝐟 =50Hz, , Z = √R 2 + X C 2, Z = √R2 + (, , 1, , )2, , 2πfC, , Z = √2002 + (, , 1, 2x3.14x50x15x 10−6, , )2, , Z = √2002 + 212.32, 𝐙 = 291.5Ω, The current in the circuit is, I=, 𝐈=, , V, Z, 𝟐𝟐𝟎, 𝟐𝟗𝟏.𝟓, , =0.755A, , (b) The current is the same throughout the circuit., VR = IR =0.755 Ax200 Ω =151V, VC = IX C =0.755 A x 212.3 Ω =160.3V, Algebraic sum of VR and VC =151V+160.3V=311.3V, This is more than source voltage and is not possible., There is a phase difference of 900 betweenVR and VC . Therefore, the total, of these voltages must be obtained using the Pythagorean theorem., V= √𝐕𝐑 𝟐 + 𝐕𝐂 𝟐 =√𝟏𝟓𝟏𝟐 + 𝟏𝟔𝟎. 𝟑𝟐 =220V, , Resonance, A system oscillating with its natural frequency is driven by an energy source, at a frequency that is near the natural frequency, the amplitude of oscillation, is found to be large. This phenomenon is called resonance., A familiar example of this phenomenon is a child on a swing. If the child, pulls on the rope at regular intervals and the frequency of the pulls is almost, the same as the frequency of swinging, the amplitude of the swinging will be, large.

Page 111 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example, Figure shows the variation of i m with ω in a RLC series circuit with, L = 1.00 mH, C = 1.00 nF for two values of R:, (i) R = 100 Ω and (ii) R = 200 Ω. For the source applied vm = 100 V., For R = 100 Ω, 𝐯, 𝟏𝟎𝟎, 𝐢𝐦 = 𝐦 =, 𝐑, 𝟏𝟎𝟎, = 𝟏A, For R = 200 Ω, 𝐯, 𝟏𝟎𝟎, 𝐢𝐦 = 𝐦 =, 𝐑, 𝟐𝟎𝟎, = 𝟎. 𝟓A, , Tuning of a radio or TV, Resonant circuits have a variety of applications, for example, in the tuning, mechanism of a radio or a TV set. The antenna of a radio accepts signals of, dfferent frequencies from many broadcasting stations . But to hear one, particular radio station, we tune the radio. In tuning, we vary the, capacitance of a capacitor in the tuning circuit such that the resonant, frequency of the circuit becomes nearly equal to the frequency of the radio, signal received. When this happens, the amplitude of the current with the, frequency of the signal of the particular radio station in the circuit is, maximum., Resonance phenomenon is exhibited by a circuit only if both L and C are, present .Only then do the voltages across L and C cancel each other., We cannot have resonance in RL and RC circuit., , Bandwidth, , 𝐯, , At resonant frequency 𝛚𝟎 , current is maximum 𝐢𝐦𝐚𝐱, = 𝐦, 𝐦, 𝐑, For values of ω other than 𝛚𝟎 the amplitude of the current is less than the, maximum value., Let 𝛚𝟏 and 𝛚𝟐 be two frequencies on either side of 𝛚𝟎 the current, 1, amplitude is, times its maximum value. At this value, the power dissipated, √2, , by the circuit becomes half.

Page 115 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , a)A capacitor with initial charge 𝐪𝐦 connected to an ideal inductor. The, 𝐪𝐦 𝟐, , electrical energy stored in the charged capacitor is 𝐔𝐄 =, . Since, there is, 𝟐𝐂, no current in the circuit, energy in the inductor is zero. 𝐔𝐁 = 𝟎, b) When the switch is closed and the capacitor starts to discharge . As the, current increases, it sets up a magnetic field in the inductor and thereby,, some energy gets stored in the inductor in the form of magnetic energy., 𝐔𝐄 ≠ 𝟎 , 𝐔𝐁 ≠ 𝟎, c)As the current reaches its maximum value 𝐢𝐦 , (at t = T/4) , all the energy, 𝟏, is stored in the magnetic field, 𝐔𝐁 = 𝐋𝐢𝐦 𝟐, 𝟐, , The capacitor now has no charge and hence no energy. 𝐔𝐄 = 𝟎., The maximum electrical energy equals the maximum magnetic energy., d)The current now starts charging the capacitor, but with opposite polarity, as in initial state., 𝐔𝐄 ≠ 𝟎 , 𝐔𝐁 ≠ 𝟎, e)This process continues till the capacitor is fully charged (at t = T/2) ,all, the energy is stored in the electric field with a polarity opposite to its initial, state., 𝐔𝐄 =, , 𝐪𝐦 𝟐, 𝟐𝐂, , and 𝐔𝐁 = 𝟎., , The whole process will now repeat itself till the system reverts to its, original state. Thus, the energy in the system oscillates between the, capacitor and the inductor.

Page 116 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Note that the above discussion of LC oscillations is not realistic for two, reasons:, (i), , Every inductor has some resistance. The effect of this resistance is to, introduce a damping effect on the charge and current in the circuit and, the oscillations finally die away., (ii) Even if the resistance were zero, the total energy of the system would, not remain constant. It is radiated away from the system in the form of, electromagnetic waves (discussed in the next chapter). In fact, radio, and TV transmitters depend on this radiation., , Transformer, , A transformer consists of two sets of coils, insulated from each other. They, are wound on a soft-iron core, One of the coils called the primary coil has, NP turns. The other coil is called the secondary coil; it has NS turns. Often the, primary coil is the input coil and the secondary coil is the output coil of the, transformer.

Page 118 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Thus for a step up transformer secondary voltage will be greater than, primary voltage,but the secondary current will be less than primary current., , Step-down Transformer, , For a step down transformer the number of turns in the secondary will be, less than that in the primary( 𝐍𝐬 ˂ 𝐍𝐏 ), , Thus for a step up transformer secondary voltage will be less than primary, voltage, but the secondary current will be greater than primary current., , Energy Losses in a Transformer, (i)Flux Leakage:, There is always some flux leakage; that is, not all of the flux due to primary, passes through the secondary due to poor design of the core or the air gaps, in the core. It can be reduced by winding the primary and secondary coils, one over the other., (ii)Resistance of the windings :, The wire used for the windings has some resistance and so, energy is lost, due to heat produced in the wire(I2 R). In high current, low voltage windings,, these are minimised by using thick wire., (iii)Eddy currents loss:, The alternating magnetic flux induces eddy currents in the iron core and, causes heating. The effect is reduced by having a laminated core., (iv)Hysteresis loss:, The magnetisation of the core is repeatedly reversed by the alternating, magnetic field. This produces hysteresis and energy is lost as heat. This can, be minimised by using a magnetic material which has a low hysteresis, loss(e.g- soft iron core).

Page 119 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 8, Electromagnetic Waves, Introduction, An electrical current produces a magnetic field around it. Further, a, magnetic field changing with time gives rise to an electric field. Is the, converse also true? Does an electric field changing with time give rise to a, magnetic field?, According to James Clerk Maxwell , time-varying electric field, generates magnetic field. Maxwell formulated a set of equations involving, electric and magnetic fields, known as Maxwell’s equations. Maxwell’s, equations predicted the existence of electromagnetic waves, which are, (coupled) timevarying electric and magnetic fields that propagate in space., Hertz, in 1885, experimentally demonstrated the existence of, electromagnetic waves. Its technological use by Marconi and others led in, due course to the revolution in communication that we are witnessing today.

Page 121 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Electromagnetic waves, Sources of Electromagnetic Waves, ▪ A stationary charge produces only electrostatic fields., ▪ Charges in uniform motion (steady currents) can produce magnetic, fields that, do not vary with time., ▪ An oscillating charge(accelerating charge) produces an oscillating, electric field in space, which produces an oscillating magnetic field,, which in turn, is a source of oscillating electric field, and so on. The, oscillating electric and magnetic fields thus regenerate each other, as, the electro magnetic wave propagates through the space., Thus an oscillating charge(accelerating charge) is the source, of electromagnetic waves., An electric charge oscillating harmonically with frequency 𝑣, produces, electromagnetic waves of the same frequency 𝑣., ▪ The experimental demonstration of electromagnetic wave in the radio, wave region was done by Hertz in1887., ▪ Seven years after Hertz, Jagdish Chandra Bose, succeeded in producing, and observing electromagnetic waves of much shorter wavelength, (25 mm to 5 mm)., ▪ At around the same time, Guglielmo Marconi succeeded in transmitting, electromagnetic waves over distances of many kilometres. Marconi’s, experiment marks the beginning of the field of communication using, electromagnetic waves., , Nature of Electromagnetic Waves, 1) In an e.m waves are transverse waves in which the electric and magnetic, fields are perpendicular to each other, and also to the direction of, propagation., 2) The speed of e.m.wave in vacuum is,, , 𝐜=, , 𝟏, √𝛍𝟎 𝛆𝟎, , 3)The speed of of electromagnetic waves in a material medium is, , 𝐜=, , 𝟏, √𝛍𝛆, , 4) The electric and the magnetic fields in an electromagnetic wave are, related as, 𝐄𝟎, 𝐁𝟎, , =𝐜, , 5) No material medium is required for the propagation of e.m.wave.

Page 122 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , 6) Electromagnetic waves carry energy as they travel through space and this, energy is shared equally by the electric and magnetic fields., 7)Electromagnetic waves transport momentum as well. When these waves, strike a surface, total momentum delivered to this surface is,, 𝐔, , p=𝐜, , , where U is the energy, , Expression for electric field and magnetic field, Consider an electromagnetic wave propagating along the z direction. Let the, electric field 𝐸𝑥 is along the x-axis and the magnetic field 𝐵𝑦 is along the yaxis. Then, , 𝐄𝐱 = 𝐄𝟎 sin (k z– ωt), 𝐁𝐲 = 𝐁𝟎 sin (k z– ωt), Here 𝐤 =, , 𝟐𝛑, 𝛌, , k is the propagation constant, , ω =𝟐𝝅𝒗, 𝜔, 𝑘, , Speed,, , =, , c=, , 2𝜋𝜈, 2𝜋, 𝜆, , ω is the angular frequency, = 𝑣𝜆 = 𝑐, , 𝛚, 𝐤, , Example, A plane electromagnetic wave of frequency 25 MHz travels in free space, along the x-direction. At a particular point in space and time, E = 6.3ĵ V/m., What is B at this point?, 𝐄𝟎, 𝐁𝟎, , =𝐜, , 𝐁𝟎 =, , 𝐄𝟎, c, , 6.3, , =3 x 108 =2.1 x10−8 T, , E is along y-direction and the wave propagates along x-axis., Therefore, B should be in a direction perpendicular to both x- and y-axes., i.e., B is along z-axis.

Page 123 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example, The magnetic field in a plane electromagnetic wave is given by, 𝐵𝑦 = 2 × 10−7 sin (0.5×103 𝑥 + 1.5×1011 t) T., a) What is the wavelength and frequency of the wave?, b) Write an expression for the electric field., (a), , 𝐵𝑦 = 2 × 10−7 sin (0.5×103 𝑥 + 1.5×1011 t), Comparing with general expression for magnetic field of an em, wave travelling in x direction,, , By = B0 sin (kx– ωt), k=0.5×103, 2π, k= λ =0.5×103, 2π, , λ = 0.5×103, , =12.56 × 10−3 m, , ω =1.5×1011, ω =2𝜋𝑣 =1.5×1011, 𝑣=, , 1.5×10, , 11, , 2π, , =0.24 x1011 Hz, b) B is along y-direction and the wave propagates along x-axis., Therefore, E should be in a direction perpendicular to both x- and y-axes., i.e., E is along z-axis., , So expression for electric field is ,, Ez = E0 sin (k x– ωt), E0, =c, B, 0, , E0 =B0 𝑥 𝑐, =2 × 10−7 x 3 × 108, =60 V/m, 𝐄𝐳 = 60 sin (0.5×𝟏𝟎𝟑 𝒙 + 1.5×𝟏𝟎𝟏𝟏 t) V/m

Page 124 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Electromagnetic Spectrum, The classification of em waves according to frequency is the electromagnetic, spectrum. There is no sharp division between one kind of wave and the next., , Radio waves, ▪ Radio waves are produced by the accelerated motion of charges in, conducting wires., ▪ Frequency range from 500 kHz to about 1000 MHz., ▪ (i)They are used in radio and television communication systems., (ii)Cellular phones use radio waves., , Microwaves, ▪ Microwaves (short-wavelength radio waves), are produced by special, vacuum tubes called, klystrons, magnetrons and Gunn diodes., ▪ Frequencies in the gigahertz (GHz) range,, ▪ (i)Used for radar systems used in aircraft navigation ., (ii)Used in speed guns used to time fast balls, tennisserves,, and automobiles., (iii) Microwaves are used in microwave ovens , for cooking.

Page 125 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , How is food cooked in microwave ovens?, In microwave ovens, the frequency of the microwaves is selected to match, the resonant frequency of water molecules so that energy from the waves is, transferred efficiently to the kinetic energy of the molecules. This raises the, temperature of any food containing water., , Infrared waves, ▪ Infrared waves are produced by hot bodies and molecules., ▪ (i) Infrared lamps are used in physical therapy., (ii) Infrared radiation plays an important role in maintaining the, earth’s warmth or average temperature through the greenhouse effect., (iii)Infrared detectors are used in Earth satellites, both for, military purposes and to observe growth of crops., (iv)LEDs emit infrared waves, which are used in the remote, switches of TV sets, video recorders and hi-fi systems., Why IR waves are called heat waves?, Infrared waves are sometimes referred to as heat waves. This is because, water molecules present in most materials readily absorb infrared waves, ( CO2 , NH3 , also absorb infrared waves). After absorption, their thermal, motion increases, that is, they heat up and heat their surroundings., Greenhouse Effect, Incoming visible light is absorbed by the earth’s surface and reradiated as, infrared (longer wavelength) radiations. This radiation is trapped by, greenhouse gases such as carbon dioxide and water vapour. This trapped, Infrared radiation maintains the earth’s warmth., , Visible rays, ▪ Electrons in atoms emit The eye light when they move from, Photocells one energy level to a Photographic film lower energy, level’, ▪ Frequency range of 4 × 1014 Hz to 7 × 1014 Hz, Wavelength range of about 700 – 400 nm., Our eyes are sensitive to this range of wavelengths. Different animals are, sensitive to different range of wavelengths. For example, snakes can detect, infrared waves, and the ‘visible’ range of many insects extends well into the, utraviolet.

