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Electrostatics : Electric charge, Electric Field and Electric potential, CHARGE AND COULOMB’S LAW, 1., , The law, governing the force between electric charges is known as, (a) Ampere's law, , 2., , (b) Ohm's law, (b) Half, (b) 1 : 1, , (d) Increases if, , q3, , is of the same sign as, , (d)1 : 25, , If third charge, , q3, , is brought near, the force of, , (c)Remains unchanged, q1, , and decreases if, , q3, , is of opposite sign, , Let Fg and Fe represents gravitational and electrostatic force respectively between electrons situated, at a distance 10 cm. The ratio of Fg / Fe is of the order of, (b) 10, , (d) 10−43, , (c) 1043, , The ratio of the forces between two small spheres with constant charge, dielectric constant K is, (a) 1 : K, , 7., , q2 ., , (b) Increases, , (a) 1036, 6., , (d)Four times, , (c)5 : 1, , A charge q1 exerts some force on a second charge, q1 exerted on q 2, (a) Decreases, , 5., , (c)Double, , There are two charges +1 µC and +5 µC. The ratio of the forces acting on them will be, (a) 1 : 5, , 4., , (d)Coulomb's law, , When the distance between the charged particles is halved, the force between them becomes, (a) One-fourth, , 3., , (c)Faraday's law, , (b) K : 1, , (c) 1 : K 2, , (a), , in air, , (b), , in a medium of, , (d) K 2 : 1, , A soap bubble is given a negative charge, then its radius, (a) Decreases, , (b) Increases, , (c)Remains unchanged, , (d) Nothing can be predicted as information is insufficient, 8., , Four charges are arranged at the corners of a square, , ABCD, , , as shown in the adjoining figure., , The force on the charge kept at the centre O is, (a) Zero, , (b) Along the diagonal, , (c) Along the diagonal, 9., , A, +q, , BD, , B, +2q, , AC, , (d) Perpendicular to side, , O, , AB, , In the absence of other conductors, the surface charge density, (a) Is proportional to the charge on the conductor and its surface area, , – 2q, D, , +q, C, , (b) Inversely proportional to the charge and directly proportional to the surface area, (c) Directly proportional to the charge and inversely proportional to the surface area, (d) Inversely proportional to the charge and the surface area, 10. A body can be negatively charged by, , (a) Giving excess of electrons to it, , (b) Removing some electrons from it, , (c) Giving some protons to it, , (d) Removing some neutrons from it, , 11. The minimum charge on an object is, , (a) 1 coulomb, , (b) 1 stat coulomb, , (c) 1.6 × 10 −19 coulomb, , (d) 3.2 × 10 −19 coulomb, , 12. Out of gravitational, electromagnetic, Vander Waals, electrostatic and nuclear forces; which two are, , able to provide an attractive force between two neutrons, (a) Electrostatic and gravitational, , (b) Electrostatic and nuclear, , (c) Gravitational and nuclear, , (d) Some other forces like Vander Waals, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 13. A total charge Q is broken in two parts Q1 and Q 2 and they are placed at a distance R from each, , other. The maximum force of repulsion between them will occur, when, (a), , Q2 =, , Q, Q, , Q1 = Q −, R, R, , (b) Q2, , =, , Q, 2Q, , Q1 = Q −, 4, 3, , (c) Q2, , =, , Q, 3Q, , Q1 =, 4, 4, , (d) Q1, , =, , Q, Q, , Q2 =, 2, 2, , 14. Three charges 4 q, Q and q are in a straight line in the position of 0, l / 2 and l respectively., , The resultant force on, , q, , will be zero, if, , (a) – q, , (b), , Q=, , (c) − q, , − 2q, , (d) 4q, , 2, , 15. An isolated solid metallic sphere is given +Q charge. The charge will be distributed on the sphere, , (a) Uniformly but only on surface, (b) Only on surface but non-uniformly, (c) Uniformly inside the volume, (d) Non-uniformly inside the volume, 16. Two small spheres each having the charge +Q are suspended by insulating threads of length L from, a hook. This arrangement is taken in space where there is no gravitational effect, then the angle, between the two suspensions and the tension in each will be, (a), , 180 o ,, , Q2, , 1, , 4πε 0 (2L), , (b), , 2, , 90 o ,, , 1, , Q2, , 4πε 0 L, , 2, , (c) 180 o ,, , Q2, , 1, , 4πε 0 2L, , (d) 180 o ,, , 2, , 1, , Q2, , 4πε 0 L2, , 17. Two charges each of 1 coulomb are at a distance 1 km apart, the force between them is, , (a) 9 ×103 N, 18. Two charges, , +2C, , (b) 9 ×10−3 N, (c) 1.1×10−4 N, and +6C are repelling each other with a force of, , charge, then the value of the force will be, (a) 4 N (Attractive), (b) 4 N (Repulsive), , (d) 104 N, 12 N . If each charge is given, , (c) 8 N (Repulsive), , −2C, , of, , (d) Zero, , 19. Dielectric constant of pure water is 81. Its permittivity will be, , (a), , 7.12 × 10 −10 MKS, , units, , (b) 8.86 × 10 −12 MKS units, , (c) 1.02 × 10 13, , MKS, , units (d) Cannot be calculated, , 20. There are two metallic spheres of same radii but one is solid and the other is hollow, then, , (a) Solid sphere can be given more charge, (c) They can be charged equally (maximum), , (b) Hollow sphere can be given more charge, (d) None of the above, , 21. In general, metallic ropes are suspended on the carriers which take inflammable material. The reason is, , (a), (b), (c), (d), , There speed is controlled, To keep the centre of gravity of the carrier nearer to the earth, To keep the body of the carrier in contact with the earth, Nothing should be placed under the carrier, , 22. Three equal charges are placed on the three corners of a square. If the force between q1 and q 2 is F12, , and that between, (a), , q1 and q 3, , is, , F13 ,, , the ratio of magnitudes, , F12, F13, , is, , (b) 2, (c) 1 / 2, (d) 2, 23. ABC is a right angled triangle in which AB = 3 cm & BC = 4 cm . And ∠ ABC = π/2. The three charges, +15, + 12 and −20 e.s.u. are placed respectively at A, B and C. The force acting on B is, (e.s.u.= electrostatic unit of charge), (a) 125 dynes, (b) 35 dynes, (c) 25 dynes, (d)Zero, 24. With the rise in temperature, the dielectric constant K of a liquid, (a) Increases, (b) Decreases, (c) Remains unchanged, (d)Charges erratically, 1/ 2, , 25. Two charges q1 and q 2 are placed in vacuum at a distance d and the force acting between them is F ., , If a medium of dielectric constant 4 is introduced around them, the force now will be, (a), , 4F, , (b), , 2F, , (c), , F, 2, , (d), , F, 4, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 26. Force of attraction between two point charges Q and – Q separated by d metre is Fe . When these, , charges are placed on two identical spheres of radius R = 0.3 d whose centres are d metre apart, the, force of attraction between them is, (b) Equal to Fe, (c) Less than Fe, (d)Less than Fe, (a) Greater than Fe, 14, 27. When 10 electrons are removed from a neutral metal sphere, the charge on the sphere becomes, (a) 16 µ C, (b) −16 µ C, (c) 32 µ C, (d) −32 µ C, 28. A force F acts between sodium and chlorine ions of salt (sodium chloride) when put 1 cm apart in air., The permittivity of air and dielectric constant of water are ε 0 and K respectively. When a piece of, salt is put in water electrical force acting between sodium and chlorine ions 1 cm apart is, (a), , F, K, , (b), , FK, , (c), , ε0, , F, Kε 0, , (d), , Fε 0, K, , 29. A conductor has 14.4 × 10 −19 coulombs positive charge. The conductor has, , (Charge on electron, , = 1.6 × 10 −19 coulombs, , (a) 9 electrons in excess, , ), , (b)27 electrons in short (c)27 electrons in excess, , (d)9 electrons in short, , 30. The value of electric permittivity of free space is, , (a), , 9 × 10 9 NC 2 / m 2, , (b) 8.85 ×10−12 Nm 2 / C2s, , (c) 8.85 × 10 −12 C 2 / Nm 2, , (d) 9 × 10 9 C 2 / Nm 2, , 31. Two similar spheres having + q and − q charge are kept at a certain distance. F force acts between, , the two. If in the middle of two spheres, another similar sphere having, , +q, , charge is kept, then it, , +q, , charge, , experience a force in magnitude and direction as, (a) Zero having no direction, (c), , 8F, , towards, , −q, , (b) 8 F towards, , charge, , (d) 4 F towards, , +q, , charge, , 32. A charge Q is divided into two parts of q and Q − q . If the coulomb repulsion between them when they, , are separated is to be maximum, the ratio of, (a) 2, , (b), , Q, q, , should be, , 1/ 2, , (c)4, , (d) 1 / 4, , (c) 1.6 × 10 +19, , (d) 9 × 10 11, , 33. Number of electrons in one coulomb of charge will be, , (a), , (b) 6.25 × 10 18, , 5.46 × 10 29, , 34. When air is replaced by a dielectric medium of constant k , the maximum force of attraction between, , two charges separated by a distance, (a) Decreases, , k, , times (b) Remains unchanged, , (c) Increases, , k, , times (d) Increases, , k −1, , times, , 35. A glass rod rubbed with silk is used to charge a gold leaf electroscope and the leaves are observed to, , diverge. The electroscope thus charged is exposed to X-rays for a short period. Then, (a) The divergence of leaves will not be affected, , (b) The leaves will diverge further, , (c) The leaves will collapse, , (d) The leaves will melt, , 36. One metallic sphere A is given positive charge whereas another identical metallic sphere B of, , exactly same mass as of, , A is, , (a) Mass of, , A, , and mass of, , (c) Mass of, , B, , decreases, , B, , given equal amount of negative charge. Then, still remain equal, , (b) Mass of, , A, , increases, , (d) Mass of, , B, , increases, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 37. The force between two charges 0.06 m apart is 5 N . If each charge is moved towards the other by, 0.01 m ,, , (a), , then the force between them will become, (b), , 