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1. Electric Charges and Electric Fields, 1.1. What are point charges?, Charges whose sizes are very small compared to the distance between them are called point, charges., 1.2. What do you do to charge (Electrify) a body?, To charge a body electrons are either removed or added to the body., 1.3. When does a body is said to be charged or electrified?, If a body possesses an electric charge, it is said to be electrified., 1.4. When does a body get negatively charged?, A body gets negatively charged when it gains electrons., 1.5. When does a body get positively charged?, A body gets positively charged when it loses electrons., 1.6. Why does ebonite rod get negatively charged on rubbing with fur?, Fur loses electrons and ebonite gains electrons. Electrons in fur are loosely bound than in, ebonite., 1.7. What type of a charge a glass rod gets when it is rubbed with silk?, Positive charge., 1.8. Name the device to detect charge on a body., Gold – leaf electroscope., 1.9. What do you mean by the polarity of charge?, The property which differentiates the two kinds of charges is called polarity of charge., 1.10. What is a conductor? Give two examples., The materials which allow electrons to freely flow through them is called conductor. Ex: All, metals, Earth., 1.11. What is an insulator? Give two examples., The materials which do not allow electrons to freely flow through them is called insulator., Ex: Wood, Plastic., 1.12. What is earthing of electricity?, The process of sharing the charges with the earth is called earthing., 1.13. Mention the method of charging a conductor., i. Conduction, ii. Induction, 1.14. Mention the method of charging an insulator., Friction, 1.15. Explain charging a conductor by induction., Initially charged conductor is brought near the uncharged conductor (both are insulated from, the earth). Charged conductor induces opposite charges on the nearby end of the uncharged, conductor & like charges on the other end. If other end is earthed then the second body possesses net, amount of charge.
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1.16. What are the basic properties of charges?, i. Additivity of charges., ii. Charge is conserved., , iii. Quantisation of charges., , 1.17. What do you mean by additivity of charges?, Additivity of electric charges means that the total charge of a system is the algebraic sum of, individual charges in the system. Charge can be positive or negative., 1.18. State conservation law of charges., The total charge of an isolated system remains unchanged with time., 1.19. What is quantisation of charge?, The total charge ( ) of a body is always integral multiple of a basic quantum of charge (e), i.e., , where, Proton charge is positive and electron charge is negative., 1.20. What is the natural unit of charge? OR What is the smallest amount of charge that can be, removed from a body?, Electronic charge, 1.21. What is the magnitude of charge of an electron?, C., 1.22. What is the S I unit of charge?, coulomb (C), 1.23. How many electrons make one coulomb of charge?, OR, , electrons., , 1.24. State and explain Coulomb’s inverse square law in electrostatics., The mutual electrostatic force between two point charges is directly proportional to the, product of magnitude of charges and inversely proportional to the square of the distance between the, charges and acted along the line joining the two charges., If, and are two point charges separated by a distance in free space, then the magnitude, of force between them is given by,, , OR, , Nm2C-2 is the constant of proportionality and, space., , in free space, where, C2N-1m-2 is the permittivity of free, , 1.25. Define S.I. unit of charges from Coulomb’s inverse square law of electrostatics., One coulomb is the charge that when placed at a distance of one metre from another charge, of the same magnitude in vacuum experiences an electrical force of repulsion of magnitude, N., 1.26. Two point charges, two charges?, Repulsive force., , and, , Department of Physics, GPUC Karkala, , are such that, , . What is the nature of force between, , Page - 1 -