Page 126 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Ultraviolet rays, ▪ Ultraviolet (UV) radiation is produced by special lamps and very hot, bodies. The sun is an important source of ultraviolet light., ▪ Wavelength range of (400 nm) to (0.6 nm)., ▪ (i)UV radiations are used in LASIK, (Laser assisted in situ keratomileusis) eye surgery., (ii) UV lamps are used to kill germs in water purifiers., Why is depletion of ozone layer , a matter of international concern?, Most of the UV rays from sun is absorbed in the ozone layer in the, atmosphere at an altitude of about 40 – 50 km. UV light in large quantities, has harmful effects on humans. Exposure to UV radiation induces the, production of more melanin, causing tanning of the skin. Ozone layer in the, atmosphere plays a protective role, and hence its depletion by chlorofluorocarbons (CFCs) gas (such as freon) is a matter of international concern., UV radiation is absorbed by ordinary glass. Hence, one cannot get tanned or, sunburn through glass windows. Welders wear special glass goggles or face, masks with glass windows to protect their eyes from large amount of UV, produced by welding arcs., , X-rays, ▪ One common way to generate X-rays is to bombard a metal target by, high energy electrons., ▪ Wavelengths from about (10 nm) to (10–4 nm)., ▪ X-rays are used as a diagnostic tool in medicine and as a treatment for, certain forms of cancer., As X-rays damage or destroy living tissues and organisms, care must be, taken to avoid unnecessary or over exposure., , Gamma rays, ▪ This high frequency radiation is produced in nuclear reactions and also, emitted by radioactive nuclei., ▪ Gamma rays are the highest frequency range of the electromagnetic, spectrum and have wavelengths of from about 10–10m to 10–14m., ▪ They are used in medicine to destroy cancer cells.

Page 128 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 9, Ray Optics and Optical Instruments, Introduction, Light is an electromagnetic wave. Light travels with a speed of 3 x108 m/s in, vacuum. The speed of light in vacuum is the highest speed attainable in, nature. A light wave can be considered to travel from one point to another,, along a straight line joining them. The path is called a ray of light, and a, bundle of such rays constitutes a beam of light., , Reflection of Light by Spherical Mirrors, , Laws of Reflection, 1) The incident ray, reflected ray and the normal to the reflecting surface at, the point of incidence lie in the same plane., 2)The angle of incidence is equai to the angle of reflection(i=r)., , Sign Convention, , We follow the Cartesian sign convention to measure distances. According to, this convention,, 1) All distances are measured from the pole of the mirror or the optical, centre of the lens., 2) The distances measured in the same direction as the incident light are, taken as positive and those measured in the direction opposite to the, direction of incident light are taken as negative., 3) The heights measured upwards with respect to principal axis of the, mirror/ lens are taken as positive . The heights measured downwards, are taken as negative.

Page 129 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Focal Length of Spherical Mirrors, When a parallel beam of light, is incident on a concave mirror, the, reflected rays converge at a point F, on its principal axis . The point F is, called the principal focus of the, concave mirror., When a parallel beam of light is, incident on a convex mirror, the, reflected rays appear to diverge from, a point F on its principal axis . The, point F is called the principal focus of, the convex mirror., , Relation between Focal Length and Radius of Curvature, , Let f be the focal length and R be the radius of curvature of lens, MD, MD, From figure ,, tan θ =, ,, θ=, ------(1) (For small value of θ, tanθ ≈ θ ), R, , tan2 θ =, , MD, , Substituting θ from eq(1) in eq(2), , f, , R, , ,, , 2θ =, 2, , MD, R, 2, R, , =, =, , MD, f, , -----(2), , (tan2θ ≈ 2θ), , MD, 1, , f, , f, , 𝐑, , 𝐟=𝟐, , Some important points to consider while image formation in spherical, mirrors :▪ If rays emanating from a point actually meet at another point after, reflection , that point is called the image of the first point., ▪ The image is real if the rays actually converge to the point., ▪ The image is virtual if the rays do not actually meet but appear to, diverge from the point when produced backwards.

Page 130 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ The ray parallel to the principal axis, goes through the focus of the, mirror after reflection., ▪ The ray passing through the centre of curvature of a concave mirror, ,retraces the path., ▪ The ray passing through the focus of the concave mirror , after, reflection ,goes parallel to the principal axis., ▪ The ray incident at any angle at the pole. The reflected ray follows, laws of reflection., , The Mirror Equation, , The two right-angled triangles A′B′F and MPF are similar, B′ A′, , B′ F, , =, , PM, B′ A′, , FP, B′ F, , =, , BA, , FP, , ------------(1) (since PM = AB), , The right angled triangles A′B′P and ABP are also similar., B′ A′, , B′ P, , =, , BA, , BP, , ------------(2), , From eqns(1) and (2), B′ F, FP, , B′ P = v,, , B′ P, , =, , BP, , B′ F =v-f ,, , BP = u,, v− f, f, , =, , v, u, , Applying sign convention ,, −v− −f, −f, v−f, f, v, f, , =, =, , −1 =, , −v, −u, v, u, v, u, , FP = f,

Page 131 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Dividing by v, 1, , 𝟏, 𝐮, , f, , −, , +, , 𝟏, , 1, , =, , v, , =, , 𝐯, , 1, u, , 𝟏, 𝐟, , This relation is known as the mirror equation., , Linear Magnification (m), Linear magnification (m) is the ratio of the height of the image (h′) to the, height of the object (h)., 𝐡′, , 𝐦=, , 𝐡, , From above figure, B′ A′, BA, , =, , B′ P, BP, , With the sign convention,, −h′, h, h′, h, , 𝐦=, , 𝐡′, 𝐡, , =, =, , =, , −v, −u, −v, u, , −𝐯, 𝐮, , Example, An object is placed at (i) 10 cm, (ii) 5 cm in front of a concave mirror of, radius of curvature 15 cm. Find the position, nature, and magnification of the, image in each case.

Page 132 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Refraction, The direction of propagation of an obliquely incident ray of light that enters, the other medium, changes at the interface of the two media. This, phenomenon is called refraction of light., , Laws of Refraction, i)The incident ray, the refracted ray and the normal to the interface at the, point of incidence, all lie in the same plane., ii)The ratio of the sine of the angle of incidence to the sine of angle of, refraction is constant, 𝐬𝐢𝐧 𝐢, 𝐬𝐢𝐧 𝐫, , = 𝐧𝟐𝟏, , where n21 is a constant, called the refractive index of the second, medium with respect to the first medium., n, n21 = 2, n1, , This equation is known as Snell’s law of refraction., ▪ When a ray travels from rarer to denser, medium, the refracted ray bends towards, the normal., i.e., if n21 > 1, i.e., n2 > n1 , r < i, , ▪ When a ray travels from denser to rarer, medium, the refracted ray bends away from, the normal., i.e., if n21 < 1, i.e., n2 < n1 , r > i

Page 133 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Some Elementary Results Based on The Laws of Refraction, (i)Lateral Shift, , For a rectangular slab, refraction takes place at two interfaces (air-glass and, glass-air). The emergent ray is parallel to the incident ray—there is no, refraction and reflection of light, but it does suffer lateral displacement/, shift with respect to the incident ray., , (ii)Apparent depth, , The bottom of a tank filled with water appears to be raised ., For viewing near the normal direction ,, Apparent depth =, , 𝐡𝟏 =, , 𝐫𝐞𝐚𝐥 ⅆ𝐞𝐩𝐭𝐡, 𝐑𝐞𝐟𝐫𝐚𝐜𝐭𝐢𝐯𝐞 𝐈𝐧ⅆ𝐞𝐱, , 𝐡𝟐, 𝐧, , iii)Advance sunrise and delayed sunset

Page 134 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The sun is visible a little before the actual sunrise and until a little after the, actual sunset due to refraction of light through the atmosphere. Due to this,, the apparent shift in the direction of the sun is by about half a degree and, the corresponding time difference between actual sunset and apparent, sunset is about 2 minutes., The apparent flattening (oval shape) of the sun at sunset and sunrise is also, due to the atmospheric refraction., , Total Internal Reflection, When a ray of light enters from a denser medium to a rarer medium, if the, angle of incidence is greater than the critical angle (ic ) for the given pair of, media, the incident ray is totally reflected. This is called total internal, reflection., , Explanation:When a ray of light enters from a denser medium to a rarer medium, it bends away, from the normal., ▪ The incident ray AO1 is partially reflected (O1 C) and partially refracted(O1 B) ., ▪ As the angle of incidence increases, the angle of refraction also increases.(for, ray AO2 ), ▪ When the angle of incidence becomes equal to the critical angle(ic ) for the, given pair of media, the angle of refraction becomes 90º.(for rayAO3 ), ▪ If the angle of incidence is increased further ( ray AO4 ), refraction is not, , possible, and the incident ray is totally reflected., Conditions for Total Internal Reflection, ▪ The ray of light should enter from a denser medium to a rarer, medium., ▪ The angle of incidence should be greater than the critical angle (ic ), for the given pair of media .

Page 135 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Critical Angle, The angle of incidence in the denser medium, corresponding to an angle of, refraction 90º, is called the critical angle (i c ) for the given pair of media., Let the second medium be air., By Snell’s law, , sin i, sin r, , n2, , =, , n1, , When, sin ic, sin 90, , =, , sin ic =, , =, , 1, n, , i=ic ,, , r=90, , 1, n, 1, n, , 𝟏, , n= 𝐬𝐢𝐧 𝐢, , 𝐜, , This is the relation connecting refractive index and critical angle., , Total internal reflection in nature and its technological applications, (i)Mirage:, On hot summer days, the air near the ground becomes hotter than the air at, higher levels. So air near the ground has less refractive index than that, above . As a result, when light from a tall object such as a tree reaches, ground, it successively bends away from the normal and undergoes total, internal reflection, if the angle of incidence for the air near the ground, exceeds the critical angle.To a distant observer, the light appears to be, reflected from the ground, and an inverted images of distant tall objects is, seen. This optical illusion is called mirage. This type of mirage is especially, common in hot deserts., , Some of you might have noticed that while moving in a bus or a car during a, hot summer day, a distant patch of road, especially on a highway, appears to, be wet. But, you do not find any evidence of wetness when you reach that, spot. This is also due to mirage.

Page 136 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , (ii) Diamond:, The brilliance of diamond is mainly due to the total internal reflection of, light inside them. The critical angle for diamond-air interface (≅ 24.4°) is, very small, therefore once light enters a diamond, it is very likely to undergo, total internal reflection inside it. By cutting the diamond suitably, multiple, total internal reflections can be made to occur., , (iii)Prism:, Prisms designed to bend light by 90º or by 180º make use of total internal, reflection .In these cases, the critical angle ic for the material of the prism, must be less than 45º., , Such a prism is also used to invert images without changing their size., , (iv) Optical fibres:, Now-a-days optical fibres are extensively used for transmitting audio and, video signals through long distances. Optical fibres make use of the, phenomenon of total internal reflection. Optical fibres are fabricated with, high quality composite glass/quartz fibres., , Each fibre consists of a core and cladding. The refractive index of the, material of the core is higher than that of the cladding. When a signal in the, form of light is directed at one end of the fibre at a suitable angle, it, undergoes repeated total internal reflections along the length of the fibre, and finally comes out at the other end . Since light undergoes total internal, reflection at each stage, there is no appreciable loss in the intensity of the, light signal.

Page 142 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Graph between the angle of deviation and angle of incidence - i-d curve, , Dispersion by a Prism, The phenomenon of splitting of light into its component colours is known as, dispersion., , When a narrow beam of sunlight, usually called white light, is incident on a, glass prism, the emergent light is seen to be consisting of seven coloursviolet, indigo, blue, green, yellow, orange and red (given by the acronym, VIBGYOR). The red light bends the least, while the violet light bends the, most., Dispersion takes place because the refractive index of medium for different, wavelengths (colours) is different., Thick lenses could be assumed as made of many prisms, therefore, thick, lenses show chromatic aberration due to dispersion of light., Sir Isaac Newton put another similar prism, but in an inverted position,, , He first prism splits the white light into its component colours, while the, inverted prism recombines them to give white light., , Some Natural Phenomena Due to Sunlight, The rainbow, The rainbow is a phenomenon due to combined effect of dispersion,, refraction and reflection of sunlight by spherical water droplets of rain. An, observer can therefore see a rainbow only when his back is towards the sun.

Page 143 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Primary rainbow, The primary rainbow is a result of three-step process, that is, refraction,, reflection and refraction. For primary rainbow , red colour on the top and, violet on the bottom., , ▪ Sunlight is first refracted as it enters a raindrop. Red bent the least, and violet bent the most., ▪ These component rays then strike the inner surface of the water, drop and undergo total internal reflection if i > ic (48º, in this, case)., ▪ The reflected light is refracted again as it comes out of the drop., The violet light emerges at an angle of 40º and red light emerges at an angle, of 42º, related to the incoming sunlight. For other colours, angles lie in, between these two values., Secondary Rainbow, When light rays undergoes two internal reflections inside a raindrop,, instead of one as in the primary rainbow, a secondary rainbow is formed., The secondary rainbow is a result of four-step process, that is, refraction,, two internal reflections and refraction. For secondary rainbow , violet colour, on the top and red on the bottom., , The intensity of light is reduced at the second reflection and hence the, secondary rainbow is fainter than the primary rainbow.