7.20 N, , (c) 22.50 N, , 11 .25 N, , (d) 45.00 N, , 38. Two charged spheres separated at a distance d exert a force F on each other. If they are immersed in, , a liquid of dielectric constant 2, then what is the force (if all conditions are same), (a), , F, 2, , (b), , (c) 2F, , F, , (d) 4 F, , 39. Two point charges +3µC and +8 µC repel each other with a force of 40 N . If a charge of −5 µC is added, , to each of them, then the force between them will become, (b) +10 N, (c) +20 N, (d) −20 N, (a) −10 N, 19, 40. When 10 electrons are removed from a neutral metal plate, the electric charge on it is, (d), 10–19 C, (a) –1.6 C, (b) + 1.6 C, (c)10+19 C, 41. Electric charges of 1µC, − 1µC and 2µC are placed in air at the corners A, B and C respectively of an, equilateral triangle ABC having length of each side 10 cm. The resultant force on the charge at C is, (a) 0.9 N, (b) 1.8 N, (c)2.7 N, (d)3.6 N, 42. Charge on α -particle is, (b) 1.6 × 10 −19 C, (c) 3.2 × 10 −19 C, (d) 6.4 × 10 −19 C, (a) 4.8 × 10 −19 C, 43. Two small conducting spheres of equal radius have charges +10 µC and −20 µC respectively and placed, at a distance R from each other experience force F1 . If they are brought in contact and separated to, the same distance, they experience force, , F2 . The, , ratio of, , F1, , to, , F2, , is, , (a) 1 : 8, (b) –8 : 1, (c)1 : 2, (d) –2 : 1, 44. Two charges each equal to 2µC are 0.5m apart. If both of them exist inside vacuum, then the force, between them is, (a) 1.89 N, (b) 2.44 N, (c) 0.144 N, (d) 3.144 N, 45. Two charges are at a distance ‘d’ apart. If a copper plate (conducting medium) of thickness, , d, 2, , is, , placed between them, the effective force will be, (a) 2F, (b) F / 2, (c) 0, (d) 2 F, 46. Two electrons are separated by a distance of 1Å. What is the coulomb force between them, (a) 2.3 × 10 −8 N, (b) 4.6 × 10 −8 N, (c) 1.5 × 10 −8 N, (d) 2.3 ×10−18 N, 47. Two copper balls, each weighing 10g are kept in air 10 cm apart. If one electron from every 10 6 atoms, , is transferred from one ball to the other, the coulomb force between them is (atomic weight of, copper is 63.5), (b) 2.0 × 10 4 N, (c) 2.0 × 10 8 N, (d) 2.0 × 10 6 N, (a) 2.0 × 10 10 N, 48. A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of, , inner radius b and outer radius c is concentric with the solid sphere and has a net charge – Q., The surface charge density on the inner and outer surfaces of the spherical shell will be, (a), , −, , (b), , −, , (c), , 0,, , (d), , 2Q, Q, ,, 4πb 2 4πc 2, Q, 4πb, , 2, , ,, , a, , Q, 4πc, , b, , 2, , c, , Q, 4πc 2, , Q, Q, ,, 2, 4πb 4πc 2, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 49. Three charges each of magnitude q are placed at the corners of an equilateral triangle, the, , electrostatic force on the charge placed at the center is (each side of triangle is L), (a) Zero, , (b), , q2, 4πε 0 L2, 1, , (c), , 3q 2, 4πε 0 L2, 1, , (d), , 1 q2, 12πε 0 L2, , 50. Two charges placed in air repel each other by a force of 10 −4 N . When oil is introduced between the, , charges, the force becomes, (a) 2.5, , 2.5 × 10 −5 N . The, , dielectric constant of oil is, , (b) 0.25, , (c) 2.0, , (d)4.0, , 51. Three charges are placed at the vertices of an equilateral triangle of side ‘a’ as shown in the following, , figure. The force experienced by the charge placed at the vertex A in a direction normal to BC is, (a), , Q 2 /(4πε 0a2 ), , (b), , − Q 2 /(4πε 0 a2 ), , A, , +Q, , (c) Zero, (d), , –Q, , Q 2 /(2πε 0a2 ), , a, , B, , C, , +Q, , 52. Two particles of equal mass m and charge q are placed at a distance of 16 cm. They do not, , experience any force. The value of, (a) 1, , q, m, , is, , πε 0, , (b), , G, , G, 4πε 0, , (c), , (d), , 4πε 0G, , 53. When a glass rod is rubbed with silk, it, , (a) Gains electrons from silk, , (b) Gives electrons to silk, , (c) Gains protons from silk, , (d) Gives protons to silk, , 54. An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius r., , The coulomb force, (a), , −K, , e2, rˆ, r3, , F, , between the two is (Where, (b), , K, , e2 , r, r3, , K=, , 1, 4πε 0, , ), 2, , (c) − K e3, r, , , r, , 2, , (d) K e2, r, , rˆ, , 55. A body has – 80 micro coulomb of charge. Number of additional electrons in it will be, , (a), , (b), , 8 × 10 −5, , 80 × 10 −17, , (c) 5 × 10 14, , (d) 1.28 × 10 −17, , 56. Two point charges placed at a certain distance r in air exert a force F on each other. Then the, , distance r' at which these charges will exert the same force in a medium of dielectric constant k is, given by, (a) r, , (b) r/k, , (c), , r/ k, , (d) r, , k, , 57. Dielectric constant for metal is, , (a) Zero, , (b) Infinite, , (c)1, , (d)Greater than 1, , 58. A charge of Q coulomb is placed on a solid piece of metal of irregular shape. The charge will, , distribute itself, (a) Uniformly in the metal object, (b) Uniformly on the surface of the object, (c) Such that the potential energy of the system is minimised, (d) Such that the total heat loss is minimised, SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 59. Five balls numbered 1 to 5 are suspended using separate threads. Pairs (1, 2), (2, 4) and (4, 1) show, , electrostatic attraction, while pair (2, 3) and (4, 5) show repulsion. Therefore ball 1 must be, (a) Positively charged, , (b)Negatively charged, , (c) Neutral, , (d)Made of metal, , 60. Equal charges q are placed at the four corners A, B, C, D of a square of length a . The magnitude of the, , force on the charge at B will be, (a), , 3q 2, 4πε 0 a, , (b), , 2, , , , 4πε 0 a, , 2  q 2,  4πε a 2, 2, 0, , , (c)  1 + 2, , 4q 2, 2, , , , , , (d)  2 +, , , 1  q 2, 2, 2  4πε 0 a, , 61. Two identical conductors of copper and aluminium are placed in an identical electric fields. The, , magnitude of induced charge in the aluminium will be, (a) Zero, , (b) Greater than in copper, , (c)Equal to that in copper, , (d)Less than in copper, , 62. Two spherical conductors B and C having equal radii and carrying equal charges in them repel each, , other with a force F when kept apart at some distance. A third spherical conductor having same, radius as that of B but uncharged is brought in contact with B, then brought in contact with C and, finally removed away from both. The new force of repulsion between B and C is, (a), , (b), , F/4, , (c) F / 8, , 3F / 4, , (d) 3F / 8, , 63. When a body is earth connected, electrons from the earth flow into the body. This means the body, , is….., (a) Unchanged, , (b) Charged positively, , (c)Charged negatively, , (d)An insulator, , 64. The charges on two sphere are +7µC and – 5µC respectively. They experience a force F. If each of them, , is given and additional charge of – 2µC, the new force of attraction will be, (a) F, , (b) F / 2, , (c) F /, , 3, , (d)2F, , 65. The ratio of electrostatic and gravitational forces acting between electron and proton separated by a, , will be (Charge on electron = 1.6 × 10–19 C, mass of electron = 9.1 × 10–31 kg, mass of, , distance, , 5 × 10 −11 m,, , proton =, , 1.6 × 10 −27 kg, G = 6.7 × 10 −11 Nm 2 / kg 2 ), , (a) 2.36 × 1039, , (b) 2.36 × 1040, –6, , (c)2.34 × 1041, , (d)2.34 × 1042, , –6, , –3, , 66. Two point charges 3 × 10 C and 8 × 10 C repel each other by a force of 6 × 10 N. If each of them is, , given an additional charge – 6 × 106 C, the force between them will be, (a) 2.4 × 10–3 N (attractive), , (b)2.4 × 10–9 N (attractive), , (c) 1.5 × 10–3 N (repulsive), , (d)1.5 × 10–3 N (attractive), , 67. Two equally charged, identical metal spheres A and B repel each other with a force 'F'. The spheres, , are kept fixed with a distance 'r' between them. A third identical, but uncharged sphere C is brought, in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the, net electric force on C is, (a) F, , (b) 3F/4, , (c) F/2, , (d)F/4, , 68. Two charges of equal magnitudes and at a distance r exert a force F on each other. If the charges are, , halved and distance between them is doubled, then the new force acting on each charge is, (a) F / 8, , (b) F / 4, , (c)4 F, , (d)F / 16, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 69. An infinite number of charges, each of charge 1 µC, are placed on the x-axis with co-ordinates x = 1,, , 2, 4, 8, ....