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1.27. Explain Coulomb’s law in vector form., Let and be the position vectors of two charges and, . From the figure,, . The force on, by, is, and the force on, , by, , where, is unit vector in the direction of, the direction opposite to ., Note: i. For like charges –, , is, , ,, , and, , is unit vector in, , Y, , O, , X, , Z, ii. For unlike charges –, , iii. In both cases,, , ., , 1.28. State and explain the principle of superposition of electrostatic forces., The force on any charge due to a number of other charges is the vector sum of all the forces on, that charge due to other charges, taken one at a time., If , and are the positive charges placed at the corners, of a triangle, then total force acting on by the other two charges is, given by, , ., 3, , ., , OR, , The individual forces are not affected due to the presence of, other charges., In general,, , 2, , ., , 1.29. Define electric field., The electric field at a point is the force on unit positive charge kept at that point., Note: Mathematically the electric field due to source charge, , is given by,, , lim, q 0, , 1.30. What is the relation between electric force and electric field?, Electric force,, , , where, , – Test charge and, , – Electric field., , 1.31. What is the S.I. unit of electric field?, NC-1., 1.32. Write the expression for the electric field due to an isolated point charge., Electric field,, radially outward if charge, , , where, , – Electric field at a distance from the charge . Field is, , is positive and is radially inward if charge, , is negative., , 1.33. What is a test charge?, A charge which is negligibly small and tests the effect of a given charge is called test charge., 1.34. What is a source charge?, A charge which produces the electric field is called source charge., , Department of Physics, GPUC Karkala, , Page - 2 -
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1.35. Does the electric field satisfy superposition principle?, Yes. Electric field due to system of charges is equal to the vector sum of electric fields due to, individual charges., 1.36. In electrostatics, the gravitational forces are not taken into account. Why?, Gravitational force is about 10-39 times that of electrostatic force and it is very much lesser, compared to electrostatic forces., 1.37. State and explain the principle of superposition of electric field., The electric field at a point due to a number of charges is the, vector sum of all the fields due to the individual charges., If, and, are the point charges placed at distances, and, respectively from the point P, then resultant field at P is given by,3, , P, , ., , , where, , OR, , and, , are unit vectors., , In general,, , 2, , Note: Electric field is directed outward if, , and directed inward if, , ., , 1.38. How do you pictorially map the electric field around a charge?, Using electric field lines., 1.39. What is electric field line?, An electric field line is a curve drawn in such a way that the tangent at each point on the curve, gives the direction of electric field at that point., 1.40. Draw the electric field lines in the case of (i) two positive point charges separated by a small, distance, (ii) one positive and one negative point charges separated by a small distance. (iii) a, positive point charge, (iv) a negative point charge., i., ii., iii., iv., +q, , +q, , +q, , -q, , +q, , -q, , 1.41. What are the properties of electric field lines?, i. Field lines start from positive charges and end at negative charges., ii. Two electric field lines can never intersect since a vector cannot have two directions at a, point., iii. Electric filed lines do not form any closed loops., iv. Electric field lines are crowded in region of greater electric field., v. In the region of uniform electric field, the electric field lines are uniformly spaced parallel, straight lines., vi. Tangent drawn to the electric field lines at any point gives the direction of electric field., 1.42. What is electric flux through an area?, Electric flux through an area is the number of normal electric field lines passing through that, area., Department of Physics, GPUC Karkala, , Page - 3 -
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1.43. Write the expression for electric flux., The electric flux,, , of electric field, , given by,, (normal drawn to the area)., , , where, , through a small area, , – angle between the, , is, , and, , 1.44. Write the expression for total electric flux ( ), , where, between the, , &, , – electric field,, , – small area and, , – angle, , ., , 1.45. What is the unit of electric flux?, NC-1m2 OR Vm, Note: i. Non uniform field:, A, Surface area placed at A encloses more number of electric lines, hence field is stronger. Whereas same area placed at B encloses less number, +q, of electric lines, hence filed is weaker., ii. Uniform field:, A, Surface area placed at A and B encloses equal electric lines hence, filed is same at both the places., , B, , B, , 1.46. What is an electric dipole?, Two equal and opposite charges separated by a small distance is called electric dipole., 1.47. Define electric dipole moment., Electric dipole moment is the product of magnitude of either charge and distance between, charges., Note: Two charges, , and – separated by a distance, , form a dipole., , 1.48. Write the expression for electric dipole moment. What is its direction?, Electric dipole moment,, ., Direction is along the dipole axis from negative charge to positive charge., 1.49. What is the unit of electric dipole moment?, coulomb metre (Cm)., 1.50. Derive an expression for electric field at a distance along the axis of dipole., P, , Consider a point P at a distance from the midpoint of dipole., The electric field at P due to charge, and, where, , is the unit vector along the dipole axis from – to, , Total field at P is, , OR, , are, , and, ., , ., , . Since, , Department of Physics, GPUC Karkala, , ., Page - 4 -