Page 144 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Scattering of light, Rayleigh scattering, The amount of scattering is inversely proportional to the fourth power of, the wavelength. This is known as Rayleigh scattering., 𝟏, I∝ 𝟒, 𝝀, Light of shorter wavelengths is scattered much more than light of longer, wavelengths., Why sky appears blue?, As sunlight travels through the earth’s atmosphere, it gets scattered, (changes its direction) by the atmospheric particles. According to Rayleigh, scattering ,the amount of scattering is inversely proportional to the fourth, power of the wavelength .So violet and blue like colours are scattered more, than red. Since our eyes are more sensitive to blue than violet, we see the, sky blue., Why are clouds generally white?, When sunlight gets scattered by large particles (a >> λ) like dust, rain, drops and ice particles present in the atmosphere, all wavelengths are, scattered nearly equally(Rayleigh scattering is not obeyed). Thus, clouds, which have droplets of water with a >> λ are generally white., Why does sun look reddish at sunset and sunrise?, At sunset or sunrise, the sun’s rays have to pass through a larger distance in, the atmosphere . Most of the blue and other shorter wavelengths are, removed by scattering. The least scattered red light reaches our eyes and the, sun looks reddish. This explains the reddish appearance of the sun and full, moon near the horizon., , Optical Instruments, The eye

Page 145 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Light enters the eye through a curved front surface, the cornea., Light passes through the pupil which is the central hole in the iris. The size, of the pupil can change under control of muscles., The light is further focussed by the eye lens on the retina. The retina is a, film of nerve fibres covering the curved back surface of the eye. The retina, contains rods and cones which sense light intensity and colour, respectively,, and transmit electrical signals via the optic nerve to the brain which finally, processes this information., The focal length of the eye lens can be adjusted by the action of ciliary, muscles in order to maintain the same image-lens distance (≅ 2.5 cm). This, property of the eye is called accommodation., The closest distance for which the lens can focus light on the retina is called, the least distance of distinct vision, or the near point. The standard value for, normal vision is taken as 25 (D)., , Some defects of vision, Presbyopia, The near point increases with age, because of the decreasing effectiveness, of the ciliary muscle and the loss of flexibility of the lens. This defect of the, eye is called presbyopia. It is corrected by using a converging lens for, reading., , Myopia, If the eye-lens focusses the incoming light at a point in front of the retina, the, defect is called nearsightedness or myopia. This is due to too much, convergence in the incident beam., , Myopia can be compensated by placing a concave(diverging) lens between, the eye and the object., , Hypermetropia, If the eye-lens focusses the incoming light at a point behind the retina, the, defect is called farsightedness or hypermetropia. This is due to less, convergence in the incident beam .

Page 146 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Hypermetropia can be compensated by placing a convex(converging) lens, between the eye and the object., , Astigmatism, Astigmatism occurs when the cornea is not spherical in shape. For example,, the cornea could have a larger curvature in the vertical plane than in the, horizontal plane or vice-versa., , If a person with such a defect in eye-lens looks at a wire mesh or a grid of, lines, focussing in either the vertical or the horizontal plane may not be as, sharp as in the other plane. Astigmatism can be corrected by using a, cylindrical lens of desired radius of curvature with an appropriately directed, axis. This defect can occur along with myopia or hypermetropia., , The microscope

Page 147 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , A simple microscope or magnifier is a converging lens of small focal length., If the object is held between the focus and optical centre of lens, an erect,, magnified and virtual image is formed at near point 25 cm or more. If the, object is held at focus, the image will be formed at infinity., The linear magnification m(when image is at D), v, 1 1, m= = v ( - ), u, , m=1-, , v, v, , f, , f, , Applying sign convention , v=-D, , m=𝟏 +, , 𝐃, 𝐟, , The linear magnification m(when image is at infinity), 𝐃, , m= 𝐟, Compound Microscope, A simple microscope has a limited maximum magnification (≤ 9). For much, larger magnifications, one uses two lenses, one compounding the effect of, the other. This is known as a compound microscope., , The lens near the object, called the objective. It forms a real, inverted,, magnified image of the object. This serves as the object for the second lens,, the eyepiece, at the focal plane (or little closer) of the eyepiece . The, eyepiece functions like a simple microscope or magnifier and produces an, enlarged and virtual image at infinity, or at the near point. Clearly, the final, image is inverted with respect to the original object., Magnifiction, m= mo x me -----------(1), m0 =, , h′, h, , =, , L, f0

Page 148 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , When the final image is formed at infinity,, me =, , D, fe, , Substituting in eqn(1), 𝐋, , 𝐃, , 𝟎, , 𝐞, , m=𝐟 x 𝐟, , D= near point=25cm, f0 = focal length of objective, fe = focal length of eyepiece, L= The tube length of the compound microscope, (The distance between the second focal point, of the objective and the first focal point of the, eyepiece is called the tube length.), , Clearly, to achieve a large magnification of a small object , the objective and, eyepiece should have small focal lengths., , Telescope, Refracting Telescope, , The telescope is used to provide angular magnification of distant objects . It, also has an objective and an eyepiece. The objective has a large focal length, and a much larger aperture than the eyepiece. Light from a distant object, enters the objective and a real image is formed in the tube at its second focal, point. The eyepiece magnifies this image producing a final inverted image., The magnifying power m is the ratio of the angle β subtended at the eye by, the final image to the angle α which the object subtends at the lens or the, eye., m≈, , β, α, , ≈, , h, fe, , ⋅, , fo, h, , =, , 𝐦=, , f0, fe, , 𝐟𝟎, 𝐟𝐞

Page 149 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Terrestrial telescopes have, in addition, a pair of inverting lenses to make, the final image erect. Refracting telescopes can be used both for terrestrial, and astronomical observations., For high resolving power, optical telescopes should have objective of large, diameter. Such big lenses are very heavy and it is rather difficult and, expensive to make such large sized lenses which form images that are free, from any kind of chromatic aberration and distortions.So modern telescopes, use a concave mirror rather than a lens for the objective.( Reflecting, Telescope), , Reflecting Telescope, Telescopes with mirror objectives are called reflecting telescopes. They have, several advantages., ▪ First, there is no chromatic aberration in a mirror., ▪ Second, if a parabolic reflecting surface is chosen, spherical aberration is, also removed. Mechanical support is much less of a problem since a, mirror weighs much less than a lens of equivalent optical quality., , A reflecting telescope is that the objective mirror focusses light inside the, telescope tube. A convex secondary mirror focusses the incident light, which, passes through a hole in the objective primary mirror. It has the advantages, of a large focal length in a short telescope.

Page 150 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 10, Wave Optics, Introduction, In 1678, the Dutch physicist Christiaan Huygens put forward the wave, theory of light .The wave model could satisfactorily explain the phenomena, of reflection , refraction, interference, diffraction and polarisation ., , Wavefront, A locus of points, which oscillate in phase is called a wavefront; thus a, wavefront is defined as a surface of constant phase., The speed with which the wavefront moves outwards from the source is, called the speed of the wave. The energy of the wave travels in a direction, perpendicular to the wavefront., , Spherical Wavefront, For a point source emitting waves uniformly in all directions, the, wavefronts will be spherical ., , Plane Wavefront, At large distance from a source, a small portion of the sphere can be, considered as a plane and is known as a plane wavefront., , Huygens Principle, According to Huygens principle, each point of the wavefront acts as a source, secondary wavelets and if we draw a common tangent to all these secondary, wavelets, we obtain the new position of the wavefront at a later time.

Page 152 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , AB is the incident wavefront and EC is the reflected wavefront., Let v be the velocity of the wave ,then, AE = BC = v𝜏, AC = AC (common side), So the triangles EAC and BAC are congruent ., , Therefore, , i=r, Angle of incidence=Angle of reflection, This is the law of reflection., , Refraction of a plane wave by a thin prism, , The emerging wavefront is also plane wavefront,but tilted., , Refraction of a plane wave by a convex lens, , The emerging wavefront is spherical and converges to the point F which is, known as the focus., , Reflection of a plane wave by a concave mirror, , The reflected wavefront is a spherical converging to the focal point F.

Page 153 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The doppler effect, The apparent change in frequency of light seen by an observer , whenever, there is a relative motion between source and observer is called Doppler, Effect., When the source moves away from the observer the frequency as measured, by the source will be smaller and the wavelength increases. This increase in, wavelength due to doppler effect is called red shift., When source moving towards the observer, there is an apparent increase in, frequency and decrease in wavelength. This is referred to as blue shift., The Doppler shift can be expressed as, 𝜟𝒗, 𝒗, , =−, , 𝒗𝒓𝒂ⅆ𝒊𝒂𝒍, 𝒄, , 𝒗𝒓𝒂ⅆ𝒊𝒂𝒍 is the component of the source velocity along the line joining the, observer to the source relative to the observer; 𝒗 radial is considered positive, when the source moves away from the observer., , Superposition Principle, According to superposition principle , the resultant displacement produced, by a number of waves in a medium is the vector sum of the displacements, produced by each of the waves., , Coherent sources, Two sources are said to be coherent if they emit light waves of same, frequency and same phase or constant phase difference., , Two needles oscillating in phase in water represent two coherent sources., , Interference, Interference is the phenomenon in which two waves superpose to form a, resultant wave of greater or lower amplitude., The interference can be constructive or destructive.

Page 154 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Condition for constructive interference, If the path difference at a point is an integral multiple of, λ, there will be constructive interference and a bright, fringe is formed at that point, S2P – S1P = nλ, , where (n = 0, 1, 2, 3,...), , Condition for destructive interference, If the path difference at a point is an odd integral multiple, of λ/2 , there will be destructive interference and a dark, fringe is formed at that point, 𝟏, , S2P – S1P = = (n+ ) λ, 𝟐, , where (n = 0, 1, 2, 3,...)

Page 155 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Two sodium lamps illuminating two pinholes cannot produce, interference fringes. Why?, If we use two sodium lamps illuminating two pinholes we will not observe, any interference fringes. This is because the light wave emitted from an, ordinary source (like a sodium lamp) undergoes abrupt phase changes .Thus, the light waves coming out from two independent sources of light will not, have any fixed phase relationship and would be incoherent and cannot, produce interference pattern., , Interference of Light Waves and Young’s Experiment, , The British physicist Thomas Young made two pinholes S1 and S2 (very, close to each other) on an opaque screen. These were illuminated by, another pinholes which is illuminated by a bright source. Light waves spread, out from S and fall on both S1 and S2. S1 and S2 then behave like two coherent, sources because light waves coming out from S1 and S2 are derived from the, same original source and interference pattern with altermate bright and, dark fringes is formed on the screen., , Expression for the fringe width (Band width), , Cosider two coherent sources separated by a distance d with a screen placed, at a distance D from the coherent sources., 𝑑 2, , 𝑑 2, , (𝑆2 𝑃)2 − (𝑆1 𝑃)2 = [𝐷2 + (𝑥 + ) ] − [𝐷2 + (𝑥 − ) ], 2, 2, = [𝐷2 + 𝑥 2 + 2𝑥𝑑 +, , 𝑑2, 4, , ] − [𝐷2 + 𝑥 2 − 2𝑥𝑑 +, , (𝑆2 𝑃)2 − (𝑆1 𝑃)2 = 2𝑥𝑑 ------------------------(1), (S2P + S1P) (S2P – S1P) = 2xd, , 𝑑2, 4, , ]

Page 156 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , (S2P – S1P) =, , 2𝑥𝑑, , 2𝑥𝑑, , =, , (S2P+ S1P), 𝒙ⅆ, , 2D, , (S2P – S1P) =, -----------------(1), 𝐃, Let the point P corresponds to maximum brightness(bright band).Then, S2P – S1P = nλ, (n = 0, 1, 2, 3,...) --------------(2), From eq (1) and(2) ,, , 𝑥𝑑, D, , = nλ, , Thus for the nth bright band,, , xn=, , For the (n+1)th bright band,, , xn+1=, , Bandwidth ,, , nλ𝐷, d, (n+1)λ𝐷, d, , β = xn+1 –xn, β=, , β=, , (n+1)λ𝐷, d, , −, , nλ𝐷, d, , 𝛌𝑫, ⅆ, , This is the expression for the fringe width., The central point O will be bright as the path difference is zero., Thus bandwidth can be increased by, ▪ Increasing the distance of screen (D)from coherent sources, ▪ Decreasing the distance between the coherent sources., ▪ Increasing the wavelength of source., The graph of the intensity distribution in Young’s double-slit experiment., , What is the effect on the interference fringes in a Young’s double-slit, experiment,if the monochromatic source is replaced by a source of white, light?, The interference patterns due to different component colours of white light, overlap (incoherently). The central bright fringes for different colours are at, the same position. Therefore, the central fringe is white. The fringe closest, on either side of the central white fringe is red and the farthest will appear, blue. After a few fringes, no clear fringe pattern is seen.

Page 157 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example, Two slits are made one millimetre apart and the screen is placed one metre, away. What is the fringe separation when bluegreen light of wavelength 500, nm is used., Fringe spacing , β =, β=, , λ𝐷, d, 500x10−9 𝑥1, 1x10−3, , = 5 × 10–4 m = 0.5 mm, , Example, In a double slit experiment, the slits are separated by 0.03 cm and the screen, is placed 1.5 m away. The distance between the central fringe and the fourth, bright fringe is 1 cm. Determine the wavelength of the light used in the, experiment., 4β =1cm, β =1/4 =0.25cm =0.25x10-2m, β=, λ=, , λ𝐷, d, β𝑑, 𝐷, 0.25x10−2 x0.03𝑥10−2, , =, 1.5, = 0.005x10-4=500x10-9=500nm, , Diffraction, Diffraction is the phenomenon of bending of light around the corners of an, obstacle , into the region of geometrical shadow of the obstacle., If we look clearly at the shadow cast by an opaque object, close to the region, of geometrical shadow, there are alternate dark and bright regions just like, in interference. This happens due to the phenomenon of diffraction., Diffraction is a general characteristic exhibited by all types of waves, be it, sound waves, light waves, water waves or matter waves., Since the wavelength of light is much smaller than the dimensions of most, obstacles; we do not encounter diffraction effects of light in everyday, observations.

Page 158 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The single slit, , When a single narrow slit is illuminated by a monochromatic source, a broad, pattern with a central bright region is seen on the screen. On both sides,, there are alternate dark and bright regions, the intensity becoming weaker, away from the centre. This is diffraction pattern., , Single slit diffraction experiment, , Consider a parallel beam of light falling normally on a single slit LN of width, a. The diffracted light goes on to meet a screen. The midpoint of the slit is M., The path difference NP – LP between the two edges of the slit,, NP – LP = NQ, = a sin θ, NP – LP≈ aθ, , For central maximum, At the central point C on the screen,, the angle θ =0, Path differences aθ =0, All the parts of the slit contribute in phase.This gives maximum intensity at C, called central maximum.