∞. If a charge of 1 C is kept at the origin, then what is the net force acting on 1 C charge, (a) 9000 N, , (b) 12000 N, , (c)24000 N, , (d)36000 N, , (c) 1.1 × 1019, , (d)1.1 × 102, , 70. The number of electrons in 1.6C charge will be, , (a), , (b), , 1019, , 10 20, , 71. Four metal conductors having different shapes are mounted on insulating stands and charged. The, , one which is best suited to retain the charges for a longer time is, (a) A sphere, , (b ) Cylindrical, , (c) Pear, , (d) Lightning conductor, , 72. Identify the wrong statement in the following. Coulomb's law correctly describes the electric force that, , (a) Binds the electrons of an atom to its nucleus, (b) Binds the protons and neutrons in the nucleus of an atom, (c) Binds atoms together to form molecules, (d) Binds atoms and molecules together to form solids, ELECTRIC FIELD AND POTENTIAL, 1., , A charge q is placed at the centre of the line joining two equal charges Q. The system of the three, charges will be in equilibrium, if, (a), , 2., , −, , Q, 2, , (b), , −, , q, , is equal to, , Q, 4, , (c), , +, , Q, 4, , (d), , +, , Q, 2, , Inside a hollow charged spherical conductor, the electric potential, (a) Is constant, (b) Varies directly as the distance from the centre, (c) Varies inversely as the distance from the centre, (d) Varies inversely as the square of the distance from the centre, , 3., , Two small spheres each carrying a charge, , q, , are placed, , r, , metre apart. If one of the spheres is taken, , around the other one in a circular path of radius r , the work done will be equal to, , 4., , 5., , (a) Force between them ×r, , (b)Force between them ×2πr, , (c) Force between them/2πr, , (d)Zero, , The electric charge in uniform motion produces, (a) An electric field only, , (b) A magnetic field only, , (c) Both electric and magnetic field, , (d) Neither electric nor magnetic field, , Two charged spheres of radii 10 cm and 15 cm are connected by a thin wire. No current will flow, if, they have, , 6., , (a) The same charge on each, , (b)The same potential, , (c) The same energy, , (d)The same field on their surfaces, , The electric field inside a spherical shell of uniform surface charge density is, (a) Zero, , (b)Constant, less than zero, , (c)Directly proportional to the distance from the centre, , (d)None of the above, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 7., , The electric potential, , V, , at any point O (x, y, z all in metre) in space is given by, , The electric field at the point, (a) 8 V/m along negative, (b) 8 V/m along positive, , ., , is, , X − axis, , X − axis, , (c) 16 V/m along negative, (d) 16 V/m along positive, 8., , (1m, 0, 2m), , V = 4 x 2 volt, , X − axis, , Z − axis, , A hollow metal sphere of radius 5 cm is charged so that the potential on its surface is 10 V. The, potential at the centre of the sphere is, , 9., , (a) 0 V, , (b) 10 V, , (c) Same as at point 5 cm away from the surface, , (d) Same as at point 25 cm away from the surface, , If a unit positive charge is taken from one point to another over an equipotential surface, then, (a) Work is done on the charge, , (b) Work is done by the charge, , (c) Work done is constant, , (d) No work is done, , 10. The electric field lines around a negative point charge are, , (a) Circular, anticlockwise, 11. Charges of +, , 10, × 10 −9 C, 3, , (b) Circular, clockwise, , (c) Radial, inward, , (d) Radial, outward, , are placed at each of the four corners of a square of side, , the intersection of the diagonals is, (a) 150 2 volt, (b) 1500 2 volt, , (c) 900, , 8 cm ., , The potential at, , (d) 900 volt, , 2 volt, , 12. A uniform electric field having a magnitude E0 and direction along the positive X − axis exists. If the, , potential, (a), , V, , is zero at, , V( x ) = + xE 0, , x =0,, , (b), , then its value at, , Vx = − xE 0, , X = +x, , will be, (c) Vx, , (d) Vx, , = + x 2 E0, , = − x 2 E0, , 13. Three charges 2q, − q, − q are located at the vertices of an equilateral triangle. At the centre of the, , triangle, (a) The field is zero but potential is non-zero, (b) The field is non-zero but potential is zero, (c) Both field and potential are zero, (d) Both field and potential are non-zero, 14. Figure shows the electric lines of force emerging from a charged body. If the electric field at A and B, are, , EA, , and, , (a), , E A > EB, , (b), , E A < EB, , (c), , EA =, , EB, r, , (d), , EA =, , EB, , EB, , respectively and if the displacement between A and B is, , r, , then, , A, , r, , r2, , B, , 15. ABC is an equilateral triangle. Charges + q are placed at each corner. The electric field at O will be, , (a), (b), , 1, , 4πε 0 r 2, 1 q, 4πε 0 r, , (c) Zero, (d), , +q, , q, , 1, , r, r, +q, , 3q, , A, , B, , O, , r, +q, C, , 4πε 0 r 2, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 16. In the electric field of a point charge q , a certain charge is carried from, , point, , A, , to, , B, C, D, , and, , E . Then the, , (a) Is least along the path, , AB, , (b) Is least along the path, , AD, , (c) Is zero along all the paths, (d) Is least along, , A, , work done, +q, , AB, AC, AD, , and, , E, , B, , AE, , C, , D, , AE, , 17. The magnitude of electric field intensity E is such that, an electron placed in it would experience an, , electrical force equal to its weight is given by, (a), , mg, e, , (b), , mge, , (c), , e, mg, , (d), , e2, m2, , g, , 18. A conductor with a positive charge, , (a) Is always at, , + ve, , potential, , (b) Is always at zero potential, , (c) Is always at negative potential, , (d) May be at, , + ve ,, , zero or, , −ve, , potential, , 19. An electron and a proton are in a uniform electric field, the ratio of their accelerations will be, , (a) Zero, , (b)Unity, , (c) The ratio of the masses of proton and electron, (d) The ratio of the masses of electron and proton, 20. Two parallel plates have equal and opposite charge. When the space between them is evacuated, the, , electric field between the plates is, , 2 × 10 5 V / m ., , When the space is filled with dielectric, the electric, , field becomes 1 × 10 5 V / m . The dielectric constant of the dielectric material, (a) 1/2, , (b) 1, , (c) 2, , (d) 3, , 21. The insulation property of air breaks down at E = 3 × 10 6 volt/metre. The maximum charge that can be, , given to a sphere of diameter, (a), , (b), , 2 × 10 −2, , 5m, , is approximately (in coulombs), (c) 2 × 10 −4, , 2 × 10 −3, , (d) 2 × 10 −5, , 22. The distance between the two charges 25 µC and 36 µC is 11cm At what point on the line joining the, , two, the intensity will be zero, (a) At a distance of, , 5 cm from 25 µC, , (b) At a distance of, , 5 cm from 36 µC, , (c) At a distance of, , 10 cm from 25 µC, , (d) At a distance of, , 11 cm from 36 µC, , 23. Two spheres A and B of radius 4 cm and 6cm are given charges of 80 µc and 40 µc respectively. If they, , are connected by a fine wire, the amount of charge flowing from one to the other is, (a), , 20 µC from A to B, , (b), , 16 µC, , from, , A to B, , (c), , 32 µC from B, , to, , A, , (d) 32 µC from, , A to B, , 24. A charge particle is free to move in an electric field. It will travel, , (a) Always along a field line, , (b)Along a field line, if its initial velocity is zero, , (c) Along a field line, if it has some initial velocity in the direction of an acute angle with the field line, (d) None of the above, 25. If E is the electric field intensity of an electrostatic field, then the electrostatic energy density is, , proportional to, (a), , E, , (b), , E2, , (c) 1 / E 2, , (d) E 3, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 26. A metallic sphere has a charge of 10 µC . A unit negative charge is brought from A to B both 100 cm, , away from the sphere but A being east of it while, (a) Zero, , (b), , B being, , on west. The net work done is, , (c) −2 / 10, , 2 / 10 joule, , (d) −1 / 10, , joule, , joule, , 27. Two charges +4 e and +e are at a distance x apart. At what distance, a charge q must be placed from, , charge, (a), , + e so that, , it is in equilibrium, (b), , x/2, , (c) x / 3, , 2x / 3, , (d) x / 6, , 28. An uncharged sphere of metal is placed in between two charged plates as shown. The field lines look, , like, + + + + + + +, , + + + + + + +, , – – – – – – –, A, , – – – – – – –, B, , (a), , + + + + + + +, , + + + + + + +, , – – – – – – –, C, , – – – – – – –, D, , (b) B, , A, , (c) C, , (d), , D, , 29. The electric field required to balance a proton of mass 1.7 × 10 −27 kg and charge 1.6 × 10 −19 C is nearly, , (a), , (b), , 1 × 10 −7 V / m, , (c) 1 × 10 7, , 1 × 10 −5 V / m, , (d) 1 × 10 5, , V /m, , V /m, , 30. On rotating a point charge having a charge q around a charge Q in a circle of radius r. The work done will be, , (a), , (b), , q × 2πr, , q × 2πQ, r, , (c) Zero, , (d), , Q, 2ε 0 r, , 31. Two point charges Q and – 3Q are placed at some distance apart. If the electric field at the location, , of, (a), , Q, , is, , E, , then at the locality of, (b), , −E, , −3Q ,, , it is, (c) −3 E, , E/3, , (d) − E / 3, , 32. The number of electrons to be put on a spherical conductor of radius 0.1 m to produce an electric field, , of, , 0.036 N / C, , just above its surface is, , (a), , 2.7 × 10, , (b), , 5, , (c) 2.5 × 10 5, , 2.6 × 10 5, , (d) 2.4 × 10 5, , 33. Two plates are 2 cm apart, a potential difference of 10 volt is applied between them, the electric field, , between the plates is, (a), , (b), , 20 N / C, , (c), , 500 N / C, , (d) 250, , 5N /C, , N /C, , 34. The intensity of the electric field required to keep a water drop of radius 10 −5 cm just suspended in air, , when charged with one electron is approximately, (a), , (b), , 260 volt / cm, , 260 newton / coulomb, , (c) 130 volt / cm, , (d) 130 newton / coulomb, , (g = 10 newton / kg, e = 1.6 × 10 −19 coulomb ), , 35. Conduction electrons are almost uniformly distributed within a conducting plate. When placed in an, , electrostatic field, (a) Is zero, , E,, , the electric field within the plate, (b) Depends upon, , E, , (c)Depends upon, , E, , (d) Depends upon the atomic number of the conducting element, 36. Three particles, each having a charge of 10 µC are placed at the corners of an equilateral triangle of, , side, , 10 cm . The, , (a) Zero, , electrostatic potential energy of the system is (Given, (b) Infinite, , (c) 27 J, , 1, = 9 × 10 9 N − m 2 / C 2 ), 4πε 0, , (d) 100 J, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 37. The electric field near a conducting surface having a uniform surface charge density σ is given by, , (a), , σ, ε0, , and is parallel to the surface, , (b), , 2σ, , (c), , σ, ε0, , and is normal to the surface, , (d), , 2σ, , ε0, ε0, , and is parallel to the surface, and is normal to the surface, , 38. There is an electric field E in X-direction. If