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1.1 INTRODUCTION, We have the experience of seeing a spark or hearing a crackle when we take off our synthetic, , clothes or sweater, in dry weather. Another example of electric discharge is the lightning that we, see in the sky during thunderstorms. We also experience a sensation of an electric shock either, while opening the door of a car or holding the iron bar of a bus after sliding from our seat., , The reason for these experiences is discharge of electric charges through our body, which, , were accumulated due to friction between materials on rubbing [of insulating surfaces]. This is, 1 . ;, , due to generation of_static e ricity/frictional ricit, Static means anything that does not move or change with time. Electrostatics deals with, , the study of forces, fields and potentials arising from static charges., , , , 1.2 ELECTRIC CHARGE E, Amber rubbed with wool or silk cloth attracts light objects[Thales of Miletus, Greece, argund, 600 BC]. The name electricity is coined from the Greek word elektron meaning amber), , Cut out long thin strips of white paper and lightly iron them. Take them near a TV screen or, computer monitor. You will see that the strips get attracted to the screen. In fact they remain, stuck to the screen for a while., , It was observed that if two glass rods rubbed with wool or silk cloth are, , brought close to each other, they repel each other [Fig. 1.1(a)]., , SX, , SS. Class rod, By, , , , , y ,, | Silk thread | i oad |euethead, ~ A eee, , wy, C \ \, Plastic rod Qe rod f J % \ f, 4 Ret ' 6 @ b 6, a, , , , y} 3, ef J, , we we {a td Wy, , a“ : FIGURE 1.1 Rods and pit like ct pel and, , , , (b) () unlike charges altract each other, , The two strands of wool or two pieces of silk cloth, with which the rods were rubbed, also repel, each other. However, the glass rod and.wool attracted each other. Similarly, two plastic rods, rubbed with cat’s fur repelled each other [Fig. 1.1(b)] but attracted the fur. ‘, , On the other hand, the plastic rod attracts the glass rod [Fig.1.1(c)]and repel the silk or, wool with which the glass rod is rubbed. The glass rod repels the fur. / If a plastic rod rubbed, with fur is made to touch two small pith balls suspended by silk or nylon thread, then the balls, repel each other [Fig. 1.1(d)] and are also repelled by the rod., , A similar effect is found if the pith balls are touched with a glass rod rubbed with silk [Fig., 1.1(e)]. / A pith ball touched with glass rod attracts another pith ball touched with plastic rod, [Fig. 1.1(f)]., , There were only two kinds of an entity which is called the electric charge. We say that, the bodies like glass or plastic rods, silk, fur and pith balls are electrified. They acquire an, electric charge on rubbing. The experiments on pith balls suggested that there are two kinds of, electrification and we find that (i) like charges repel and (ii) unlike charges attract each, other., If the electrified, glass rod is brought in contact with silk, with which it was rubbed, they no, longer attract each other. They also do not attract or repel other light objects as they did on, , being electrified. Thus, the charges acquired after rubbing are lost when the charged bodies are., brought in contact. The charges were ositive and negative bythe American, , scientist Benjamin Franklin., By convention, the charge on glass rod or cat’s fur is called positive and that on, ik is termed . If an object possesses an electric charge, it is said to, , be electrified or charged. When it has no charge it is said to be neutral., , A simple apparatus to detect charge on a body Is the gold-leaf electroscope (Fig., 1,2(a)]. “, , ,
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. Metal knob, , , , , , fa) @), , It consists of a vertical metal rod housed in a box, with two thin gold leaves attached to its, bottom end. 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. 3, , (Why material bodies acquire charge?, All matter is made up of atoms and/or molecules, Although normally the materials are, electrically neutral, they do contain charges; but their charges are exactly balancedy Forces that, hold the molecules together, forces that hold atoms together in a solid, the adhesiVe force of, glue, forces associated with surface tension; all are basically electrical in nature, arising from, the forces between charged particles. Thus the electric force is all pervasive., , Co solids, some of the electrons, being less tightly bound in the atom, are the charges which, charged positively by losing, , are transferred from one body to the other. A body can thus be sitiv, , some of its electrons. Similarly, a body can be charged negatively by gaining electrons. When, , we rub a glass rod with silk, some of the electrons from the rod are transferred to the silk cloth., Thus the rod gets positively charged and the silk gets negatively charged., , No new charge is created in the process of rubbing) The number of electrons, that are :, transferred, is a very small fraction of the total number of electrons in. the material body. Only, the less tightly bound electrons in a material body can be transferred from it to another by, tubbing. Therefore, when a body is rubbed with another, the bodies get charged and that is why, we have to stick to certain pairs of materials to notice charging on rubbing the bodies., , 1.3 CONDUCTORS AND INSULATORS, A metal rod held in hand and rubbed with wool will not show any sign of being charged., However, if a metal rod with a wooden or plastic handle is rubbed without touching its metal, part, it shows signs of charging., , ‘Some substances readily allow passage of, electricity through others do not. Those, which allow electricity to pass through them easily are called chats. ‘They have electric, charges (electrons) that are comparatively free to move inside the material. Metals, human and, animal bodies and earth are conductors. »- 3. rj ‘, , Most of the non-metals like glass, porcelain, plastic, nylon, wood offer high resistance to, the passage They are called insulators. :, When a re S, , , , , , put on an ins, , ; d on combing dry, but a metal article like spoon does not. The charges on metal leak through our body to the, ground as both are conductors of electricity. ik a, When we bring a charged body in contact with the earth, all, disappears by causing a momentary current to pass to the, conductor (such as our body). This process ring |, , grounding or earthing., , appliances. A thit