Page 159 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , For secondary maxima, For secondary maxima,, Path difference ,, , 1, , aθ = (n+ ) λ, 2, 𝟏, , 𝛌, , 𝟐, , 𝒂, , θ = (n+ ), , where n = ±1, ±2, ±3, ...., , For secondary minima, For secondary minima,, Path differences ,, , aθ = nλ, 𝛌, θ= n, , 𝒂, , where n = ±1, ±2, ±3, ...., , Difference between Interference and Diffraction, , Holding two blades to form a single slit. A bulb filament, viewed through this shows clear diffraction bands., , Cosistency with Principle of Conservation of Energy., In interference and diffraction, light energy is redistributed. If it reduces in, one region, producing a dark fringe, it increases in another region,, producing a bright fringe. There is no gain or loss of energy, which is, consistent with the principle of conservation of energy., , Resolving power of optical instruments, When a parallel beam of light is incident on a convex lens, because of, 1.22 λf, 0.61 λf, diffraction effects, the beam gets focused to a spot of radius ≈, =, 2𝑎, , 𝑎

Page 160 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , where f is the focal length of the lens and 2a is the diameter of the circular, aperture or the diameter of the lens., Although the size of the spot is very small, it plays an important role in, determining the limit of resolution of optical instruments like a telescope or, a microscope., , Resolving Power of Telescope, For the two stars to be just resolved, f Δθ ≈, , 0.61 λf, 𝑎, , The limit of resolution,, Δθ ≈, Resolving power of telescope =, , 0.61 λ, 𝑎, , 𝒂, 𝟎.𝟔𝟏 𝛌, , This implies that the telescope will have better resolving power if a is large., It is for this reason that for better resolution, a telescope must have a large, diameter objective., , Resolving power of microscope, , The minimum separation,, dmin=, , 1.22 λf, 𝐷, , 𝐷, , but =2 tan β, 𝑓, , dmin=, , 1.22 λ, 2 tan β

Page 161 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , For small β , tan β ≈sin β, dmin=, , 1.22 λ, 2 sin β, , If the medium between the object and the objective lens is not air but a, medium of refractive index n,, 1.22 λ, dmin=, 2 nsin β, , Resolving power of microscope=, , 𝟐 𝐧 𝐬𝐢𝐧 𝛃, 𝟏.𝟐𝟐 𝛌, , n sinβ is called the numerical aperture, The resolving power can be increased by choosing a medium of higher, refractive index. Usually an oil having a refractive index close to that of the, objective glass is used. Such an arrangement is called an ‘oil immersion, objective’. It is not possible to make sinβ larger than unity. Thus,the, resolving power of a microscope is basically determined by the wavelength, of the light used., , Polarisation, A wave propagating in x direction in a horizontally string ,with, displacement in y direction can be represented as, y (x,t) = a sin (kx – ωt), It is referred to as a y-polarised wave., Since each point on the string moves on a straight line, the wave is also, referred to as a linearly polarised wave., As the string always remains confined to the x-y plane , it is also referred to, as a plane polarised wave., , Polarisation of Light, Unpolarised Light, For an unpolarised light the vibrations of electric vector takes all possible, directions in the transverse plane. Natural light, e.g., from the sun is, unpolarised., , Plane Polarised Light, For a plane polarised light the vibrations of electric field vector are, restricted in one direction .

Page 162 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Polaroids, Polaroids are thin plastic like sheets, which consists of long chain molecules, aligned in a particular direction. The electric vectors along the direction of, the aligned molecules get absorbed. Thus, if an unpolarised light wave is, incident on a polaroid ,it transmits only one component of electric field, vectors which are parallel to its pass axis and the resulting light is c linearly, polarised or plane polarised., Polaroids are used in sunglasses, wind screens in trains and aeroplanes, in, 3D cameras., , Polarisation, The phenomenon of restricting the electric field vibrations of light to one, plane is called polarisation., , Malus’ Law, When an unpolarised light is passed through two polaroids P1 and P2 and if, the angle between the polaroids is varied from 0º to 90º, the intensity of the, transmitted light will vary as:, I = 𝐈𝟎 𝐜𝐨𝐬 𝟐 𝛉, where I0 is the intensity of the polarized light after passing through P1 . This, is known as Malus’ law., , Polarisation by scattering

Page 163 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , When a scattered light is observed in a direction perpendicular to the, direction of incidence, it is found to be plane polarised., The scattering of light by molecules was intensively investigated by C.V., Raman and his collaborators in Kolkata in the 1920s. Raman was awarded, the Nobel Prize for Physics in 1930 for this work., , Polarisation by reflection, , When a ray of light incident at Brewster’s angle iB , on the boundary, between two transparent media, the reflected light is plane polarised and, also the refracted are reflected rays are perpendicular to each other., Brewster’s angle iB is also called the angle of polarisation, , Brewster’s law, Brewster’s law states that the tangent of the Brewster’s angle is equal to the, refractive index of the medium., 𝒏 = 𝒕𝒂𝒏 𝐢𝐁, Proof, , At Brewster’s angle,, , By Snell’s law, , i= 𝐢𝐁, r + 𝐢𝐁 = 𝟗𝟎, r =90 - 𝐢𝐁, 𝒔𝒊𝒏𝐢𝐁, 𝒏=, 𝒏=, , 𝐬𝐢𝐧 (𝟗𝟎 − 𝐢𝐁 ), 𝒔𝒊𝒏𝐢𝐁, , 𝐜𝐨𝐬 𝐢𝐁, , 𝒏 = 𝒕𝒂𝒏 𝐢𝐁

Page 165 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 11, Dual Nature of Radiation and Matter, Introduction, ▪ It was found that at low pressure ,when an electric field is applied to, the gas in the discharge tube, a fluorescent glow appeared on the glass, opposite to cathode. These cathode rays were discovered, in 1870, by, William Crookes who later, in 1879, suggested that these rays, consisted of streams of fast moving negatively charged particles., ▪ By applying mutually perpendicular electric and magnetic fields across, the discharge tube, J. J. Thomson determined experimentally the, speed and the specific charge [charge to mass ratio (e/m)] of the, cathode ray., ▪ In 1887, it was found that certain metals, when irradiated by, ultraviolet light, emitted negatively charged particles having small, speeds. Also, certain metals when heated to a high temperature were, found to emit negatively charged particles. The value of e/m of these, particles was found to be the same as that for cathode ray particles., These observations thus established that all these particles, although, produced under different conditions, were identical in nature. J. J. Thomson,, in 1897, named these particles as electrons, and suggested that they were, fundamental, universal constituents of matter.In 1913, the American, physicist R. A. Millikan performed oil-drop experiment and measured the, charge of electron as 1.602 × 10–19 C. Millikan’s experiment established that, electric charge is quantised., , Electron emission, If an electron attempts to come out of the metal, the metal surface acquires a, positive charge and pulls the electron back to the metal. The electron can, come out of the metal surface only if it has got sufficient energy to overcome, the attractive pull., , Work Function, The minimum energy required to eject an electron from the metal, surface is called work function. The work function is denoted by ϕ0 ., ▪ Work function is measured in electron volt (eV)., ▪ ϕ0 depends on properties of metal and nature of its surface.

Page 166 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ One electron volt is the energy gained by an electron when it has been, accelerated by a potential difference of 1 volt., 1 eV = 1.602 ×10–19 J., , The work function of platinum is the highest (ϕ0 = 5.65 eV) while it is the, lowest (ϕ0 = 2.14 eV) for caesium., The minimum energy required for the electron emission from the metal, surface can be supplied to the free electrons by any one of the following, physical processes:, , (i)Thermionic emission, By suitably heating, the free electrons will get sufficient thermal energy to, escape from the metal surface., , (ii)Field Emission, By applying a very strong electric field (of the order of 108 V/m) to a metal,, electrons will get sufficient energy to escape from the metal, as in a spark, plug., , (iii) Photo-electric emission, When light of suitable frequency incident on a metal surface, electrons are, emitted from the metal surface. These photo(light)-generated electrons are, called photoelectrons., , Photoelectric Effect, Hertz’s observations, The phenomenon of photoelectric emission was discovered in 1887 by, Heinrich Hertz (1857-1894)., He observed that when light falls on a metal surface, the electrons escaped, from the surface of the metal into the surrounding space.

Page 167 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Hallwachs’ and Lenard’s observations, Lenard (1862-1947) observed that when ultraviolet radiations were, allowed to fall on the emitter plate of an evacuated glass tube enclosing two, electrodes (metal plates), current flows in the circuit., Hallwachs, in 1888, connected a negatively charged zinc plate to an, electroscope and found that negatively charged particles were emitted from, the zinc plate under the action of ultraviolet light., It was found that zinc, cadmium, magnesium, etc., responded only to, ultraviolet light, having short wavelength, to cause electron emission from, the surface., However, some alkali metals such as lithium, sodium, potassium, caesium, and rubidium were sensitive even to visible light., , Photoelectric Effect, The phenomenon of emission of electrons when photosensitive substances, are illuminated by light of suitable frequency is called photoelectric effect., , Experimental Study of Photoelectric Effect, , Experimental arrangement consists of an evacuated glass/quartz tube, having a photosensitive plate C and another metal plate A. Monochromatic, light from the source S of sufficiently short wavelength passes through the, window W and falls on the photosensitive plate C (emitter). A transparent, quartz window permits ultraviolet radiation to pass through it and irradiate, the photosensitive plate C. The electrons are emitted by the plate C and are, collected by the plate A (collector), by the electric field created by the, battery. The polarity of the plates C and A can be reversed by a commutator., When the collector plate A is positive with respect to the emitter plate C, the, electrons are attracted to it. The emission of electrons causes flow of, electric current in the circuit. The photoelectric current can be increased or, decreased by varying the potential of collector plate A with respect to the

Page 168 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , emitter plate C. The intensity and frequency of the incident light can also be, varied., , 1.Effect of intensity of light on photocurrent, , When intensity of incident radiation is increased( keeping the frequency, of the incident radiation and the accelerating potential fixe), the number of, photoelectrons emitted per second increases and hence the photoelectric, current also increases., i.e., the photocurrent increases linearly with intensity of incident light., , 2.Effect of potential on photoelectric current, , When the positive potential of collector (A) is increased the photoelectric, current increases until all the electrons are collected by the collector(A)., Then the photocurrent becomes maximum and is called saturation current., Now the collector is made negative with respect to emitter C. Then the, photocurrent decreases with increases in negative potential and finally, becomes zero. The minimum negative potential of emitter plate A for which, the photocurrent stops or bocomes zero is called the cut off potential or, stopping potential (V0), At stopping potential,, Kmax = e V0, 𝟏, mvmax2 = e V0, 𝟐

Page 169 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , 3.Effect of Intensity of incident radiation on stopping potential, , The experiment is repeated with incident radiation of the same frequency, but different intensities I1, I2 and I3 (I3 > I2 > I1).When the intensity of, incident radiation is increased ,number of photo electrons emitted per, second increases and hence the the saturation current increases. But as the, kinetic energy of photoelectrons remains constant and the stopping, potential also remains constant., i.e., for a given frequency of incident radiation, the stopping potential is, independent of intensity of radiation., , 4.Effect of frequency of incident radiation on stopping potential, , The experiment is repeated at same intensity of light radiation but differenr, frequencies 𝑣1 , 𝑣2 𝑎𝑛𝑑 𝑣3 such that 𝑣1 > 𝑣2 > 𝑣3 . When the frequency of, incident radiation increases, the kinetic energy of photoelectrons increases, and hence the stopping potential also increases. But as the intensity does not, change , the saturation current will be the same for different frequencies., i.e., the stopping potential increases with increase in frequency of incident, radiation.

Page 170 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Laws of Photoelectric Effect, i.For a given photosensitive material and frequency of incident radiation,, the photoelectric current is directly proportional to the intensity of, incident light., ii.For a given photosensitive material and frequency of incident radiation,, saturation current is found to be proportional to the intensity of incident, radiation whereas the stopping potential is independent of its intensity ., iii.For a given photosensitive material, there exists a certain minimum cutoff frequency of the incident radiation, called the threshold frequency(𝑣0 ), below which no emission of photoelectrons takes place, no matter how, intense the incident light is. Above the threshold frequency, the stopping, potential or equivalently the maximum kinetic energy of the emitted, photoelectrons increases linearly with the frequency of the incident, radiation, but is independent of its intensity, iv.The photoelectric emission is an instantaneous process without any, apparent time lag., , Threshold Frequency, Threshold frequency is the minimum cut-off frequency of the incident, radiation, below which photo emission is not possible, no matter how, intense the incident light is., , Photoelectric Effect and Wave Theory of Light, The phenomena of interference, diffraction and polarisation were explained, by the wave picture of light. But the wave picture is unable to explain the, most basic features of photoelectric emission., ▪, According to the wave picture of light, the free electrons at the, surface of the metal absorb the radiant energy continuously. The, greater the intensity of radiation, the greater should be the energy, absorbed by each electron. This is contradictory to the observations of, photoelectric effect., ▪, As large number of electrons absorb energy, the energy absorbed, per electron per unit time turns out to be small. It can take hours or, more for a single electron to pick up sufficient energy to overcome the, work function and come out of the metal. This is contrast to, observation that the photoelectric emission is instantaneous.