the work done on moving a charge 0.2 C through a, , distance of, (a), , 2m, , along a line making an angle, (b), , 3 N /C, , 60 °, , with the X-axis is 4.0, what is the value of, (c) 5 N / C, , 4 N /C, , E, , (d) 6N/C, , 39. Four equal charges Q are placed at the four corners of a square of each side is ' a' . Work done in, , removing a charge – Q from its centre to infinity is, (a) 0, , (b), , 2Q 2, 4πε 0a, , (c), , 2Q 2, πε 0 a, , (d), , Q2, 2πε 0 a, , 40. A particle A has charge +q and a particle B has charge + 4 q with each of them having the same mass., , When allowed to fall from rest through the same electric potential difference, the ratio of their, v, speed A will become, vB, (a) 2 : 1, (b) 1 : 2, (c) 1 : 4, (d) 4 : 1, 41. A deuteron and an α − particle are placed 1 Å apart in air. The magnitude of electric field due to, , deuteron at, , α − particle is, , (b) 2.88 ×1011 N / C, , (a) Zero, , (c) 1.44 ×1011 N / C, , (d) 5.76 ×1011 N / C, , 42. Angle between equipotential surface and electric field lines is, , (a) Zero, , (b), , (c), , 180 °, , (d), , 90 °, , 45 °, , 43. Below figures (1) and (2) represent electric field lines. Which is correct statement, , (a) Figure (1) represents magnetic lines of force, (b) Figure (2) represents magnetic lines of force, (c) Figure (1) represents electric lines of force, , (2), , (1), , (d) Both figure (1) and figure (2) represent magnetic lines of force, 44. The unit of electric field is not equivalent to, , (a), , (b), , N /C, , (d) J / C − m, , (c) V / m, , J/C, , 45. A flat circular disc has a charge +Q uniformly distributed on the disc. A charge +q is thrown with, , kinetic energy, , E, , towards the disc along its normal axis. The charge, , (a) Hit the disc at the centre, , q, , will, , (b) Return back along its path after touching the disc, , (c) Return back along its path without touching the disc, (d) Any of the above three situations is possible depending on the magnitude of E, 46. At what distance from a point charge the electric field is 500 V / m and the potential is 3000 V ?, , (a) 6 m, (b) 12 m, 47. The magnitude of electric field, (a) Is same throughout, (c) Varies as, , 1/ r ,, , where, , (d) Varies as, , 1/ r 2 ,, , where, , E, , (c) 36 m, (d) 144 m, in the annular region of a charged cylindrical capacitor, (b)Is higher near the outer cylinder than near the inner cylinder, , is the distance from the axis, , r, r, , is the distance from the axis, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 48. A metallic solid sphere is placed in a uniform electric field., , 1, , 1, , 2, , 2, , (b) 2, , 3, , 3, , (d) 4, , 4, , 4, , The field lines follow the path(s) shown in figure as, (a) 1, (c) 3, , 49. The distance between a proton and electron both having a charge 1.6 × 10 −19 coulomb , of a hydrogen, , atom is, (a), , 10 −10 metre, , . The value of intensity of electric field produced on electron due to proton will be, , 2.304 × 10 −10 N / C, , (b), , (c) 16 V / m, , 14 .4 V / m, , (d) 1.44 × 10 11 N / C, , 50. What is the magnitude of a point charge due to which the electric field at 30 cm away has a magnitude, 2 newton / coulomb, , (a), , ?, , 2 × 10 −11 coulomb, , [1 / 4πε 0 = 9 × 10 9 Nm 2 / C 2 ], , (b), , 3 × 10 −11 coulomb, , (c) 5 × 10 −11 coulomb, , (d) 9 × 10 −11 coulomb, , 51. Two charge + q and − q are situated at a certain distance. At the point exactly midway between them, , (a) Electric field and potential both are zero, , (b) Electric field is zero but potential is not zero, , (c) Electric field is not zero but potential is zero, , (d) Neither electric field nor potential is zero, , 52. Two positive charges of 20 coulomb and Q coulomb are situated at a distance of 60 cm . The neutral point, , between them is at a distance of, (a) 30 C, (b) 40 C, , 20 cm, , from the, , 20 coulomb, , charge. Charge, , (c) 60 C, , 53. In the figure the charge Q is at the centre of the circle., , is, (d) 80 C, , Q, , P, , K, , Work done is maximum when another charge is taken from point P to, (a) K, L, Q, (b) L, (c) M, M, N, (d) N, 54. A mass m = 20 g has a charge q = 3.0 mC . It moves with a velocity of 20 m / s and enters a region of, electric field of 80 N / C in the same direction as the velocity of the mass. The velocity of the mass after, 3 seconds in this region is, (a) 80 m / s, (b) 56 m / s, (c) 44 m / s, (d) 40 m / s, 55. Four identical charges + 50 µC each are placed, one at each corner of a square of side 2 m . How much, external energy is required to bring another charge of, (a), , (b), , 64 J, , + 50 µC, , from infinity to the centre of the square, , (c) 16 J, , 41 J, , (d) 10 J, , 56. In Millikan's oil drop experiment an oil drop carrying a charge Q is held stationary by a potential, , difference, , 2400 V, , between the plates. To keep a drop of half the radius stationary the potential, , difference had to be made, (a), , Q, 4, , 600 V, , . What is the charge on the second drop, , (b) Q, , (d) 3Q, , (c) Q, , 2, , 2, , 57. A charge of 5 C experiences a force of 5000 N when it is kept in a uniform electric field. What is the, , potential difference between two points separated by a distance of, (a), , 10 V, , (b), , (c) 1000 V, , 250 V, , 1 cm, , (d) 2500 V, , 58. Two insulated charged conducting spheres of radii 20 cm and 15 cm respectively and having an equal, , charge of 10 C are connected by a copper wire and then they are separated. Then, (a) Both the spheres will have the same charge of 10 C, (b) Surface charge density on the, , 20 cm, , sphere will be greater than that on the, , 15 cm, , sphere, , (c) Surface charge density on the, , 15 cm, , sphere will be greater than that on the, , 20 cm, , sphere, , (d) Surface charge density on the two spheres will be equal, SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 59. Equal charges q are placed at the vertices A and B of an equilateral triangle ABC of side a . The, , magnitude of electric field at the point, (a), , q, , (b), , 4πε 0 a 2, , C, , is, , 2q, , [MP PMT 1997], (c), , 4πε 0 a 2, , 3q, , (d), , 4πε 0 a 2, , q, 2πε 0 a 2, , 60. Two equal charges q are placed at a distance of 2a and a third charge −2q is placed at the midpoint., , The potential energy of the system is, (a), , q, , 2, , (b), , 8πε 0 a, , [MP PMT 1997], , 2, , 6q, 8πε 0 a, , (c) −, , 7q 2, 8πε 0 a, , (d), , 9q 2, 8πε 0 a, , 61. Two point charges 100 µ C and 5 µ C are placed at points A and B respectively with AB = 40 cm . The, , work done by external force in displacing the charge, π, , ABC =, , (a), , 2, , and, , 5µC, , from, , B, , to, , C,, , where, , BC = 30 cm ,angle, , 1, = 9 × 10 9 Nm 2 / C 2, 4πε 0, , (b), , 9J, , 81, J, 20, , 9, J, 25, , (d) − 9 J, , (c) Vm, , (d)N/m, , (c), , 4, , 62. The SI unit of electric field is, , (a) N/C, , (b) J/C, , 63. Equal charges are given to two spheres of different radii. The potential will, , (a) Be more on the smaller sphere, , (b) Be more on the bigger sphere, , (c) Be equal on both the spheres, , (d) Depend on the nature of the materials of the spheres, , 64. An alpha particle is accelerated through a potential difference of 10 6 volt . Its kinetic energy will be, , (a), , (b), , 1 MeV, , 2 MeV, , (c), , (d) 8 MeV, , 4 MeV, , 65. A charge of 5 C is given a displacement of 0.5 m . The work done in the process is 10 J . The potential, , difference between the two points will be, (a), , (b), , 2V, , 0.25 V, , (c) 1 V, , (d) 25 V, , 66. The electric potential V is given as a function of distance x (metre) by V = (5 x 2 + 10 x − 9) volt . Value of, , electric field at, (a), , x =1m, , is, (b), , 20 V / m, , 6V /m, , (c) 11 V / m, , (d) −23 V / m, , 67. Two metal pieces having a potential difference of 800 V are 0.02 m apart horizontally. A particle of, , mass, , 1.96 × 10 −15 kg, , is suspended in equilibrium between the plates. If, , e, , is the elementary charge, then, , charge on the particle is, (a), , (b), , e, , 3e, , (c) 6e, , (d) 8e, , 68. The figure shows some of the electric field lines corresponding to an electric field. The figure suggests, , (a), , E A > E B > EC, , (b), , E A = E B = EC, , (c), , E A = EC > E B, , (d), , E A = EC < E B, , A, , B, , C, , 69. Two spheres of radius a and b respectively are charged and joined by a wire. The ratio of electric, , field of the spheres is, (a), , a/b, , (b), , b/a, , (c) a 2 / b 2, , (d) b 2 / a 2, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 70. A particle of mass m and charge q is placed at rest in a uniform electric field E and then released., , The kinetic energy attained by the particle after moving a distance, (a), , (b), , qEy 2, , (c), , qE 2 y, , y, , is, (d) q 2 Ey, , qEy, , 71. A hollow insulated conducting sphere is given a positive charge of 10 µ C . What will be the electric, , field at the centre of the sphere if its radius is 2 meters, (a) Zero, , (b), , (c) 20 µ Cm −2, , 5 µ Cm −2, , (d) 8 µ Cm −2, , 72. An electron of mass me initially at rest moves through a certain distance in a uniform electric field in, , time, , t1 ., , A proton of mass, , mp, , also initially at rest takes time, , t2, , to move through an equal distance in, , this uniform electric field. Neglecting the effect of gravity, the ratio of, (a) 1, , (b), , (c) (me / m p )1 / 2, , (m p / me )1 / 2, , t 2 / t1, , is nearly equal to, , (d) 1836, , 73. A cube of side b has a charge q at each of its vertices. The electric field due to this charge, , distribution at the centre of this cube will be, (a), , (b), , q / b2, , (c) 