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Foot,, , fof, , Hy Fat, , Tt FV, , —ye, When we touch a pith ball with an el ier, lectrified plastic rod, some of the negative charges on the, rod are transferred to the pith ball and it also gets charged. Thus the pith ball is uaae by, contact. It is then repelled by the plastic rod but is attracted by a glass rod which is oppositely, charged. 3 ativack +e i, , i -t -f 2f oo, , 7, FIGURE 1.4 Charging by induction, , When a charged body is brought near an uncharged conductoi unted on an insulati, the nearer end of the conductor acquires opp. charge & the farther end the same charge., , es two metal spheres, A and B, supported on insulating stands, im contact as shown in, , ig. 1.4(a)., , (ii) Bring a positively charged rod near one of the spheres; say A, without touching the, sphere) The free electrons in the spheres are attracted towards the rod. This leaves an excess, OF positive charge on the rear surface of sphere B[ Fig. Ane left surface of sphere A,, has an excess of negative charge and the right surface of Sphere B, has an excess of, positive charge. The process is called induction of charge and happens almost instantly.), The accumulated charges remain on the surface, as shown, till the glass rod is held near the, sphere. If the rod is removed, the charges are not acted by any outside force and they, redistribute to their original neutral state., , ( (iii) Separate the spheres by a small distance while the glass rod is still held near sphere A, as, ‘shown in Fig. 1.4(c). The two spheres are found to be oppositely charged and attract each, other., , Tiv) Remove the rod. The charges on spheres rearrange themselves as shown in Fig. 1.4(d)., Now, separate the spheres quite apart. The charges on them get uniformly distributed over, them, as shown in Fig. 1.4(e).In this process; the metal spheres will each be equal and, oppositely charged. This is charging by induction) The positively charged glass rod does not, lose any of its charge, contrary to the process of charging by contact., , When electrified rods are brought near light objects [insulators], a similar effect takes, place. The rods induce opposite charges on the near surfaces of the objects and similar charges, move to the farther side of the object., , The centers of the two types of charges are slightly separated. We know that opposite, charges attract while similar charges repel. However, the magnitude of force depends on the, distance between the charges and in this case the force of attraction overweighs the force of, repulsion. As a result the particles like bits of paper or pith balls, being light, are pulled towards, , the rods., Example 1.1 How can you charge a metal sphere positively without touching it?, , Solution Figure 1.5(a) shows an uncharged metallic sphere on an insulating metal stand. Bring, negative! 4 r ‘© the metallic as shown in Fig. 1.5(b). As the rod is, , brought close to the sphere, the free electrons in the sphere move away due to repulsion and, start piling up at the farther end. The iv due to deficit of, electrons. This process of charge distribution stops when the net force on the free electrons, inside the metal is zero, by a conducting wire. The will flow to the ground while the positive charges ey wa, end eee ae there due, , f the negative cha ‘on the as shown i. ‘c). Disconnect the, pared “the positive charge continues to be held at the near end [Fig. 1.5(d)}., in Fig. 1.5(e).
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rae, , , , , 4, , In this experiment, the metal sphere gets charged by the process of induction and the rod does, , not lose any of its charge. Similar steps are involved in chargi, its ¢ ir ging a metal sphere negatively b, induction, by bringing a positively charged rod near it. In this case the electron Will Tow from, , the ground to the sphere when the sphere is connected to the ground with a wil, , , , , , , , 1.5 BASIC PROPERTIES OF ELECTRIC CHARGE, , If the sizes of charged bodies are very small as compared to the distances between them, we, , treat them as point charges,, , 1.5.1 Additivity of charges, , If a system contains two point charges qi and q2, the total charge of the system is obtained, , ne, by adding algebraically g1 and q2, i.e., charges add up like real numbers or they are, , scalars., , 1.5.2 Charge is conserved, , When bodies are charged by rubbing, there is transfer of electrons from one body to the other;, , no new charges are either created or destroyed. Due to interactions among the bodies, charges, , may get redistributed but it is found that the total charge of the isolated system is always, , conserved., , 1.5.3 Quantisation of charge, , All free charges are integral multiples of a basic unit of charge denoted by e. Thus charge g ona, , body is always given by [q = ne where nis any integer, positive or negative. This basic unit of, , charge is the charge that an electron or proton carries. By convention, the charge