Page 172 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , This equation shows that the graph between stopping potential 𝑉0 and, ℎ, frequency 𝑣 is a straight line with slope which is a constant independent of, 𝑒, nature of material., , From graph , slope, , 𝑽𝟎, 𝒗, , =, , 𝒉, 𝒆, , The x- intercept of this graph gives work function., The graph shows that, (i), (ii), , the stopping potential V0 varies linearly with the frequency of, incident radiation for a given photosensitive material., there exists a certain minimum cut-off frequency ν0 for which the, stopping potential is zero, , For two metals A and B these graphs metal A metal B will be parallel straight, lines

Page 173 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Particle Nature of Light –The Photon, 1) In the interaction of light with matter , light behaves as if it is made up of, particles called photon., 2) Each photon has energy, E=hν and momentum p= hν/c and speed c= 3x, 108 m/s, 3) All photons of light of a particular frequency ν, or wavelength λ, have the, same energy and momentum p, whatever the intensity of radiation may be., 4) When intensity of light is increased only the number of photons, increases, but the energy of photon is independent of intensity of light., 5) Photons are electrically neutral. They are not deflected by electric and, magnetic fields., 6) In photon-particle collision total energy and total momentum are, conserved. However, the number of photons may not be conserved in a, collision. The photon may be absorbed or a new photon may be created., , Example, Monochromatic light of frequency 6.0 ×1014 Hz is produced by a laser. The, power emitted is 2.0 ×10–3 W., (a) What is the energy of a photon in the light beam?, (b) How many photons per second, on an average, are emitted by the, source?, (a) Each photon has an energy E = h ν = 6.63 ×10–34x6.0 ×1014 Hz, = 3.98 × 10–19 J, (b), , 𝑃, , 2𝑥10−3, , 𝐸, , 3.98𝑥10−19, , N= =, , = 5 x1015photons per second, , Example, The work function of a metal is 6eV. If two photons each having energy 4 eV, strike the metal surface. Will the emission be possible? Why?, No, photo emission is not possible., Photo emission is possible only if ℎ𝑣 > 𝜙0, Here energy of incident photon is less than work function, and hence photo emission is not possible.

Page 174 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example, The work function of caesium is 2.14 eV., a) Find the threshold frequency for caesium., b) the wavelength of the incident light if the photocurrent is brought, to zero by a stopping potential of 0.60 V., 𝜙, a), 𝑣0 = 0, ℎ, 𝜙0 =2.14 eV =2.14 x1.6x10-19 J, h=6.63 x10-34Js, 𝑣0 =, b), , 2.14 𝑥1.6𝑥10−19, 6.63 𝑥10−34, , =5.16 x1014 Hz, , e V0 = ℎ𝑣 − 𝜙0, ℎ𝑣 = e V0−𝜙0, 𝑐, ℎ = e V0−𝜙0, 𝜆, , λ=, =, , hc, eV0 −ϕ0, 6.63 x10−34 x3 x108, , 1.6 x10−19 x0.6−2.14 x1.6x10−19, , =454 nm, , Wave Nature of Matter, ▪, The wave nature of light shows up in the phenomena of, interference, diffraction and polarisation. On the other hand, in, photoelectric effect and Compton effect which involve energy and, momentum transfer, radiation behaves as if it is made up of particles –, the photons., ▪, The gathering and focussing mechanism of light by the eye-lens is, well described in the wave picture. But its absorption by the rods and, cones (of the retina) requires the photon picture of light., A natural question arises: If radiation has a dual (wave-particle) nature,, might not the particles of nature (the electrons, protons, etc.) also exhibit, wave-like character?, Louis Victor de Broglie argued that moving particles of matter should, display wave-like properties under suitable conditions., As nature is symmetrical , the two basic physical entities of nature – matter, and energy, must have symmetrical character. If radiation shows dual, aspects, matter should also exhibit dual nature.

Page 175 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , de Broglie Relation -Wavelenth of matter wave, De Broglie proposed that the wave length λ associated with a particle of, momentum p is given as, 𝒉, , 𝒉, , λ = 𝒑= 𝒎𝒗 ----------(1), where m is the mass of the particle and v its speed., λ is called de Broglie wavelength., The dual aspect of matter is evident in the de Broglie relation. Here λ is a, wave attribute while the momentum p is a particle attribute. Planck’s, constant h relates the two attributes., For an electron of mass m and velocity v, 1, 𝑝2, K = m v2 =, ,, 2, 2𝑚, P2 =2mK, P=√2𝑚𝐾, , λ=, , 𝒉, √𝟐𝒎𝑲, , ------------(2), , For an electron accelerated from rest through a potential V., The kinetic energy K = e V, , λ=, , 𝒉, √𝟐𝒎𝒆𝑽, , -------------(3), , Substituting the numerical values of h, m, e,, , λ=, , 𝟏.𝟐𝟐𝟕, √𝑽, , nm -----------(4), , Why macroscopic objects in our daily life do not show wave-like properties?, The de Broglie wavelength of a ball of mass 0.12 kg moving with a speed of, 20 m s–1 is ,, ℎ, , 6.6 𝑥10−34, , λ=, =, = 2.76x10-34 nm, 𝑚𝑣, 0.12 𝑥20, This wavelength is so small that it is beyond any measurement. This is the, reason why macroscopic objects in our daily life do not show wave-like, properties. But in the sub-atomic domain, the wave character of particles is, significant and measurable., , Example, What is the de Broglie wavelength associated with an electron moving with, a speed of 5.4×106 m/s?, λ=, , ℎ, 𝑚𝑣, , =, , 6.6 𝑥10−34, 9.1 𝑥 10−31 𝑥 5.4 𝑥106, , = 0.135 nm, , This wavelength is measurable. i.e., in the sub-atomic domain, the wave, character of particles is significant and measurable.

Page 176 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example, What is the de Broglie wavelength associated with an electron, accelerated, through a potential differnece of 100 volts?, 1.227, λ=, nm, √𝑉, , =, , 1.227, √100, , nm = 0.123 nm, , The de Broglie wavelength associated with an electron in this case is of the, order of X-ray wavelengths., , Heisenberg’s uncertainty principle, The matter–wave picture incorporates the Heisenberg’s uncertainty, principle., Heisenberg’s uncertainty principle states that, it is not possible to measure, both the position and momentum of an electron (or any other particle) at, the same time exactly., 𝒉, Δx Δp ≈, 𝟐𝝅, Δx is the uncertainty in the specification of position, Δp is the uncertainty in the specification of momentum., If Δx is zero; then Δp must be infinite in order that the product is non-zero., Similarly, if Δp is zero, Δx must be infinite., Ordinarily, both Δx and Δp are non-zero such that their product is of the, ℎ, order of = ., 2𝜋, , The matter wave description of an electron with an uncertainty in position, (Δx) and an uncertainty in momentum (Δp)., (Here λ and x are not definite ), , The matter wave description of an electron with definite momentum., i.e., Δp = 0 (and Δ x → ∞., (Here λ is definite but x not definite i,e.,electron extends all over space).

Page 177 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Davisson and Germer Experiment, The wave nature of electron was first experimentally verified by Davisson, and Germer in 1927 (and independently by G P Thomson in 1928) Davisson, and Thomson shared Nobel prize for their experimental discovery of, diffraction of electrons by crystals., , ▪, A collimated beam of electron from an electron gun is allowed to, fall on a Nickel target. The intensity of scattered beam in a given, direction is measured by a movable detector., ▪, The variation of intensity of scattered electron with the angle of, scattering is obtained at different accelerating potential from 44V to, 54V .It was found that a strong peak appeared in intensity of scattered, electron for an accelerating voltage of 54V and scattering angle, 𝜃 = 500., ▪, The appearance of peak in particular direction is due to, constructive interference of electron beams scattered from different, layers of regularly spaced atoms of the crystal., ▪, From the electron diffraction measurement ,the wavelength of, matter wave was found to be 0.165nm., ▪, The de Broglie wavelength λ associated electron for 54V is, 1.227, 1.227, λ=, nm = λ =, nm =0.167nm, √𝑉, , √54, , Thus theoritical value agrees with experimentally obtained de Broglie, wavelength. DavissonGermer experiment thus confirms the wave nature of, electrons and the de Broglie relation.

Page 178 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 12, Atoms, Thomson Model of Atom- (plum pudding model), The first model of atom was proposed by J. J. Thomson in 1898., ▪ According to this model, the positive charge of the atom is uniformly, distributed throughout the volume of the atom ., ▪ The negatively charged electrons are embedded in it like seeds in a, watermelon., This model is also called plum pudding model of the atom., , Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom, Ernst Rutherford , a former research student of J. J. Thomson, proposed a, classic experiment of scattering of these α-particles by atoms to investigate, the atomic structure. The explanation of the results led to the birth of, Rutherford’s planetary model of atom (also called the nuclear model of the, atom)., , Alpha-Particle Scattering, At the suggestion of Ernst Rutherford, in 1911, H. Geiger and E. Marsden, performed scattering experiment., , Alpha-particles emitted by a 214, 83𝐵𝑖 radioactive source were collimated into a, narrow beam by passing through lead bricks. The beam was allowed to fall, on a thin foil of gold of thickness 2.1 × 10–7 m. The scattered alpha-particles, were observed through a rotatable detector consisting of zinc sulphide, screen and a microscope., , Observations, ▪ Many of the α-particles pass through the foil. It means that, they do not suffer any collisions., ▪ Only 0.14% of the incident α-particles scatter by more than 1º., ▪ About 1 in 8000 of incident α-particles deflect by more than 90º.

Page 179 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Rutherford argued that , greater part of the mass of the atom and its positive, charge were concentrated tightly at its centre. When the incoming α-particle, make a close encounter with the positive charge ,that would result in a large, deflection., , Rutherford’s nuclear model of the atom, ▪ Most of an atom is empty space., ▪ The entire positive charge and most of the mass of the atom, are concentrated in the nucleus with the electrons some, distance away., ▪ The electrons would be moving in orbits about the nucleus just, as the planets do around the sun., ▪ The size of the nucleus to be about 10–15 m to 10–14 m., ▪ The electrostatic force of attraction, between the, revolving electrons and the nucleus provides the, centripetal force to keep them in their orbits., , Impact Parameter (b), , Impact parameter is the perpendicular distance of the initial velocity vector, of the 𝛂 𝐩𝐚𝐫𝐭𝐢𝐜𝐥𝐞 from the centre of the nucleus., , Alpha-particle trajectory, The trajectory traced by an α-particle depends on the impact parameter, b of, collision., , ▪ For an α-particle close to the nucleus , impact parameter is, small and it suffers large scattering., ▪, For head on collision, the impact parameter b=0 and, α particle rebounds back ie,angle of scattering 𝜃 =1800., ▪, For large impact parameter, the angle of scattering will be, small ( 𝜃 ≈00) and such α particles go undeviated.

Page 180 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Electron orbits, The electrostatic force of attraction(Fe), between the revolving electrons and, the nucleus provides the centripetal force (Fc) to keep them in their orbits., Fc = Fe, mv2, r, , =, , 1, , e2, , 4πε0 r2, , The kinetic energy (K) of electron, 𝟏, , 𝟐, , K = 𝒎𝒗 =, 𝟐, , 𝐞𝟐, 𝟖𝛑𝛆𝟎 𝐫, , The potential energy (U) of electron, U=, , −𝐞𝟐, 𝟒𝛑𝛆𝟎 𝐫, , (The negative sign in U signifies that the electrostatic force is in the –r, direction.), Thus the total energy E of the electron in a hydrogen atom is, E = K+U, E=, , e2, 8πε0 r, , −, , −𝐞𝟐, , e2, 4πε0 r, , E = 𝟖𝛑𝛆, , 𝟎𝐫, , The total energy of the electron is negative. This implies the fact that the, electron is bound to the nucleus. If E were positive, an electron will not, follow a closed orbit around the nucleus., , Limitations of Rutherford Model, Rutherford nuclear model has two main difficulties in explaining the, structure of atom:, (a) Rutherford model could not explain stability of, matter. The accelerated electrons revolving around the, nucleus loses energy and must spiral into the nucleus., This contradicts the stability of matter., (b) It cannot explain the characteristic line spectra of atoms of, different elements., , Bohr Model of Hydrogen Atom, Niels Bohr made certain modifications in Rutherford’s model using the, ideas of quantum hypothesis. Bohr combined classical and early quantum, concepts and gave his theory in the form of three postulates.

Page 183 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Excited States, When Hydrogen atom receives energy by the process such as collisions, the, atoms may acquire sufficient energy to raise the electrons to higher energy, states. Then atom is said to be in an excited state., For first excited state (second energy level), −13.6, n =2,, E2 = 2 eV = -3.4 eV, 2, For second excited state (third energy level), −13.6, n =3 ,, E3 = 2 eV = -1.51 eV, 3, And so on.., , The energy level diagram for the hydrogen atom, , Ionisation Energy, The minimum energy required to free the electron from the ground state of, the atom is called the Ionisation energy., Ionisation energy of an atom is always positive., Ionisation energy of Hydrogen atom = E∞ - E1, = 0 – ( -13.6) eV = 13.6 eV., Ionisation energy of Hydrogen atom is 13.6 eV, The energy required to excite an electron in Hydrogen atom from ground, state to its first excited state is, 𝐄𝟐 -𝐄𝟏 = -3.6 eV – (-13.6) eV = 10.2 eV, The energy required to excite an electron in Hydrogen atom from ground, state to its second excited state is, 𝐄𝟑 -𝐄𝟏 = -1.51 eV – (-13.6) eV = 12.09 eV, And so on…

Page 184 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Atomic Spectra, Each element has a characteristic spectrum of radiation, which it emits., There are two types of spectra-Emission spectrum and Absorption, spectrum., , Emission Spectrum, When an atomic gas or vapour is excited at low pressure, by passing an, electric current through it, the emitted radiation has a spectrum which, contains certain specific wavelengths only. A spectrum of this kind is termed, as emission line spectrum and it consists of bright lines on a dark, background. Study of emission line spectra of a material is used for, identification of the gas., , Absorption Spectrum, When white light passes through a gas and we analyse the transmitted light, using a spectrometer we find some dark lines in the spectrum. These dark, lines correspond precisely to those wavelengths which were found in the, emission line spectrum of the gas. This is called the absorption spectrum of, the material of the gas., , Spectral series of Hydrogen Atom, Hydrogen is the simplest atom and therefore, has the simplest spectrum., The spacing between lines within certain sets of the hydrogen spectrum, decreases in a regular way . Each of these sets is called a spectral series. The, first series was observed Johann Jakob Balmer the visible region of the, hydrogen spectrum. This series is called Balmer series ., , The line with the longest wavelength, 656.3 nm in the red is called Hα, The line with the shortest wavelength, 364.6 nm is called 𝐻∞ .