32q / b 2, , q / 2b 2, , (d) Zero, , 74. A charged water drop whose radius is 0.1 µm is in equilibrium in an electric field. If charge on it is, , equal to charge of an electron, then intensity of electric field will be (g = 10 ms −2 ), (a), , (b), , 1.61 N / C, , (c) 262 N / C, , 26 .2 N / C, , (d) 1610 N / C, , 75. Four charges are placed on corners of a square as shown in figure having side of 5 cm ., , If Q is 1µC, then electric field at centre will be, (a), , 1.02 × 10 7 N / C, , upwards, , (b), , 2.04 × 10 7 N / C, , downwards, , (c), , 2.04 × 10 7 N / C, , upwards, , (d), , 1.02 × 10 7 N / C, , downwards, , Q, , – 2Q, , –Q, , + 2Q, , 76. A sphere of radius 1 cm has potential of 8000 V , then energy density near its surface will be, , (a), , 64 × 10 5 J / m 3, , (b), , (c) 32 J / m 3, , 8 × 10 3 J / m 3, , (d) 2.83 J / m 3, , 77. Point charges +4 q, − q and +4 q are kept on the x − axis at points x = 0, x = a and x = 2a respectively, then, , (a) Only, , is in stable equilibrium, , (b) None of the charges are in equilibrium, , (c) All the charges are in unstable equilibrium, , (d) All the charges are in stable equilibrium, , q, , 78. Two point charges of 20 µ C and 80 µ C are 10 cm apart. Where will the electric field strength be zero, , on the line joining the charges from, (a), , (b), , 0.1 m, , 20 µ C, , charge, (c), , 0.04 m, , 0.033 m, , (d) 0.33 m, , 79. How much kinetic energy will be gained by an α − particle in going from a point at 70 V to another, , point at, (a), , 40 eV, , 50 V, , (b), , (c) 40 MeV, , 40 keV, , (d) 0 eV, , 80. If a charged spherical conductor of radius 10 cm has potential V at a point distant 5 cm from its centre,, , then the potential at a point distant, (a), , 1, V, 3, , (b), , 2, V, 3, , 15 cm, , from the centre will be, (c) 3 V, 2, , (d) 3V, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 81. Two unlike charges of magnitude q are separated by a distance 2d . The potential at a point midway, , between them is, (a) Zero, , (b), , 1, 4πε 0, , (c), , 1 q, ., 4πε 0 d, , (d), , 1 2q, ., 4πε 0 d 2, , 82. What is the potential energy of the equal positive point charges of 1µC each held 1 m apart in air, , (a), , (b), , 9 × 10 −3 J, , (c), , 9 × 10 −3 eV, , 2eV / m, , (d)Zero, , 83. An oil drop having charge 2e is kept stationary between two parallel horizontal plates 2.0 cm apart, , when a potential difference of 12000 volts is applied between them. If the density of oil is 900 kg/m3,, the radius of the drop will be, (a) 2.0 × 10 −6 m, , (b), , (c), , 1.7 × 10 −6 m, , 1.4 × 10 −6 m, , (d) 1.1 × 10 −6 m, , 84. The ratio of momenta of an electron and an α-particle which are accelerated from rest by a, , potential difference of 100 volt is, (a) 1, , (b), , 2me, mα, , (c), , me, mα, , (d), , me, 2mα, , 85. A proton is accelerated through 50,000 V. Its energy will increase by, , (a) 5000 eV, , (b), , 8 × 10 −15 J, , (c)5000 J, , (d)50,000 J, , 86. When a proton is accelerated through 1V, then its kinetic energy will be, , (a) 1840 eV, , (b) 13.6 eV, , (c) 1 eV, , (d)0.54 eV, , 87. An electron enters between two horizontal plates separated by 2mm and having a potential, , difference of 1000V. The force on electron is, (a), , 8 × 10 −12 N, , (b), , 8 × 10 −14, , N, , (c) 8 × 10 9 N, , (d) 8 × 10 14 N, , 88. Two metal spheres of radii R1 and R2 are charged to the same potential. The ratio of charges on the, , spheres is, (a), , (b), , R1 : R2, , (c) R12 : R22, , R1 : R2, , (d), , R13: R23, , 89. Electric charges of +10 µC, + 5 µC, − 3µC and +8 µC are placed at the corners of a square of side, , 2, , m. the, , potential at the centre of the square is, (a) 1.8 V, , (b), , 1.8 × 10 6, , V, , (c), , 1.8 × 10 5 V, , (d) 1.8 × 10 4 V, , 90. What is the magnitude of a point charge which produces an electric field of 2 N/coulomb at a, , distance of 60 cm ( 1 / 4πε 0 = 9 × 10 9 N − m 2 / C 2 ), (a), , 8 × 10 −11 C, , (b), , 2 × 10 −12 C, , (c), , 3 × 10 −11 C, , (d) 6 × 10 −10 C, , 91. The electric field due to a charge at a distance of 3 m from it is 500 N/coulomb. The magnitude of the, , charge is, ,  1, N − m2 , = 9 × 10 9, , , coulomb 2 ,  4πε 0, , (a) 2.5 µC, , (b) 2.0 µC, , (c)1.0 µC, , (d) 0.5 µC, , 92. Two charges of 4 µC each are placed at the corners A and B of an equilateral triangle of side length, , 0.2 m in air. The electric potential at C is, (a), , 9 × 10 4 V, , (b), , 18 × 10 4 V, ,  1, N - m2 , = 9 × 10 9, , , C 2 ,  4πε 0, , (c), , 36 × 10 4 V, , (d) 36 × 10 −4 V, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 93. Electric field strength due to a point charge of 5 µC at a distance of 80 cm from the charge is, , (a), , 8 × 10 4 N/C, , (b), , 7 × 10 4 N/C, , (c), , 5 × 10 4 N/C, , (d) 4 × 10 4 N/C, , 94. Ten electrons are equally spaced and fixed around a circle of radius R. Relative to V = 0 at infinity, the, , electrostatic potential V and the electric field E at the centre C are, (a) V ≠ 0 and, , , E≠0, , (b), , and, , V≠0, , , E=0, , , E=0, , (c) V = 0 and, , , E≠0, , (d) V = 0 and, , 95. Two positive point charges of 12 µC and 8 µC are 10cm apart. The work done in bringing them 4 cm closer is, , (a) 5.8 J, , (b) 5.8 eV, , (c) 13 J, , (d)13 eV, , 3, , 96. Three identical point charges, as shown are placed at the vertices of, , an isosceles right angled triangle. Which of the numbered vectors, , M, , coincides in direction with the electric field at the mid-point M of the hypotenuse, (a) 1, , (b) 2, , (c)3, , 2, 4, , 1, , (d)4, , 97. The displacement of a charge Q in the electric field E = e1ˆi + e2ˆj + e3kˆ is rˆ = aˆi + bˆj . The work done is, , (a), , (b), , Q(ae1 + be 2 ), , (c) Q(e1 + e2 ), , Q (ae1 )2 + (be 2 )2, , (d) Q(, , a2 + b 2, , e12 + e22 ) (a + b), , 98. The potential at a point, due to a positive charge of 100 µC at a distance of 9m, is, , (a), , 10 4 V, , (b), , 10 5 V, , (c) 10 6 V, , (d) 10 7 V, , 99. There is a solid sphere of radius ‘R’ having uniformly distributed charge. What is the relation, , between electric field ‘E’ (inside the sphere) and radius of sphere ‘R’ is, (a), , (b), , E ∝ R−2, , (c) E ∝, , E ∝ R −1, , 1, R3, , (d) E ∝ R 2, , 100. Two charges +5 µC and +10 µC are placed 20 cm apart. The net electric field at the mid-Point between, , the two charges is, (a), , 4.5 × 10 6, , (c), , 13 .5 × 10 6, , N/C directed towards, N/C directed towards, , N/C directed towards, , +10 µC, , (d) 13.5 × 10 6 N/C directed towards, , +10 µC, , (b), , +5 µC, +5 µC, , 4.5 × 10 6, , 101. Which of the following is deflected by electric field, , (a) X-rays, 102., , (b), , γ, , -rays, , (c) Neutrons, , As shown in the figure, charges, , +q, , and, , −q, , (d), , are placed at the vertices, , triangle. The potential at the vertex A is, (a), (c), 103., , 1, 4πε 0, 1, 4πε 0, , ., , ., , 2q, , q, , (d), , a2 + b 2, , 1, 4πε 0, , B, , -particles, , and, , C, , of an isosceles, , A, , (b) Zero, , a2 + b 2, , α, , a, , ., , b, , (−q), , B, , a2 + b 2, , b, –q, , +q, , C, , Consider the points lying on a straight line joining two fixed opposite charges. Between the, , charges there is, (a) No point where electric field is zero, , (b) Only one point where electric field is zero, , (c) No point where potential is zero, , (d) Only one point where potential is zero, , 104., , A charged particle of mass, , strength, (a), , 10 7 NC −1, , − 20 × 10 −5 µC, , 5 × 10 −5 kg, , is held stationary in space by placing it in an electric field of, , directed vertically downwards. The charge on the particle is, (b), , − 5 × 10 −5 µC, , (c), , 5 × 10 −5 µC, , (d) 20 × 10 −5 µC, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 105., , Three charges, , Q, + q, , and, , are placed at the vertices of a right-angled isosceles triangle as, , +q, , shown. The net electrostatic energy of the configuration is zero if Q is equal to, (a), (b), , −q, −2q, 2+ 2, , (c), , −2q, , (d), , +q, , 106., , Q, , 1+ 2, , +q, , Two electric charges, , 12 µC, , and, , −6 µC, , +q, , a, , are placed 20 cm apart in air. There will be a point P on the, , line joining these charges and outside the region between them, at which the electric potential is, zero. The distance of P from, (a) 0.10 m, 107., , −6 µC, , charge is, , (b) 0.15 m, , (c) 0.20 m, , (d)0.25 m, , In the given figure distance of the point from A where the electric field is zero is, (b) 10 cm, , (c) 33 cm, , (d) None of these, , 108., , B, , A, , (a) 20 cm, , 10 µC, , 20 µC, 80 cm, , Figures below show regular hexagons, with charges at the vertices. In which of the following, , cases the electric field at the centre is not zero, q, , q, , q, , q, q, , q, , q, , q, , 2q, , q, , q, , (a) 1, , 2q, , 2q, , –q, , 2q, , q, , q, , q, , q, , (2), , (1), , 109., , –q, , 2q, 2q, , 2q, , q, , (3), , (b)2, , (4), , (c) 3, , (d)4, , An electron is moving towards x-axis. An electric field is along y-direction then path of electron is, , (a) Circular, , (b) Elliptical, , (c)Parabola, , (d) Hyperbola, , 110. An electron enters in an electric field with its velocity in the direction of the electric field lines. Then, , (a) The path of the electron will be a circle, , (b) The path of the electron will be a parabola, , (c) The velocity of the electron will decrease, , (d) The velocity of the electron will increase, , 111. An electron of mass m and charge e is accelerated from rest through a potential difference V in, , vacuum. The final speed of the electron will be, (a) V e / m, (b) eV / m, (c) 2eV / m, (d) 2eV / m, 112. The radius of a soap bubble whose potential is 16V is doubled. The new potential of the bubble will be, (a) 2V, (b) 4V, (c), 8V, (d), 16V, 113. The dimension of, , ½ ε0 E 2, , (ε 0 : permittivity of free space;, , −1, , (a) MLT, (b) ML2 T −2, (c), ML−1 T −2, 114. In the rectangle, shown below, the two corners have charges, The work done in moving a charge, (a) 2.8 J, , (b) 3.5 J, , (c) 4.5 J, , (d) 5.5 J, , +3.0 µC, , from, , B, , to, , A, , E : electric, , (d), q1 = −5 µC, , is (take, , field) is, ML2 T −1, , and, , 1 / 4πε 0 = 10, , 10, , q 2 = +2.0 µC ., , N - m2 / C 2 ), A, , q1, , 5 cm, , B, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR, , 15 cm, , q2