on an, , electron is taken to be negative; therefore charge on an electron is written as -e and that on a, , proton as +e. The quantization of charge was first suggested by the experimental laws of, , electrolysis discovered by English experimentalist Faraday. It was experimentally demonstrated _, , by Millikan in 1912. the value of the basic unit of charge is e = 1.602192 x 10°" C Thus, there, , are about 6 x 102° electrons in a charge of -1C. Keg oe, ec exo?, , COULOMB’S LAW, , Force between two point charges varied inversely as the square of the distance between the, , charges and was directly proportional to the product of the magnitude of the two charges and, , acted along the line joining the two charges., , Thus, if two point charges q1, g2 are separated by a distance r in vacuum, the magnitude of the, , Pek fa_al, force (F) between them is given by r i ‘, In SI units, the value of k is about 9 x 10°. Forgi =q2=1C,r=1m F=9 x 10°N. That is,, 1 C is the charge that when placed at a distance of 1 m from another charge of a jue, , i ) experience: i i itude 9 x 10° N. One, magnitude ja vacuum experiences an eléctrical force of repulsion of magnitu, coulomb is evidently too big a unit to be used. In practice, in electrostatics, one uses smaller, units like 1 mC or 1 uC. The constant k in Eq. (1.1) is usually put as k = 1/4ne0 for later, , pe hal, , 7 2 : sabite afi, so that Coulomb's law is written as 4r_ 1 €0 is called the permittivity of, , convenience, :, : &)= 8.854 x 10? C* N'm? the force Fi2 on charge q1, , free_space. The value of €0 in SI units is, f 1, — 4 2 fi. =—Fay, , = 4, due to charge q2, is ™% a, Coulomb's force law between two point c, , , , harges gi and q2 located at ri and r2 is, , he ~, tn. + F,, Bm, U- in, Bont OM ginal org, verse, a+ve, sero Nb >O ) he, Fi, - ., Sepa 7 Mk, Par az A hy oe Dh<O = ve. , Spp- charges, attraction, i Me, Thus, Coulomb's law agrees with the Newton's third law., , SB ie i
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Fxy, Fe xy, re <*, , bh, , oa BETWEEN MULTIPLE CHARGES, ‘orce on any charge due to a number of other charges is the vector sum of, all the forces on, that charge due to the other charges, taken one at a time. The individual forces are unaffected, due to the presence of other charges. This is termed as the principle of superposition., Ina system of charges gi,q2, ..., qn, The total force F1 on the charge q1, due to all other, charges, is then given by the vector sum of the forces Fi2,° E23). “Pies, , , , , , , , , , , , + toe. Udy - ag ] Gi ne Oh., FL= F,+F,+..4 F, = m7 ae i+ tt fj +...+ he I, pag >, ee 12 13 in ~ay, , i ‘ 1, The vector sum is obtained as usual by the parallelogram law of addition of vectors. All of, electrostatics is basically a consequence of Coulomb's law and the superposition principle., , ELECTRIC FIELD DUE TO A POINT CHARGE, , Let us consider a point charge Q placed in vacuum, at the origin O. If we place another point, charge q at a point P, where OP = r, then the charge Q will exert a force on q as per Coulomb's, law. Charge Q produces an electric field everywhere in the surrounding. When another charge q, is brought at some point P, the field there acts on it and produces a force. The electric field, , B(x)--— 8} £16), , produced by the charge Q at a point ris given as 4zsr° where r* = r/r, is a unit vector, from the origin to the point r. Thus, Eq.(1.6) specifies the value of the electric field for each, value of the position vector r. The word “field” signifies how some distributed quantity (which, could be a scalar or a vector) varies with position. The effect of the charge has been, incorporated in the existence of the electric field. We obtain the force F exerted by a charge Q, , p-__ M1,, , , , , , “ona charge gq, as 4m, r’ F(r) = qg E(r) (1.8) Equation (1.8) defines the SI unit of electric, , field as N/C*. = «tL @, , Grae! =E = E, 1. If g is unity, the electric field due to’a charge Q is numerically equal to the force exerted by, it. Thus, the e/ectric field due to a charge Q at a point in space may be defined as the force that, a unit positive charge would experience if placed at that point. The charge Q, which is producing, the electric field, is called a source charge and the charge q, which tests the effect of a source, , ae, , , , , , , , E= lim, —, charge, is called a test charge.[make q negligibly small] woh gq), 2. The electric field E due to Q, is independent of q. This is because F is proportional to q, the, force F on the charge q due to the charge Q depends on the particular location of charge q., Thus, the electric field E due to Q is also dependent on the space coordinate r., , 3. For a positive charge, the electric field will be directed radially outwards from the charge. If, the source charge is negative, the electric field vector, at each point, points radially inwards., , a fu, 4. At equal distances from the charge Q, the magnitude of its electric field E is same. The, magnitude of electric field E due to a point charge is thus same on a sphere with the point, charge at its centre; in other words, it has a spherical symmetry., , Electric field due to a system of charges, , Consider a system of charges g1, q2, .... gn with position vectors r1,r2, ..., 17 relative to some, origin © electric field at a point in space due to the system of charges is defined to be the, , force experienced by a unit test charge placed at that point, without disturbing the original, , positions of charges qi, q2, ..., qn. We can use Coulomb's law and the superposition principle to, determine this fi it a point P denoted by position vector r. i i, y the wirerreanl principle, the electric field E at due to the system of charges is, (r) = El (r) + E2 (r) +... + En(r) rs Yet pomh PD