Page 187 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , De Broglie’s Explanation of Bohr’s second postulate of Quantisation, De Broglie argued that electron in its circular orbit behaves as a particle, wave. The particle wave can produce standing wave under resonant, condition., , For 𝒏𝒕𝒉 orbit of radius 𝑟𝑛 , the resonant condition is, 2 π 𝑟𝑛 = n λ----------- (1) where n=1,2,3….., But by de Broglie hypothesis , for matter waves, 𝐡, λ = ---------------(2), 𝐦𝐯, , Substituing eqn (2) in eqn (1),, 𝐡, 2 π rn = n, 𝐧𝐡, , 𝐦𝐯, , mv 𝐫𝐧 =, where n=1,2,3……, 𝟐𝛑, This Bohr’s second postulate of Quantisation., , Limitations of Bohr Atom Model, (i), , (ii), , The Bohr model is applicable to hydrogenic atoms. It cannot be, extended two or more electron atoms. Difficulty lies in the fact that, each electron interacts not only with the positively charged nucleus, but also with all other electrons., While the Bohr’s model correctly predicts the frequencies of the, light emitted by hydrogenic atoms, the model is unable to explain, the intensity variations of the frequencies in the spectrum.

Page 188 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 13, Nuclei, Introduction, The volume of a nucleus is about 10–12 times smaller than the volume of the, atom. In other words, an atom is almost empty. If an atom is enlarged to the, size of a classroom, the nucleus would be of the size of pinhead., Nevertheless, the nucleus contains most (more than 99.9%) of the mass of, an atom., , Atomic Masses and Composition of Nucleus, The mass of an atom is very small. Kilogram is not a very convenient unit to, measure such small quantities. Therefore, a different mass unit is used for, expressing atomic masses. This unit is the atomic mass unit (u)., , Atomic Mass Unit (u), Atomic mass unit (u) is defined as 1/12th of the mass of the carbon (12C), atom., 𝐦𝐚𝐬𝐬 𝐨𝐟 𝐭𝐡𝐞 𝐨𝐧𝐞 𝐂−𝟏𝟐 𝐚𝐭𝐨𝐦, 1u =, 𝟏𝟐, 𝟏.𝟗𝟗𝟐𝟔𝟒𝟕 𝒙 𝟏𝟎−𝟐𝟔, , =, 𝟏𝟐, =1.660539 10-27 kg, Accurate measurement of atomic masses is carried out with a mass, spectrometer., , Composition of Nucleus, The composition of a nucleus can be described using the following terms, and symbols:, Z - atomic number = number of protons = number of electrons, N - neutron number = number of neutrons=A-Z, A - mass number = Z + N = total number of protons and neutrons ., Protons and neutrons are also called nucleons. Thus the number of, nucleons in an atom is its mass number A., ▪, ▪, ▪, ▪, ▪, ▪, , All the electrons of an atom are outside the nucleus., The total charge of the atomic electrons is (–Ze), The total cherge of the nucleus is (+Ze)., Atom is electrically neutral, The mass of proton , mp =1.00727 u = 1.67262 10-27 kg, The mass of neutron , mn = 1.00866 u = 1.6749×10–27 kg

Page 189 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ Neutron was discovered by James Chadwick., ▪ Chadwick was awarded the Nobel Prize in Physics in 1935 for his, discovery of the neutron., , Isotopes, Isotpes are different types of atoms of the same element, with same atomic, number ,but different mass number .They exhibit the same chemical, properties, but differ in mass., ▪ Chlorine has two isotopes having masses 34.98 u and 36.98 u. The, relative abundances of these isotopes are 75.4 and 24.6 per cent,, respectively. Thus, the average mass of a chlorine atom is obtained by, the weighted average of the masses of the two isotopes, which works, out to be, 75.4 x34.98+ 24.6x 36.98, =, 𝟏𝟎𝟎, = 35.47 u, which agrees with the atomic mass of chlorine., ▪ The lightest element, hydrogen has three isotopes ,, Proton( 11H), - contains one proton only, 2, Deuterium( 1H) - contains one proton and one neutron., Tritium( 31H), - contains one proton and two neutrons., Tritium nuclei, being unstable, do not occur naturally and, are produced artficially in laboratories., ▪ The element gold has 32 isotopes, ranging from, A =173 to A = 204., , Isobars, All nuclides with same mass number A , but with different atomic number, are called isobars., For example, the nuclides ( 31H) and ( 32He)are isobars., , Isotones, Nuclides with same neutron number N but different atomic number Z are, called isotones., 197, For example 198, 80Hg 79Au are isotones., , Size of The Nucleus, By performing scattering experiments in which fast electrons, instead of αparticles, are projectiles that bombard targets made up of various elements,, the sizes of nuclei of various elements have been accurately measured.

Page 190 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Radius of nucleus, A nucleus of mass number A has a radius, R = R0 A1/3, where R0 = 1.2 × 10–15 m., , Volume of nucleus, 4, , V= πR3, =, , 3, 4, , 𝟏⁄ 𝟑, π (𝐑 𝟎 𝐀 𝟑 ), , 3, 4, , = π(𝐑 𝟎 )𝟑 𝐀, 3, The volume of the nucleus is proportional to A, , Density of nucleus, Nuclear density=, , mass, volume, Amp, , =4, , π(𝐑 𝟎 )𝟑 𝐀, mp, , 3, , =4, , π(𝐑 𝟎 )𝟑, 3, , = constant, , Thus the density of nucleus is a constant, independent of A, for all nuclei., , Example, Given the mass of iron nucleus as 55.85u and A=56, find the nuclear, density?, mFe = 55.85 u = 9.27 × 10–26 kg, m, Nuclear density =4 Fe 𝟑, 𝜋(𝐑 𝟎 ) 𝑨, 9.27 × 10–26, , 3, , =4, , 𝜋(1.2 × 10–15 )𝟑 𝒙 𝟓𝟔, , 3, , = 2.29 × 1017 kg m–3, , Mass – Energy, Einstein showed that mass is another form of energy and one can convert, mass-energy into other forms of energy, say kinetic energy and vice-versa., Einstein gave the famous mass-energy equivalence relation, , E = mc 2, c is the velocity of light in vacuum.c= 3×108 m s–1., Experimental verification of the Einstein’s mass-energy relation has been, achieved in the study of nuclear reactions. In a reaction the conservation law, of energy states that the initial energy and the final energy are equal, provided the energy associated with mass is also included.

Page 191 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example, Calculate the energy equivalent of 1 g of substance., E = mc 2, = 1x10–3 × ( 3 × 108 ) 2, = 10–3 × 9 × 1016, = 9 × 1013 J, Thus, if one gram of matter is converted to energy, there is a release of, enormous amount of energy., , Example, Find the energy equivalent of one atomic mass unit, first in Joules and then, in MeV., 1u = 1.6605 × 10–27 kg, E = mc 2, =1.6605 × 10–27 x(3 x 108)2, E = 1.4924 × 10–10 J, Energy equivalent in MeV., 1eV = 1.602 x10-19J, 1.4924 × 10–10, E=, 1.602 x10−19, = 0.9315 × 109 eV, = 931.5 MeV, , Mass Defect and Binding Energy, Mass Defect (ΔM), The nucleus is made up of neutrons and protons. Therefore it may be, expected that the mass of the nucleus is equal to the total mass of its, individual protons and neutrons., The nuclear mass M is always less than the total mass, of its constituents, (protons and neutrons). The difference in mass of a nucleus and its, constituents is called the mass defect., ΔM = [𝐙 𝐦𝐩 + (𝐀 − 𝐙)𝐦𝐧 ] − 𝐌, For example, let us consider 168O ; a nucleus which has 8 neutrons and 8, protons., Mass of 8 neutrons = 8 × 1.00866 u, Mass of 8 protons = 8 × 1.00727 u, The expected mass of 168O nucleus = 16.12744 u, The atomic mass of 168O from mass spectroscopy experiments= 15.99493 u

Page 192 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Substracting the mass of 8 electrons (8 × 0.00055 u), The mass of 168O nucleus =15.99493 u -(8 × 0.00055 u)= 15.99053 u, , Mass defect ΔM =16.12744 -15.99053 u, = 0.13691u, , Binding Energy, The energy equivalent of mass defect is called binding energy., Eb = Δ Mc2, ▪ If we separate a nucleus into its nucleons, we would have to supply a, total energy equal to Eb, to those particles., ▪ If a certain number of neutrons and protons are brought together to, form a nucleus of a certain charge and mass, an energy Eb will be, released ., , Binding Energy Per Nucleon, A more useful measure of the binding between the constituents of the, nucleus is the binding energy per nucleon, Ebn,, The binding energy per nucleon, Ebn, is the ratio of the binding energy Eb of, a nucleus to the number of the nucleons, A, in that nucleus., , Ebn = Eb / A, It is the average energy per nucleon needed to separate a nucleus into its, individual nucleons., , The plot of binding energy per nucleon versus mass number, , Observations:, (i), , In the mass number range A = 30 to 170 ( 30 < A < 170), the, binding energy per nucleon is nearly constant, about 8, MeV/nucleon., (ii) The maximum of about 8.75 MeV for A = 56 I,e,.for 56Fe nucleus., (iii) Ebn is lower for both light nuclei with A< 30 and for heavy nuclei, with A>170.

Page 193 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , We can draw some conclusions from these two observations:, (i), , The nuclear force is attractive and sufficiently strong to produce a, binding energy of a few MeV per nucleon., (ii) The constancy of the binding energy in the range 30 < A < 170, indicates that the nuclear force is short-ranged. A nucleon influences, only nucleons close to it and this property is called saturation property, of the nuclear force., (iii) A very heavy nucleus, say A = 240, has lower binding energy per, nucleon .Such a heavy nucleus breaks into two lighter nuclei, thereby, increasing the binding energy per nucleon and the nucleons get more, tightly bound. Energy would be released in the process and this is an, implication of through fission., (iv) Two very light nuclei (A ≤ 10) have lower binding energy per nucleon, .They join to form a heavier nucleus , thereby increasing the binding, energy per nucleon and the nucleons get more tightly bound. Energy, would be released in such a process and this is an implication of, through of fusion., , Nuclear Force, The nuclear force binds the nucleons together inside the nucleus., (i), The nuclear force is much stronger than the Coulomb repulsive, force between protons inside the nucleus and the gravitational, force between the masses., (ii), The nuclear force between two nucleons falls rapidly to zero as, their distance is more than a few femtometres. The force is, attractive for distances larger than 0.8 fm and repulsive if they are, separated by distances less than 0.8 fm., , A rough plot of the potential energy between, two nucleons as a function of distance. The, potential energy is a minimum at a distance r0, of about 0.8 fm., , (iii), , The nuclear force between neutron-neutron, proton-neutron and, proton-proton is approximately the same. The nuclear force does, not depend on the electric charge.

Page 194 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Radioactivity, A .H. Becquerel discovered radioactivity in 1896. Radioactivity is a nuclear, phenomenon in which an unstable nucleus undergoes a decay.This is, referred to as radioactive decay., Three types of radioactive decay occur in nature :, α-decay in which a helium nucleus (He) is emitted;, β-decay in which electrons or positrons (particles with the same mass as, electrons, but with a charge exactly opposite to that of electron) are emitted;, γ-decay in which high energy (hundreds of keV or more) photons are, emitted., , Law of radioactive decay, This law states that the number of nuclei undergoing the decay per unit time, is proportional to the total number of nuclei in the sample., If N is the number of nuclei in the sample and ΔN undergo decay in time Δt, then, dN, = −λN, dt, dN, , = −λdt, Now, integrating both sides of the above equation,we get,, dN, ∫, = −λ∫ dt, N, ln N − ln N0 = −λ (t – t 0 ), Here N0 is the number of radioactive nuclei in the sample at time t 0 and N is, the number of radioactive nuclei at any subsequent time t. Setting t 0 =0, N, ln = −λt, N, , N0, , Taking exponential on both sides, N, = e−λt, N0, , N =𝐍𝟎 𝐞−𝛌𝐭, , Decay Rate, Decay rate is the number of nuclei decaying per unit time., dN, R =R =-, , dt, d, , dt, , N0 e−λt, , R = λN0 e−λt, , R = 𝐑 𝟎 𝐞−𝛌𝐭 where R 0 = λN

Page 195 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The total decay rate R of a sample of one or more radionuclides is called the, activity of that sample., The SI unit for activity is becquerel., 1 becquerel = 1Bq = 1 decay per second, An older unit is curie., 1 curie = 1 Ci = 3.7 × 𝟏𝟎𝟏𝟎 Bq (decays per second), , Half-life ( 𝑻𝟏⁄ ), 𝟐, , Half-life is the time at which the number of radioactive nuclei reduce to, half of their initial value., N = N0 e−λt, At, , t = T1⁄ ,, 2, , N0, 2, 1, 2, , N0, , N=, , = N0 e, =e, , 2, , −λ T1⁄, , 2, , −λ T1⁄, , 2, , ln 2 = λ T1⁄, , 2, , T1⁄ =, 2, , 𝐓𝟏⁄ =, 𝟐, , ln 2, λ, , 𝟎.𝟔𝟗𝟑, 𝛌, , Mean life τ, mean life τ, is the time at which the number of radioactive nuclei reduces to, 𝑒 −1 of their initial value., , τ=, T1⁄ =, 2, , 𝟏, 𝝀, , 0.693, λ, , =0.693 τ, , 𝐓𝟏⁄ =0.693 τ, 𝟐, , Example, Tritium has a half-life of 12.5 y undergoing beta decay. What fraction of a, sample of pure tritium will remain undecayed after 25 y., By definition of half-life, half of the initial sample will remain undecayed, after 12.5 y. In the next 12.5 y, one-half of these nuclei would have decayed., Hence, one fourth of the sample of the initial pure tritium will remain, undecayed.