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Electrostatics : Electric charge, Electric Field and Electric potential, 115. A cube of a metal is given a positive charge Q. For the above system, which of the following, , statements is true, (a) Electric potential at the surface of the cube is zero, , (b)Electric potential within the cube is zero, , (c) Electric field is normal to the surface of the cube, , (d) Electric field varies within the cube, , 116. If q is the charge per unit area on the surface of a conductor, then the electric field intensity at a, , point on the surface is, (a), ,  q, , ε,  0, , , , , , , (c), ,  q, , ε,  0, , , , , , , 117., , , , , , , normal to surface, , (d) , ,  q,  2ε 0, , , , , , , tangential to surface, , has a charge, , (+ Q), , (b) , , tangential to surface, , A hollow conducting sphere of radius, , potential within the sphere at a distance, (a) Zero, 118., ,  q,  2ε 0, , normal to surface, , (b), , R, r=, , 1 Q, 4πε 0 r, , R, 3, , on its surface. What is the electric, , from its centre, (c), , 1 Q, 4πε 0 R, , (d), , 1 Q, 4πε 0 r 2, , A spherical conductor of radius 2m is charged to a potential of 120 V. It is now placed inside, , another hollow spherical conductor of radius 6m. Calculate the potential to which the bigger sphere, would be raised, (a) 20 V, 119., , (b) 60 V, , A charge, , charge, , (+ Q), , (−q), , (c) 80 V, , and another charge, , fixed at B, the charge, , (+ Q), , (−q), , are kept at two points A and B respectively. Keeping the, , at A is moved to another point C such that ABC forms an, , equilateral triangle of side l. The net work done in moving the charge, (a), , 1 Qq, 4πε 0 l, , (b), , 1 Qq, 4πε 0 l 2, , (d) 40 V, , (c), , 1, Qql, 4πε 0, , (−q), , is, (d)Zero, , 120., , A particle of mass ‘m’ and charge ‘q’ is accelerated through a potential difference of V volt, its, energy will be, (a), , qV, , (b), , mqV, , (c)  q V, m, , (d), , q, mV, , 121., , Two spheres A and B of radius ‘a’ and ‘b’ respectively are at same electric potential. The ratio of, the surface charge densities of A and B is, , (a), , a, b, , (b), , b, a, , 2, , (c) a 2, b, , 2, , (d) b 2, a, , 122., , Potential at a point x-distance from the centre inside the conducting sphere of radius R and, charged with charge Q is, (a), , Q, R, , (b), , Q, x, , (c), , Q, x2, , (d) xQ, , 123., , Electric field intensity at a point in between two parallel sheets with like charges of same surface, charge densities (σ ) is, (a), , 124., , σ, 2ε 0, , (b), , σ, ε0, , (c)Zero, , (d) 2σ, ε0, , In an hydrogen atom, the electron revolves around the nucleus in an orbit of radius, , Then the electrical potential produced by the nucleus at the position of the electron is, (a) – 13.6 V, , (b) – 27.2, , (c)27.2 V, , (d) 13.6 V, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR, , 0.53 × 10 −10 m .

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Electrostatics : Electric charge, Electric Field and Electric potential, 125., , Consider two point charges of equal magnitude and opposite sign separated by a certain distance., The neutral point due to them, (a) Does not exist, , (b)Will be in mid way between them, , (c) Lies on the perpendicular bisector of the line joining the two, , (d)Will be closer to the negative charge, , 126., , Two small spherical balls each carrying a charge, , Q = 10 µC, , (10 micro-coulomb) are suspended by, , two insulating threads of equal lengths 1m each, from a point fixed in the ceiling. It is found that in, equilibrium threads are separated by an angle, tension in the threads (Given:, , 60 o, , between them, as shown in the figure. What is the, , 1, = 9 × 10 9 Nm / C 2 ), (4πε 0 ), , 60o, , (a) 18 N, (b) 1.8 N, , Q, , Q, , (c) 0.18 N, (d) 180 N, 127., , A ball of mass 1 g and charge 10 −8 C moves from a point A. where potential is 600 volt to the, , point B where potential is zero. Velocity of the ball at the point B is 20 cm/s. The velocity of the ball, at the point A will be, (a) 22.8 cm/s, 128., , 129., , (c)16.8 m/s, , (d)168 m/s, , The acceleration of an electron in an electric field of magnitude 50 V/cm, if e/m value of the, , electron is, (a), , (b) 228 cm/s, , 1.76 × 10 11 C/kg,, , 8.8 × 10 14 m/s, , 2, , Three charges, , is, , (b), Q, (+ q), , m/s2, , 6.2 × 10 13, , and, , (+ q), , (c) 5.4 × 10 12 m/s2, , (d)Zero, , are placed at the vertices of an equilateral triangle of side l as, , shown in the figure. If the net electrostatic energy of the system is zero, then Q is equal to, (a), ,  q, − ,  2, , (b), , (−q), , (c), , (+ q), , Q, , l, , (d) Zero, 130., , +q, , l, , l, , +q, , A positively charged particle moving along x-axis with a certain velocity enters a uniform electric, , field directed along positive y-axis. Its, (a) Vertical velocity changes but horizontal velocity remains constant, (b) Horizontal velocity changes but vertical velocity remains constant, (c) Both vertical and horizontal velocities change, (d) Neither vertical nor horizontal velocity changes, 131., , (a), 132., , Electric potential at any point is, 3 2, , (b), , V = −5 x + 3y + 15 z ,, , 4 2, , then the magnitude of the electric field is, , (c) 5, , 2, , (d)7, , The work done in bringing a 20 coulomb charge from point A to point B for distance 0.2m is 2J., , The potential difference between the two points will be (in volt), (a) 0.2, 133., , (b) 8, , (c) 0.1, , (d)0.4, , A hollow sphere of charge does not produce an electric field at any, , (a) Point beyond 2 m (b) Point beyond 10 m, , (c)Interior point, , (d)Outer point, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 134., , If, , 4 × 10 20 eV, , energy is required to move a charge of 0.25 coulomb between two points. Then what, , will be the potential difference between them, (a) 178 V, 135., , (a), 136., , (b) 256 V, , 1.6 × 10 −17 J, , A drop of, , (b), 10 −6 kg, , 1.6 × 10 21 J, , water carries, , 10 −6 C, , (d) 1.6 × 10 −34 J, , charge. What electric field should be applied to balance its, , (b) 10 V/m downward, , (c)0.1 V/m downward, , (d)0.1 V/m upward, , A charged particle of mass 0.003 gm is held stationary in space by placing it in a downward, , direction of electric field of, 138., , (c) 1.6 × 10 −29 J, , g = 10 m / s2 ), , (a) 10 V/m upward, , (a), , (d)712 V, , Kinetic energy of an electron accelerated in a potential difference of 100 V is, , weight (assume, 137., , (c)356 V, , 6 × 10 4 N / C . Then, , 5 × 10 −4 C, , (b), , 5 × 10 −10 C, , Two point charges, , +9e, , and, , the magnitude of the charge is, (c) − 18 × 10 −6 C, , (d) − 5 × 10 −9 C, , are at 16 cm away from each other. Where should another charge, , +e, , q be placed between them so that the system remains in equilibrium, (a) 24 cm from, 139., , (b) 12 cm from, , +9e, , 140., , +e, , (d)12 cm from, , +e, , If 3 charges are placed at the vertices of equilateral triangle of charge ‘q’ each. What is the net, , potential energy, if the side of equilateral, (a), , (c) 24 cm from, , +9e, , 1, , q, 4πε 0 l, , 2, , (b), , 2q, 4πε 0 l, 1, , ∆, , is l cm, , 2, , (c), , 3q 2, 4πε 0 l, 1, , (d), , 4q2, 4πε 0 l, 1, , The distance between charges 5 × 10 −11 C and − 2.7 × 10 −11 C is 0.2 m. The distance at which a third charge, , should be placed in order that it will not experience any force along the line joining the two charges is, , (a) 0.44 m, 141., , (b) 0.65 m, , If identical charges, , energy of charge, (a), , 8 2q 2, 4πε 0b, , (+ q), , (−q), , (c)0.556 m, , (d) 0.350 m, , are placed at each corner of a cube of side b, then electric potential, , which is placed at centre of the cube will be, (b), , − 8 2q 2, πε 0b, , (c) − 4, , 2q 2, πε 0b, , (d), , − 4q2, 3πε 0b, , 142. An electron having charge ‘e’ and mass ‘m’ is moving in a uniform electric field E. Its acceleration is, , (a), 143., , e2, m, , (b), , E 2e, m, , (d) mE, , (c) eE, m, , e, , Cathode rays travelling from east to west enter into region of electric field directed towards north, , to south in the plane of paper. The deflection of cathode rays is towards, (a) East, 144., , (b) South, , (c)West, , (d)North, , An α -particle is accelerated through a potential difference of 200V. The increase in its kinetic, , energy is, (a) 100 eV, 145., , (b) 200 eV, , A simple pendulum of period, , (c)400 eV, T, , (d)800 eV, , has a metal bob which is negatively charged. If it is allowed to, , oscillate above a positively charged metal plate, its period will, (a) Remains equal to T (b) Less than, 146., , A charged particle of mass, , m, , (c) Greater than, , T, , and charge, , q, , T, , (d)Infinite, , is released from rest in a uniform electric field, , Neglecting the effect of gravity, the kinetic energy of the charged particle after ‘t’ second is, (a), , Eq 2m, 2t 2, , (b), , 2E 2 t 2, mq, , (c) E, , 2, , q2t 2, 2m, , (d) Eqm, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR, , t, , E.