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Note: For short dipole: At large distances, , . Therefore,, , ., , 1.51. Derive an expression for electric field at a distance along the equatorial line of a dipole., Let P be a point at a distance from the center of electric, dipole along the equatorial line of electric dipole., Magnitude of electric field at P due to charge, and, , and – are, , P, , respectively., , The field at P due to charges is resolved. The components, along equatorial line cancel each other. The components along, dipole axis added up., Therefore,, that both components are opposite to ), , From the figure,, , (negative sign indicates, 2a, , ., , Therefore,, OR, , . Since, , Note: For short dipole: At large distances, , . Therefore,, , ., , 1.52. Define surface density, linear density and volume density of charge. Mention their units., Surface density of charge,, , , where, , Linear density of charge,, , – small length of wire. Unit: Cm-1., , , where, , Volume density of charge,, , – small surface area. Unit: Cm-2., , , where, , – small volume. Unit: Cm-3., , Note: Electric field due to continuous charge distribution,, , , where, , , volume, , density., 1.53. State and explain Gauss’s law., The total electric flux through any closed surface is equal to, , times the total charge enclosed, , by it., If a closed surface encloses a charge, , then the flux through the surface is, , , where, , is, , the permittivity of free space. Gauss law can be applied to the surface of any shape and any size,, charges may be located anywhere inside the surface. The charge outside the closed surface does not, count., 1.54. What is a Gaussian surface?, The closed surface we choose to find the electric flux and hence to apply Gauss’s law., 1.55. What is the electric flux over a closed surface enclosing an electric dipole?, Zero., , , since, , Department of Physics, GPUC Karkala, , ., Page - 5 -
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1.56. What is the magnitude of electric field inside a charged conductor?, Zero. No charge resides inside the conductor. So, , and, , ., , 1.57. Derive the expression for torque on an electric dipole placed in a uniform electric field., Consider a dipole of moment, , is placed in an electric field, , that, , such, , makes an angle with ., The magnitude of force on each charge,, . The perpendicular, distance between the lines of action of the two forces,, ., Torque on the dipole,, , B, , C, , A, OR, , . Since, , OR, , ., , ., , 1.58. What happens if a dipole is placed in non uniform field?, The dipole experiences both torque and net force., , 1.59. Derive an expression for electric field near an infinitely long straight uniformly charged wire, using Gauss’s law., An infinitely long thin straight wire with uniform linear positive charge, density is considered., A cylindrical Gaussian surface of length is considered., The flux through the two ends of cylindrical Gaussian surface is zero., (, ), The surface area of curved surface, , where is the radius of the, cylinder., Flux through curved surface,, .(, , , By Gauss law, flux, Therefore,, Vectorially,, , OR, , where, , ., , +, +, +, , P, , +, +, , is the radial unit vector., , 1.60. Derive an expression for electric field near a uniformly charged infinite plane sheet using, Gauss’s law., + +, An infinitely plane sheet with uniform surface positive charge, + + +, density is considered. A cylindrical Gaussian surface with cross sectional, + + +, area A perpendicular to the sheet is considered. Through the curved, + + +, surface of the cylinder no flux passes. (, ., Electric flux through two circular faces is, (, ., + + +, The charge enclosed by the surface, ., + +, By Gauss’s law, electric flux, , ., , Therefore,, , ., , Vectorially,, , OR, , where, , is the unit vector normal to the plane going away from it., , 1.63. Why is the electric field inside a uniformly charged spherical shell, zero? Explain., When a spherical shell is charged, the charges get distributed uniformly over its outer surface and the, charge inside the shell is zero. According to Gauss’s law, as the charge inside is zero, the electric flux at any, point inside the shell will be zero. Obviously the electric field is also zero., Department of Physics, GPUC Karkala, , Page - 6 -