Page 196 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Alpha decay, When a nucleus undergoes alpha-decay, it transforms to a different nucleus, by emitting an alpha-particle (a helium nucleus ( 42𝐻𝑒), Atomic number decreases by 2 and mass number decreases by 4., 𝐀, 𝐙𝐗, , →, , 𝐀−𝟒, 𝐙−𝟐𝐘, , + 𝟒𝟐𝐇𝐞, , 𝟐𝟑𝟖, 𝟗𝟐𝐔, , →, , 𝟐𝟑𝟒, 𝟗𝟎𝐓𝐡, , + 𝟒𝟐𝐇𝐞, , The difference between the initial mass energy and the final mass energy of, the decay products is called the Q value of the process or the disintegration, energy. Thus, the Q value of an alpha decay can be expressed as, , Q=(mX – mY - mHe)c2, Beta decay, A nucleus that decays spontaneously by emitting an electron or a positron is, said to undergo beta decay., , Beta minus (β− ) decay, In beta minus (β− ) decay, an electron o is emitted by the nucleus., In beta-minus decay, a neutron transforms into a proton inside the nucleus., , ̅, n→ p+𝒆− + 𝒗, Atomic number increases by 1 and mass number remains same., 𝟑𝟐, 𝟏𝟓𝐏, , →, , 𝟑𝟐, −, 𝟏𝟔𝐒+𝒆, , ̅, +𝒗, , Beta plus (β + ) decay, In beta plus (β + ) decay, a positron is emitted by the nucleus., In beta-plus decay, a proton transforms into neutron inside the nucleus., , p→ n+𝒆+ + 𝒗, Atomic number decreases by 1 and mass number remains same., 𝟐𝟐, 𝟏𝟏𝐍𝐚, , →, , +, 𝟐𝟐, 𝟏𝟎𝐍𝐞+𝒆, , +𝒗, , Gamma decay, When a nucleus is in an excited state, it can make a transition to a lower, energy state by the emission of electromagnetic radiation. As the energy, differences between levels in a nucleus are of the order of MeV, the photons, emitted by the nuclei have MeV energies and are called gamma rays.

Page 197 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Energy level diagram showing the emission of γ rays by a 𝟔𝟎, 𝟐𝟕𝑪𝒐 nucleus, subsequent to beta decay., , Example, The radioactive isotope D decays according to the sequence,, D, β−, D1, α, D2, If the mass number and atomic number of D2 are176 and 71respectively,, what is the mass number and atomic number of D., 180, 72D, , β−, , 180, 73D1, , α, , 176, 71D2, , mass number of D =180, atomic nimber of D =72, , Nuclear Energy, Energy then can be released if less tightly bound nuclei are transmuted into, more tightly bound nuclei. Two such processes, are fission and fusion., For the same quantity of matter, nuclear sources will give a million times, larger energy than conventional sources. One kilogram of coal on burning, gives 107 J of energy, whereas 1 kg of uranium, which undergoes fission, will, generate on fission 1014 J of energy., , Nuclear Fission, Nuclear fission is the process in which a heavier nucleus splits into lighter, nuclei with the release of large amount of energy., When a neutron was bombarded on a uranium target, the uranium nucleus, broke into two nearly equal fragments releasing great amount of energy., Example

Page 198 : Join Telegram Channel: https://t.me/hsslive, , 𝟏, 𝟎𝐧, , + 𝟐𝟑𝟓, 𝟗𝟐𝐔, , 𝟐𝟑𝟔, 𝟗𝟐𝐔, , →, , Downloaded from www.Hsslive.in ®, , →, , 𝟏𝟒𝟒, 𝟓𝟔𝐁𝐚, , +, , 𝟖𝟗, 𝟑𝟔𝐊𝐫 +, , 𝟑 𝟏𝟎𝐧, , Fission does not always produce barium and krypton. A different pair can be, produced,, 235, 1, 0n + 92U, , →, , 236, 92U, , →, , 133, 51Sb, , 99, + 41, Nb + 4 10n, , 235, 1, 0n + 92U, , →, , 236, 92U, , →, , 140, 54Xe, , 94, + 38, Sr + 2 10n, , The energy released (the Q value ) in the fission reaction of nuclei like, uranium is of the order of 200 MeV per fissioning nucleus., The enormous energy released in an atom bomb comes from uncontrolled, nuclear fission., , Nuclear reactor, The fact that more neutrons are produced in fission than are consumed, gives the possibility of a chain reaction with each neutron that is produced, triggering another fission. Enrico Fermi first suggested such a possibility in, 1939., The chain reaction is uncontrolled and rapid in a nuclear bomb explosion., The chain reaction is controlled and steady in a nuclear reactor. In a reactor,, the value of the neutron multiplication factor k is maintained at 1., Multiplication factor, Multiplication factor is the ratio of number of fission produced by a given, generation of neutrons to the number of fission of the preceding generation., If K becomes greater than one, the reaction rate and the reactor power, increases exponentially. Unless the factor K is brought down very close to, unity, the reactor will become supercritical and can even explode., , Fuel, 92, The abundant 238, U isotope, which does not fission, on capturing a neutron, leads to the formation of plutonium., 238, 92U, , +n→, , 239, 93Np, , →, , 239, 92U, , →, , 239, 93Np, , 239, −, 94Pu + e, , + e− + ν̅, , + ν̅, , Plutonium is highly radioactive and can also undergo fission under, bombardment by slow neutrons.

Page 199 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Moderators, slow neutrons have a much higher intrinsic probability of inducing fission in, 235, 92𝑈 → than fast neutrons., Therefore, in reactors, light nuclei called moderators are provided along, with the fissionable nuclei for slowing down fast neutrons. The moderators, commonly used are water, heavy water (D2O) and graphite., , Control Rods, The reaction rate is controlled through control-rods made out of neutronabsorbing material such as cadmium. In addition to control rods, reactors, are provided with safety rods which, when required, can be inserted into the, reactor and K can be reduced rapidly to less than unity., , Coolent, In pressurised-water reactor , water is used both as the moderator and as, the heat transfer medium., Water is circulated through the reactor vessel and transfers energy at high, temperature and pressure to the steam generator. In the steam generator,, evaporation provides high-pressure steam to operate the turbine that drives, the electric generator. The low-pressure steam from the turbine is cooled, and condensed to water and forced back into the steam generator., , Simplified outlines of a nuclear power plant., , The problem encountered with the nuclear power station is that the spent, fuel is highly radioactive and extremely hazardous to all forms of life on, earth. Elaborate safety measures, both for reactor operation as well as, handling and reprocessing the spent fuel, are required.

Page 200 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Nuclear Fusion – Energy Generation in Stars, Nuclear fusion is the process in which two light nuclei combine to form a, single larger nucleus, with the release of a large amount of energy. Examples, are, 1, 1, 2, +, 1H + 1H → 1H + e + ν + 0.42 MeV, 2, 1H, , + 21H → 23He + n + 3.27 MeV, , 2, 1H, , + 21H → 31H + 11H + 4.03 MeV, , Thermonuclear fusion, For nuclear fusion to occur in bulk matter the temperature of the material is, to be raised until the particles have enough energy to penetrate the, coulomb barrier. This process is called thermonuclear fusion., for thermonuclear fusion to take place, extreme conditions of temperature, and pressure are required, which are available only in the interiors of stars, including sun., The energy generation in stars takes place via thermonuclear fusion., The fusion reaction in the sun is a multi-step process called the protonproton (p, p) cycle., 1, 1H, , + 11H → 21H + e+ + ν + 0.42 MeV, , e+ + e− → γ + γ + 1.02 MeV, 2, 1H, , + 11H → 23He + γ + 5.49 MeV, , 3, 2H, , + 32H → 42He + 11H + 11H + 12.86 MeV, , The combined reaction is, 4 11H + 2 e− → 42He + 2ν + 6γ + 26.7 MeV, Or (4 11H + 4 e− ) → ( 42He + 2e− ) + 2ν + 6γ + 26.7 MeV, Thus, four hydrogen atoms combine to form an 4 2He atom with a release of, 26.7 MeV of energy., In about 5 billion years, however, the sun’s core, which by that time will be, largely helium, will begin to cool and the sun will start to collapse under its, own gravity. This will raise the core temperature and cause the outer, envelope to expand, turning the sun into what is called a red giant.

Page 201 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Chapter 14, Semiconductor Electronics:, Materials, Devices and Simple Circuits Introduction, Semiconductors are the basic materials used in the present solid state, electronic devices like diode, transistor, ICs, etc. Lattice structure and the, atomic structure of constituent elements decide whether a particular, material will be insulator, metal or semiconductor., , Classification of Metals, Conductors and Semiconductors, On the basis of conductivity:, On the basis of the relative values of electrical conductivity (σ) or resistivity, (ρ = 1/σ ), the solids are broadly classified as:, (i), , Metals: They possess very low resistivity (or high conductivity)., ρ ~ 10–2 – 10–8 Ω m, σ ~ 102 – 108 S m–1, (ii) Semiconductors: They have resistivity or conductivity intermediate, to metals and insulators., ρ ~ 10–5 – 106 Ω m, σ ~ 105 – 10–6 S m–1, (iii) Insulators: They have high resistivity (or low conductivity)., ρ ~ 1011 – 1019 Ω m, σ ~ 10–11 – 10–19 S m–1, Semiconductors which could be:, (i) Elemental semiconductors: Si and Ge, (ii) Compound semiconductors: Examples are:, • Inorganic: CdS, GaAs, CdSe, InP, etc., • Organic: anthracene, doped pthalocyanines, etc., • Organic polymers: polypyrrole, polyaniline, polythiophene, etc., Most of the currently available semiconductor devices are based on, elemental semiconductors Si or Ge and compound inorganic semiconductors., , Energy Bands In Solids

Page 202 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ Inside the crystal each electron will have a different energy level., These different energy levels with continuous energy variation form, energy bands., ▪ The energy band which includes the energy levels of the valence, electrons is called the valence band., ▪ The energy band which includes the energy levels of conduction, electrons is called the conduction band., ▪ The conduction band is above the valence band .Normally the, conduction band is empty and valence band is occupied., ▪ The gap between the top of the valence band and bottom of the, conduction band is called the energy band gap (Energy gap Eg )., It is measured in electron volt., , Classification of Metals, Conductors and Semiconductors, On the basis of energy bands, (i) metals, , In some metals, the conduction band is partially filled and the valence band, is partially empty with small energy gap and in some others the conduction, and valance bands overlap. When there is overlap electrons from valence band, can easily move into the conduction band. Therefore, the resistance of such, materials is low or the conductivity is high., (ii)Insulators

Page 203 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , In insulators a large band gap , Eg > 3 eV. There are no electrons in the, conduction band, and therefore no electrical conduction is possible. The, energy gap is so large that electrons cannot be excited from the valence band, to the conduction band by thermal excitation., (iii)Semiconductors, , In semiconductors a finite but small band gap (Eg < 3 eV) exists. Because of, the small band gap, at room temperature some electrons from valence band, can acquire enough energy to cross the energy gap and enter the conduction, band. These electrons (though small in numbers) can move in the, conduction band. Hence, the resistance of semiconductors is lower than that, of insulators., When the electrons from valence band move to the conduction band vacant, energy levels will be created in the valence band . This vacancy of electrons, is called hole. Other valence electrons can move to this hole thereby, producing hole current., , Intrinsic Semiconductor, Pure semiconductors are called ‘intrinsic semiconductors’., Si and Ge have four valence electrons. In a pure Si or Ge crystal ,each atom, make covalent bond with four neighbouring atoms and share the four, valence electrons.

Page 204 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , As the temperature increases, these electrons get more thermal energy ,, break–away the covalent bonds and become free electrons contributing to, conduction. These free electrons (with charge –q) leaves a vacancy with an, effective charge (+q ). This vacancy with the effective positive electronic, charge is called a hole., In intrinsic semiconductors, the number of free electrons, ne is equal to the, number of holes, nh., ne = nh = ni, where ni is called intrinsic carrier concentration., , The free electrons move as conduction electron and gives rise to an electron, current, Ie under an applied electric field. Under the action of an electric, field, the holes move towards negative potential giving the hole current, Ih., The total current, I is thus the sum of the electron current Ie and the hole, current Ih:, I = Ie + Ih, Energy-Band Diagram of an Intrinsic Semiconductor at T=0K, An intrinsic semiconductor will behave like an insulator at T = 0 K ., , Energy-Band Diagram of an Intrinsic Semiconductor at T > 0K

Page 205 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , At temperatures (T > 0K), some electrons are excited from the valence, band to the conduction band, leaving equal number of holes there., , Extrinsic Semiconductor, When a small amount of a suitable impurity is added to the pure, semiconductor, the conductivity of the semiconductor is increased . Such, materials are known as extrinsic semiconductors or impurity, semiconductors., The deliberate addition of a desirable impurity is called doping and the, impurity atoms are called dopants. Such a material is also called a doped, semiconductor., There are two types of dopants used in doping Si or Ge:, (i)Pentavalent (valency 5), Eg: Arsenic (As), Antimony (Sb), Phosphorous (P), etc., (ii)Trivalent (valency 3), Eg: Indium (In), Boron (B), Aluminium (A𝒍), etc., Depending on the type of impurities added, there are two types of, semiconductors –, (i) n-type semiconductor, (ii) p-type semiconductor, , n-type semiconductor, n-type semiconductor is obtained by doping Si or Ge with pentavalent atoms, (donors) like As, Sb, P, etc. The four valence electrons of pendavalent, impurity atom bond with the four silicon neighbours ,while the fifth one is, free to move in the lattice of the semiconductor ,at room temperature. Thus,, the pentavalent dopant is donating one extra electron for conduction and, hence is known as donor impurity., For n-type semiconductors, ne >> nh, Here electrons become the majority carriers and holes the minority carriers., The electron and hole concentration in a semiconductor in thermal, equilibrium is given by

Page 206 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ni 2, , nenh =, Energy bands of n-type semiconductor at T > 0K, , For n-type Si semiconductor ,the donor energy level ED ,is slightly below the, bottom EC of the conduction band .The electrons from this level move into, the conduction band with very small supply of energy., , p-type semiconductor, p-type semiconductor is obtained when Si or Ge is doped with a trivalent, impurity like A𝑙, B, In, etc. The dopant has only 3 valence electrons and can, form covalent bonds with neighbouring three Si atoms but does not have, any electron to offer to the fourth Si atom. This vacancy of electron creates a, hole. As the pendavalent impurities creates holes ,which can accept, electrons from neighbouring atom, these impurities are called acceptor, impurities., For p-type semiconductors, nh >> ne, Here holes become the majority carriers and electrons the minority carriers., The electron and hole concentration in a semiconductor in thermal, equilibrium is given by, nenh = ni 2, Energy bands of p-type semiconductor at T > 0K, , For p-type semiconductor, the acceptor energy level EA is slightly above the, top EV of the valence band . With very small supply of energy an electron, from the valence band can jump to the level EA and ionise the acceptor ., negatively.