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Electrostatics : Electric charge, Electric Field and Electric potential, 147., , A proton is about 1840 times heavier than an electron. When it is accelerated by a potential, , difference of 1 kV, its kinetic energy will be, (a) 1840 keV, 148., , (a), 149., , (b) 1/1840 keV, , A conducting sphere of radius, (b), , 3.6 × 10 6 N / C, , R = 20, , (c)1 keV, cm is given a charge, , Q = 16 µC . What is E, , (c)Zero, , 1.8 × 10 6 N / C, , A thin spherical conducting shell of radius, , R, , (q + Q) 2, 4πε 0 R, , (b), , at centre, (d) 0.9 × 10 6 N / C, , has a charge q. Another charge Q is placed at the, , centre of the shell. The electrostatic potential at a point p a distance, (a), , (d)920 keV, , 2Q, 4πε 0 R, , (c), , R, 2, , from the centre of the shell is, , 2Q, 2q, −, 4πε 0 R 4πε 0 R, , (d), , 2Q, q, +, 4πε 0 R 4πε 0 R, , 150. A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in, figure. Let VA , VB , VC be the potentials at points A, B and C respectively. Then, , (a), , (b) VB, , VC > VB, , (c) VA, , > VC, , > VB, , (d) VA, , = VC, , A, , C, , 151. A point charge is kept at the centre of a metallic insulated spherical shell. Then, , (a) Electric field outside the sphere is zero, , P, , B, , (b) Electric field inside the sphere is zero, (c) Net induced charge on the sphere is zero, (d) Electric potential inside the sphere is zero, 152. An electron moving with the speed 5 × 10 6 per second is shooted parallel to the electric field of, , intensity 103 N/C . Field is responsible for the retardation of motion of electron. Now evaluate the, distance travelled by the electron before coming to rest for an instant (m= 9 ×10−31 kg. e, (a) 7 m, 153., , (b) 0.7 mm, , (c)7 cm, , An electron enters in high potential region, , V2, , = 1.6 × 10 −19 C), , (d) 0.7 cm, , from lower potential region, , V1, , then its velocity, , (a) Will increase, (b) Will change in direction but not in magnitude, (c) No change in direction of field, (d) No change in direction perpendicular to field, 154., , The electric potential at the surface of an atomic nucleus (Z = 50) of radius 9.0× 10 −13 cm is, , (a) 80 volts, 155., , (b) 8 ×, , 10 6 volts, , (c) 9 volts, , (d)9 ×, , 10 5 volts, , A pellet carrying charge of 0.5 coulombs is accelerated through a potential of 2,000 volts. It, , attains a kinetic energy equal to, (a) 1000 ergs, 156., , (b) 1000 joules, , (c) 1000 kWh, , (d)500 ergs, , A particle has a mass 400 times than that of the electron and charge is double than that of a, , electron. It is accelerated by 5V of potential difference. Initially the particle was at rest, then its final, kinetic energy will be, (a) 5 eV, 157., , (b) 10 eV, , An electron (charge =, , 1.6 × 10 −19, , (c) 100 eV, , (d) 2000 eV, , coulomb) is accelerated through a potential of 1,00,000 volts. The, , energy required by the electron is, (a), , 1.6 × 10 −24, , joule, , (b), , 1.6 × 10 −14 erg, , (c) 0.53 × 10 −14 joule, , (d) 1.6 × 10 −14 joule, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 158., , The charge given to a hollow sphere of radius 10 cm is 3.2×10–19 coulomb. At a distance of 4 cm, , from its centre, the electric potential will be, (a), 159., , [MP PMT 1990], , (b)288 volts, , 28 .8 × 10 −9 volts, , (c)2.88 volts, , (d)Zero, , Work done in moving a positive charge on an equipotential surface is, , (a) Finite, positive but not zero, , (b) Finite, negative but not zero, , (c) Zero, , (d) Infinite, , 160., , A charge of 10 e.s.u. is placed at a distance of 2 cm from a charge of 40 e.s.u. and 4 cm from, , another charge of 20 e.s.u. The potential energy of the charge 10 e.s.u. is (in ergs), (a) 87.5, 161., , (b)112.5, , (c)150, , (d)250, , A table tennis ball which has been covered with conducting paint is suspended by a silk thread so, , that it hang between two plates, out of which one is earthed and other is connected to a high voltage, generator. This ball, (a) Is attracted towards high voltage plate and stays there, (b) Hangs without moving, (c) Swing backward and forward hitting each plate in turn, (d) Is attracted to earthed plate and stays there, 162., , A sphere of 4 cm radius is suspended within a hollow sphere of 6 cm radius. The inner sphere is, , charged to potential 3 e.s.u. and the outer sphere is earthed. The charge on the inner sphere is, (a) 54 e.s.u., 163., , (b), , 1, 4, , e.s.u., , (c), , 30 e.s.u., , (d), , State which of the following is correct, , (a) joule = coulomb × volt, , (b) joule = coulomb/volt, , (c) joule = volt × ampere, , (d) joule = volt/ampere, , 164., , 36 e.s.u., , When a positive q charge is taken from lower potential to a higher potential point, then its, , potential energy will, (a) Decrease, 165., , (b) Increases, , (d)Become zero, , When a negative charge is taken at a height from earth's surface, then its potential energy, (a) Decreases, , 166., , (c) Remain unchanged, , (b) Increases, , (c) Remains unchanged, , (d) Will become infinity, , When a charge of 3 coulombs is placed in a uniform electric field, it experiences a force of 3000, , Newton. Within this field, potential difference between two points separated by a distance of 1 cm is, (a) 10 volts, 167., , (b) 90 volts, , (c)1000 volts, , (d)3000 volts, , There are two equipotential surface as shown in figure. The distance between them is r. The, , charge of –q coulomb is taken from the surface A to B, the resultant work done will be, 1, , q, 4πε o r, , (a), , W=, , (b), , W=, , (c), , W=−, , 1, , q, , 4πε 0 r 2, , A, , r, , B, , 1, , q, 4πε 0 r 2, , (d) W = zero, SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 168.When one electron is taken towards the other electron, then the electric potential energy of the, , system, (a) Decreases, , (b) Increases, , (c) Remains unchanged, , (d)Becomes zero, , 169. A hollow metal sphere of radius 5cm is charged such that the potential on its surface is 10V., , The potential at a distance of 2cm from the centre of the sphere, (b) 10 V, , (a) Zero, 170., , (d) 10/3 V, , The work done in carrying a charge of 5 µ C from a point A to a point B in an electric field is 10mJ., , The potential difference, , (VB − VA ), , is then, , (b) – 2 kV, , (a) + 2kV, 171., , (c) 4 V, , (c) + 200 V, , (d) – 200 V, , Value of potential at a point due to a point charge is, , (a) Inversely proportional to square of the distance, , (b)Directly proportional to square of the distance, , (c) Inversely proportional to the distance, , (d)Directly proportional to the distance, , 172., , Electric potential of earth is taken to be zero because earth is a good, , (a) Insulator, , (b) Conductor, , (c) Semiconductor, , (d)Dielectric, , 173. There is 10 units of charge at the centre of a circle of radius 10m. The work done in moving 1 unit of, , charge around the circle once is, (a) Zero, 174., , (b) 10 units, , (c) 100 units, , Two parallel plates separated by a distance of, , particle of mass, , 10 −15 kg, , and charge, , 10 −11 C, , 5mm, , (d) 1 unit, , are kept at a potential difference of, , enters in it with a velocity, , 10 7 m / s., , 50 V., , A, , The acceleration of the, , particle will be, (a), 175., , (b), , 10 8 m / s2, , (c) 10 5 m / s2, , 5 × 10 5 m / s2, , (d) 2 × 10 3 m / s2, , Three point charges are placed at the corners of an equilateral triangle. Assuming only, , electrostatic forces are acting, (a) The system can never be in equilibrium, (b) The system will be in equilibrium if the charges rotate about the centre of the triangle, (c) The system will be in equilibrium if the charges have different magnitudes and different signs, (d) The system will be in equilibrium if the charges have the same magnitudes but different signs, 176., , If an insulated non-conducting sphere of radius R has charge density, , distance r from the centre of sphere, (a), 177., , ρR, 3ε 0, , (b), , (r < R), , ρ., , The electric field at a, , will be, , ρr, ε0, , (c), , ρr, 3ε 0, , (d) 3 ρ R, ε0, , Two plates are at potentials –10 V and +30 V. If the separation between the plates be 2 cm. The, , electric field between them is, (a) 2000 V/m, 178., , (b) 1000 V/m, , (c) 500 V/m, , (d) 3000 V/m, , The electric potential inside a conducting sphere, , (a) Increases from centre to surface, (b) Decreases from centre to surface, (c) Remains constant from centre to surface, (d) Is zero at every point inside, SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 179., , The wrong statement about electric field lines is, , (a) These originate from positive charge and end on negative charge, (b) They do not intersect each other at a point, (c) They have the same form for a point charge and a sphere, (d) They have physical existence, 180., , (a), 181., , A charge produces an electric field of 1 N/C at a point distant 0.1 m from it. The magnitude of charge is, , (b), , 1.11 × 10 −12 C, , the particle are respectively, 182., , (d)None of these, , 7.11 × 10 −6 C, , A charged particle is suspended in equilibrium in a uniform vertical electric field of intensity, , 20000 V/m. If mass of the particle is, (a), , (c), , 9.11 × 10 −12 C, , (b), , 4.8 × 10 −19 C, 3, , 9.6 × 10 −16 kg ,, , the charge on it and excess number of electrons on, , (g = 10 m / s2 ), , (c) 3.8 × 10 −19 C, 2, , 5.8 × 10 −19 C, 4, , (d) 2.8 × 10 −19 C, 1, , The potential at a distance R/2 from the centre of a conducting sphere of radius R will be, , (a) 0, , (b), , Q, 8πε 0 R, , (c), , Q, 4πε 0 R, , (d), , Q, 2πε 0 R, , 183. Four charges +Q, − Q, + Q, − Q are placed at the corners of a square taken in order. At the centre of the square, , (a), 184., , (b), , E = 0, V = 0, , The radius of nucleus of silver (atomic number = 47) is, , surface of nucleus is, (a), 185., , (c) E ≠ 0, V = 0, , E = 0, V ≠ 0, , 1.99 × 10 6 volt, , (d) E = 0, V ≠ 0, , 3.4 × 10 −14 m ., , The electric potential on the, , (e = 1.6 × 10 −19 C), , (b), , (c) 4.99 × 10 6 volt, , 2.9 × 10 6 volt, , (d), , 0.99 × 10 6 volt, , Charges q, 2q, 3q and 4q