Page 207 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , p-n junction, , A p-n junction can be formed by adding a small quantity of, pendavalent impurity to a p-type semiconductor or by adding a small, quantity of trivalent impurity to an n-type semiconductor., Two important processes occur during the formation of a p-n junction:, diffusion and drift., , 1.Diffusion, The holes diffuse from p-side to n-side (p → n) and electrons diffuse from nside to p-side (n → p). This motion of charge carriers give rise to Diffusion, current across the junction., Due to diffusion, a layer of positive charge (or positive space-charge region), is developed on n-side of the junction and a layer of negative charge (or, negative space-charge region) is developed on the p-side of the junction ., Depletion region (Depletion layer), The space-charge region on either side of the junction together is known as, depletion region. The depletion layer consist of immobile ion-cores and no, free electrons or holes. This is responsible for a junction potential barrier., , 2.Drift, The positive charge on n-side of the junction and negative charge on p-side, of the junction develops an electric field. Due to this field, an, electron(minority carrier) on p-side of the junction moves to n-side and a, hole(minority carrier) on n- side of the junction moves to p-side. The motion, of charge carriers due to the electric field is called drift., Initially, diffusion current is large and drift current is small. As the diffusion, process continues, the electric field strength increases and hence drift, current also increases. This process continues until the diffusion current, equals the drift current.. Thus in a p-n junction under equilibrium there is no, net current., .

Page 208 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Barrier Potential, , The loss of electrons from the n-region and the gain of electron by the pregion causes a difference of potential across the junction of the two regions., Since this potential tends to prevent the movement of electron from the n, region into the p region, it is often called a barrier potential., The barrier potential of a Ge diode is 0.2Vand that of a Si diode is 0.7V., , Semiconductor Diode, , A semiconductor diode is basically a p-n junction with metallic contacts, provided at the ends for the application of an external voltage. It is a two, terminal device., Symbol of a p-n junction Diode, , p-n junction diode under forward bias

Page 209 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , If p-side of the diode is connected to the positive terminal and n-side to the, negative terminal of the battery, it is said to be forward biased., ▪ The direction of the applied voltage (V ) is opposite to barrier potential, V0. As a result, the depletion layer width decreases and the barrier, height is reduced., ▪ The effective barrier height under forward bias is (V0 – V )., ▪ At high applied voltage, electrons from n-side cross the depletion, region and reach p-side . Similarly, holes from p-side cross the junction, and reach the n-side., ▪ This motion of majority carriers on either side gives rise to diffusion, current., ▪ The magnitude of this current is usually in mA., , p-n junction diode under reverse bias, , If n-side of the diode is connected to the positive terminal and p-side to the, negative terminal of the battery, it is said to be reverse biased., ▪ The direction of the applied voltage (V ) is same as barrier potential V0., As a result, the depletion layer width increases and the barrier height is, incresaed., ▪ The effective barrier height under reverse bias is (V0 + V )., ▪ The flow of electrons from n → p and holes from p → n is suppressed., Thus, diffusion current, decreases enormously compared to the diode, under forward bias., ▪ The electricfield of the junction is such that the minority carriers are, drifted to majority zone which gives rise to drift current., ▪ The drift current is of the order of a few μA.

Page 210 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , V-I characteristics of a silicon diode., , ▪ In forward bias, the current first increases very slowly, till the voltage, across the diode crosses a certain value. . This voltage is called the, threshold voltage or cut-in voltage (0.2V for germanium diode and 0.7, V for silicon diode)., ▪ After threshold voltage, the diode current increases significantly , even, for a very small increase in the diode bias voltage., ▪ For the diode in reverse bias, the current is very small (~μA) and, almost remains constant with change in bias. It is called reverse, saturation current. However, at very high reverse bias called break, down voltage Vbr, the current suddenly increases. The general purpose, diode are not used beyond the reverse saturation current region., Threshold Voltage, The forward voltage beyond which the diode current increases significantly, is called threshold voltage or cut-in voltage., Break down Voltage, The reverse voltage at which the reverse current increases suddenly is, called break down voltage., , Dynamic Resistance(rd), Dynamic resistance is defined as the ratio of small change in voltage ΔV to a, small change in current ΔI., 𝚫𝐕, rd =, 𝚫𝐈

Page 211 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Example, The V-I characteristic of a silicon diode is shown in the Figure. Calculate the, resistance of the diode at (a) ID = 15 mA and (b) VD = –10 V., , (a) From the curve, at I = 20 mA, V = 0.8 V, I = 10 mA, V = 0.7 V, ΔV, 0.1, rforwrd bias = =, = 10 Ω, ΔI, 10x10−3, (b) From the curve at V = –10 V, I = –1 μA,, 10, 7, rreverse bias =, −6 = 1.0 × 10 Ω, 1x10, , Application of Junction Diode as a Rectifier, The diode allows current to pass only when it is forward biased., If an alternating voltage is applied across a diode the current flows only in, that part of the cycle when the diode is forward biased. This property is, used to rectify alternating voltages ., , Rectifier, The process of conversion of ac voltage to dc voltage is called rectification, and the circuit used for rectification is called rectifier., , Half wave Rectifier

Page 212 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , In the positive half-cycle of ac there is a current through the load resistor 𝑅𝐿, and we get an output voltage, whereas there is no current in the negative, half cycle. Since the rectified output of this circuit is only for half of the input, ac wave it is called as half-wave rectifier., Input ac voltage and output voltage waveforms from the rectifier circuit., , Full wave rectifier, , ▪ For a full-wave rectifier the secondary of the transformer is provided, with a centre tapping and so it is called centre-tap transformer., ▪ During this positive half cycle, diode 𝐷1 gets forward biased and, conducts ,while 𝐷2 being reverse biased is not conducting. Hence we, get an output current and a output voltage across the load resistor 𝑅𝐿 ., ▪ During negative half cycle, diode 𝐷1 would not conduct but diode 𝐷2, conducts, giving an output current and output voltage across 𝑅𝐿 in the, same directionas in positive half., ▪ Thus, we get output voltage during both the positive as well as the, negative half of the cycle. This is a more efficient circuit for getting, rectified voltage or current than the halfwave rectifier.

Page 213 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Input ac voltage and output voltage waveforms from the rectifier circuit., , Filters, To get steady dc output from the pulsating voltage a capacitor is connected, parallel to the output terminals., The cicuits that filter out the ac ripple and give a pure dc voltage are called, filters., , Special Purpose p-n Junction Diodes, Zener diode, It is a special purpose semiconductor diode, named after its inventor C., Zener., , Symbol

Page 214 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , The I-V characteristics of a Zener diode, , ▪ It is designed to operate under reverse bias in the breakdown region, and used as a voltage regulator., ▪ Zener diode is fabricated by heavily doping both p, and n sides of the, junction., ▪ When the applied reverse bias voltage(V) reaches the breakdown, voltage (Vz) of the Zener diode, there is a large change in the current., ▪ After the breakdown voltage Vz , the Zener voltage remains constant,, even though current through the Zener diode varies over a wide range., This property of the Zener diode is used for regulating supply voltages., , Zener diode as a voltage regulator, , In the breakdown region, Zener voltage remains constant even though the, current through the Zener diode changes., This property of the Zener diode is used for regulating supply voltages.

Page 215 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , ▪ The unregulated dc voltage (filtered output of a rectifier) is connected, to the Zener diode through a series resistance Rs such that the Zener, diode is reverse biased., ▪ If the input voltage increases, the current through Rs increases . Then, current through Zener diode increases without any change in Zener, voltage., ▪ Similarly, if the input voltage decreases, the current through Rs, decreases. Then current through Zener diode decreases without any, change in Zener voltage., Thus any increase/ decrease in the input voltage results in, increase/, decrease of the voltage drop across Rs without any change in voltage across, the Zener diode. Thus the Zener diode acts as a voltage regulator. We have to, select the Zener diode according to the required output voltage and, accordingly the series resistance Rs., , Optoelectronic Junction Devices, The semiconductor diodes in which carriers are generated by photons, (photo-excitation) are called optoelectronic junction devices. Some, examples are,, (i)Photodiodes used for detecting optical signal (photodetectors)., (ii) Light emitting diodes (LED) which convert electrical energy into light., (iii)Photovoltaic devices which convert optical radiation into, electricity(solar cells)., , (i)Photodiode, , ▪ A Photodiode is operated under reverse bias., ▪ When the photodiode is illuminated with light (photons) with energy, (hν) greater than the energy gap (E g) of the semiconductor, then, electron-hole pairs are generated due to the absorption of photons., ▪ When an external load is connected, current flows., ▪ The magnitude of the photocurrent depends on the intensity of, incident light (photocurrent is proportional to incident light intensity).

Page 216 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , (ii)Light emitting diode, ▪ It is a heavily doped p-n junction which under forward bias emits, spontaneous radiation., ▪ When the diode is forward biased, electrons are sent from n → p, (where they are minority carriers) and holes are sent from p → n, (where they are minority carriers)., ▪ At the junction boundary the concentration of minority carriers, increases and the excess minority carriers recombine with majority, carriers near the junction. On recombination, the energy is released, in the form of photons, The semiconductor used for fabrication of visible LEDs must at least have a, band gap of 1.8 eV ., ▪ The compound semiconductor Gallium Arsenide – Phosphide, (GaAs1–xPx) is used for making LEDs of different colours., ▪ GaAs0.6 P0.4 (E g ~ 1.9 eV) is used for red LED., ▪ GaAs (E g ~ 1.4 eV) is used for making infrared LED., These LEDs find extensive use in remote controls, burglar, alarm systems, optical communication, etc., Extensive research is being done for developing white LEDs which can, replace incandescent lamps., Advantages of LEDs over conventional incandescent low power lamps:, (i), Low operational voltage and less power., (iii), Fast action and no warm-up time required., (iv), The bandwidth of emitted light is 100 Å to 500 Å or in, other words it is nearly (but not exactly) monochromatic., (v), Long life and ruggedness., (vi), Fast on-off switching capability., , (iii)Solar cell, A typical p-n junction and its cross sectional view

Page 217 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , A p-Si wafer is taken and a thin layer of n-Si is grown on one-side of it by, diffusion process. The other side of p-Si is coated with a metal which acts as, back contact. On the top of n-Si layer, metal finger electrode (or metallic, grid) is deposited. This acts as a front contact., , ▪ A solar cell is basically a p-n junction which generates emf when solar, radiation falls on the p-n junction., ▪ It works on the same principle (photovoltaic effect) as the photodiode,, except that no external bias is applied ., ▪ The junction area is kept much larger for solar radiation to be incident, because we are interested in more power., ▪ The generation of emf by a solar cell, when light falls on, it is due to the, following three basic processes: generation, separation and, collection—, a. generation of e-h pairs due to light (with hν > E g) close to the, junction;, b. separation of electrons and holes due to electric field of depletion, region. Electrons are swept to n-side and holes to p-side., c. the electrons reaching the n-side are collected by the front contact, and holes reaching p-side are collected by the back contact. Thus, p-side becomes positive and n-side becomes negative giving rise, to photovoltage., Solar cells are made with semiconductors like, Si (Eg = 1.1 eV),, GaAs (Eg = 1.43 eV),, CdTe (Eg = 1.45 eV),, CuInSe2 (Eg = 1.04 eV), etc., The criteria for the selection of a material for solar cell fabrication are,, (i) band gap (~1.0 to 1.8 eV),, (ii) high optical absorption (~104 cm–1),, (iii) electrical conductivity,, (iv) availability of the raw material,, (v) cost.

Page 218 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , Note that sunlight is not always required for a solar cell. Any light with, photon energies greater than the bandgap will do. Solar cells are used to, power electronic devices in satellites and space vehicles and also as power, supply to some calculators. Production of low-cost photovoltaic cells for, large-scale solar energy is a topic for research., , Digital Electronics And Logic Gates, Analogue signals, Continuous, time-varying signals( voltage or current) are called continuous, or analogue signals., , Digital sinals, In digital sinals only two values (represented by 0 or 1) of the input and, output voltage are permissible., , Logic gates, A logic gate is a digital circuit that follows curtain logical relationship, between the input and output voltages., The five common logic gates used are NOT, AND, OR, NAND, NOR., NAND and NOR gates are called universal gates, since using these gates we, can realise other basic gates OR, AND and NOT gates., Each logic gate is indicated by a symbol and its function is defined by a truth, table that shows all the possible input logic level combinations with their, respective output logic levels.

Page 219 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , (i) NOT gate, This is the most basic gate, with one input and one output. It produces a, ‘1’ output if the input is ‘0’ and vice-versa. That is, it produces an inverted, version of the input at its output. This is why it is also known as an, inverter., Symbol, , Truth Table, , (ii) OR Gate, An OR gate has two or more inputs with one output. The output Y is, 1 when either input A or input B or both are 1s. That is, if any of the, input is high, the output is high., Symbol, Truth Table, , (iii) AND Gate, An AND gate has two or more inputs and one output. The output Y, of AND gate is 1 only when input A and input B are both 1. That is, if, all the input are high, the output is high., Symbol, , Truth Table

Page 220 : Join Telegram Channel: https://t.me/hsslive, , Downloaded from www.Hsslive.in ®, , (iv) NOR Gate, It has two or more inputs and one output. OR- gate followed by a, NOT gate gives a NOT-OR gate (or simply NOR gate). Its output Y is, ‘1’ only when both inputs A and B are ‘0’. The gate gets its name from, this NOT OR behaviour., Symbol, Truth Table, , (v) NAND Gate, It has two or more inputs and one output. AND gate followed by a, NOT gate gives a NOT-AND gate (or simply NAND gate). If inputs A, and B are both ‘1’, the output Y is ‘0’. The gate gets its name from, this NOT AND behaviour., Symbol, Truth Table, , Seema Elizabeth, MARM Govt HSS Santhipuram, Thrissur