are placed at the corners A, B, C and D of a square as shown in the, , following figure. The direction of electric field at the centre of the square is along, D, , (a) AB, (b) CB, , 3q, , O, , (c) BD, , q, A, , (d) AC, 186., , C, , 4q, , Point charge, , q1 = 2µC, , and, , q2 = −1 µC, , are kept at points, , x=0, , and, , x=6, , 2q, , B, , respectively. Electrical, , potential will be zero at points, (a), 187., , x=2, , and, , x=9, , (b), , x =1, , and, , (c), , x=5, , and, , x=4, , (d) x = −2 and, , x = 12, , x=2, , Equipotential surfaces associated with an electric field which is increasing in magnitude along the, , x-direction are, (a) Planes parallel to yz-plane, , (b)Planes parallel to xy-plane, , (c) Planes parallel to xz-plane, , (d)Coaxial cylinders of increasing radii around the x-axis, , 188., , A bullet of mass 2 gm is having a charge of, , 2 µC ., , Through what potential difference must it be, , accelerated, starting from rest, to acquire a speed of, , 10 m / s, , (a) 5 kV, , (c)5 V, , 189., , (b) 50 kV, , (d) 50 V, , The points resembling equal potentials are, , (a) P and Q, , (b) S and Q, , (c) S and R, , (d) P and R, , S, P, , Q, , R, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 190., , Figure shows three points A, B and C in a region of uniform electric field, , E., , The line AB is, , perpendicular and BC is parallel to the field lines. Then which of the following holds good. Where, and, , VC, , represent the electric potential at points A, B and C respectively, , (a), , VA = VB = VC, , (b), , VA = VB > VC, , (c), , VA = VB < VC, , (d), , VA > VB = VC, , 191., , VA , VB, , A, , C, , B, , In a certain charge distribution, all points having zero potential can be joined by a circle S. Points, , inside S have positive potential and points outside S have negative potential. A positive charge,, which is free to move, is placed inside S, (a) It will remain in equilibrium, , (b) It can move inside S, but it cannot cross S, , (c) It must cross S at some time, , (d) may move, but will ultimately return to its starting point, , 192., , Infinite charges of magnitude q each are lying at x =1, 2, 4, 8... meter on X-axis. The value of, , intensity of electric field at point x = 0 due to these charges will be, (a) 12 × 109q N/C, 193., , (c)6 × 109q N/C, , (b) Zero, , (d)4 × 109q N/C, , A square of side ‘a’ has charge Q at its centre and charge ‘q’ at one of the corners. The work, , required to be done in moving the charge ‘q’ from the corner to the diagonally opposite corner is, (a) Zero, 194., , (b), , Qq, 4π ∈0 a, , A pendulum bob of mass, , 30 .7 × 10 −6 kg, , (c), , Qq 2, 4π ∈0 a, , and carrying a charge, , (d), , 2 × 10 −8 C, , Qq, 2π ∈0 a, , is at rest in a horizontal, , uniform electric field of 20000 V/m. The tension in the thread of the pendulum is, , (g = 9.8 m / s2 ), , [UPSEAT 2004], (a), 195., , (b), , 3 × 10 −4 N, , (c) 5 × 10 −4 N, , 4 × 10 −4 N, , An infinite line charge produce a field of, , density is, (a) 7.27 × 10 −4 C / m, , (b), , 7.182 × 10 8 N / C, , at a distance of 2 cm. The linear charge, , (c) 7.11 × 10 −4 C / m, , 7.98 × 10 −4 C / m, , (d) 6 × 10 −4 N, , (d) 7.04 × 10 −4 C / m, , 196., , An electron experiences a force equal to its weight when placed in an electric field. The intensity, of the field will be, (a) 1.7 × 10 −11 N / C, (b) 5.0 × 10 −11 N / C, (c) 5.5 × 10 −11 N / C, (d)56 N/C, , 197., , The dielectric strength of air at NTP is, , 3 × 10 6 V/ m, , then the maximum charge that can be given to a, , spherical conductor of radius 3 m is, (a), 198., , (b), , 3 × 10 −4 C, , 3 × 10 −3 C, , (c) 3 × 10 −2 C, , (d) 3 × 10 −1 C, , As per this diagram a point charge +q is placed at the origin O . Work done in taking another, , point charge −Q from the point A [co-ordinates, the straight path AB is, , (0, a) ], , to another point B [co-ordinates (a, 0)] along, Y, , (a) Zero, ,  − qQ 1 ,  2a, (b) , 2, ,  qQ 1  a, , (c) , 2 , ,  qQ 1 ,  2a, (d) , 2 , , A, ,  4πε 0 a , ,  4πε 0 a  2, ,  4πε 0 a , , O, , B, , X, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 199., , To charges q1 and q 2 are placed 30 cm apart, shown in the figure. A third charge q 3 is moved, , along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the, system is, , q3, k , where k, 4πε 0, , is, C, , q3, , (a) 8 q 2, 40 cm, , (b) 8 q1, (c) 6q 2, , q2, , q1, , 30 cm, , A, , (d) 6q1, , D, , B, , 200., , A charged ball B hangs from a silk thread S, which makes an angle θ with a large charged, conducting sheet P , as shown in the figure. The surface charge density σ of the sheet is, proportional to, +, (a) sinθ, +, P, +, (b) tan θ, + θ, (c) cosθ, +, S, (d) cot θ, +, +, 201., Two point charges +8q and −2q are located at x = 0 and x = L respectively., B The location of a, point on the x-axis at which the net electric field due to these two point charges is zero is, (a) 8 L, 202., , (b) 4 L, , (c) 2 L, , (d), , L, 4, , Two thin wire rings each having a radius R are placed at a distance d apart with their axes, , coinciding. The charges on the two rings are +q and −q . The potential difference between the, centres of the two rings is, (a) Zero, 203., , Q, 4πε 0, , (b), , 1,  −,  R, , , , R + d , 1, , 2, , 2, , (c) QR / 4πε 0d 2, , (d), , (a), (c), , 4σ, , εo, εo, , 204., , If, , infinitely, , −, −, , εo, , long, , Z = 3a, P, , −2σ, , k̂, , Z=a, x, , 4σ, , εo, , 2, , −σ, , k̂, , parallel, , conducting, , plates, , having, , Z = −a, , surface, , charge, , densities, , and −σ respectively, are separated by a small distance. The medium between the plates is vacuum., , ε 0 is the dielectric permittivity of vacuum, then the electric field in the region between the plates is, , (a), 205., , (d), , k̂, , Two, +σ, , (b), , k̂, , , , R + d , 1, , 2, , σ, , The electric field at point P is, 2σ, , 1,  −,  R, Z, , Three infinitely long charge sheets are placed as shown in figure., 2σ, , Q, 2πε 0, , 0 volts / meter, , (b), , σ, 2ε o, , volts / meter, , (c) σ, , εo, , (d) 2σ, , volts / meter, , εo, , volts / meter, , Four point +ve charges of same magnitude (Q) are placed at four corners of a rigid square frame, , as shown in figure. The plane of the frame is perpendicular to, , Z axis., , If a –ve point charge is placed at, Q, , a distance z away from the above frame (z<<L) then, (a) – ve charge oscillates along the, , Q, , Z axis., L, , (b) It moves away from the frame, (c) It moves slowly towards the frame and stays in the plane of the frame, (d) It passes through the frame only once., , Z-axis, Q, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR, , Q

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Electrostatics : Electric charge, Electric Field and Electric potential, 206., , At a point 20 cm from the centre of a uniformly charged dielectric sphere of radius 10 cm, the, , electric field is 100 V/m. The electric field at 3 cm from the centre of the sphere will be, (a) 150 V/m, 207., , (b) 125 V/m, , (c)120 V/m, , Charges 4Q, q and Q and placed along x-axis at positions, , (d)Zero, , x = 0, x = l / 2, , and, , x=l,, , respectively. Find, , the value of q so that force on charge Q is zero, (a) Q, 208., , (b) Q / 2, , (c) – Q / 2, , (d) – Q, , If an electron moves from rest from a point at which potential is 50 volt to another point at which, , potential is 70 volt, then its kinetic energy in the final state will be, (a) 3.2 × 10–10 J, 209., , (b) 3.2 × 10–18 J, , (c) 1 N, , In the following diagram the work done in moving a point charge from point P to point A, B and C, , is respectively as WA, WB and WC , then, (a) WA = WB = WC, , (b) WA = WB = WC = 0, , (c) WA > WB > WC, , (d) WA < WB < WC, , 210., , 2., , 3., , P, , B, , 1, Q, ., 4πε 0 R, , (b), , (c), , 1, 2Q, ., 4πε 0 R, , (d), , 1, Q, ., 4πε 0 2R, , ELECTRIC DIPOLE, , An electric dipole when placed in a uniform electric field E will have minimum potential energy, if, the positive direction of dipole moment makes the following angle with E, (a) π, (b) π / 2, (c) Zero, (d) 3π / 2, A given charge is situated at a certain distance from an electric dipole in the end-on position, experiences a force F. If the distance of the charge is doubled, the force acting on the charge will be, (a) 2F, (b) F / 2, (c) F / 4, (d) F / 8, The electric potential at a point on the axis of an electric dipole depends on the distance r of the, point from the dipole as, (a), , 4., , A, , C, , A hollow metallic sphere of radius R is given a charge Q. Then the potential at the centre is, , (a) Zero, 1., , (d) 1 dyne, , ∝, , 1, r, , (b), , An electric dipole, of intensity, , E, , ∝, , 1, , r2, of moment p, , (c) ∝ r, , (d) ∝, , 1, r3, , is placed in the position of stable equilibrium in uniform electric field, , . It is rotated through an angle, , θ, , from the initial position. The potential energy of, , electric dipole in the final position is, (a), 5., , 6., , (b), , pE cosθ, , (d) − pE cosθ, , An electric dipole is kept in non-uniform electric field. It experiences, (a) A force and a torque, , (b)A force but not a torque, , (c) A torque but not a force, , (d)Neither a force nor a torque, , An electric dipole consisting of two opposite charges of, is placed in an electric field of, (a), , 7., , (c) pE(1 − cosθ ), , pE sinθ, , 12 × 10, , −1, , Nm, , (b), , 2 × 10 5, , 12 × 10, , An electric dipole of moment, , p, , −3, , pE, , (b), , + 2 pE, , each separated by a distance of, , 3 cm, , N/C. The maximum torque on the dipole will be, (c) 24 × 10 −1 N m, , Nm, , (d) 24 × 10 −3 N m, , is placed normal to the lines of force of electric intensity, , work done in deflecting it through an angle of, (a), , 2 × 10 −6 C, , 180 °, , is, (c), , −2 pE, , (d)Zero, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR, , E,, , then the

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Electrostatics : Electric charge, Electric Field and Electric potential, 8., , The distance between the two charges, , +q, , and, , −q, , of a dipole is r . On the axial line at a distance, , d, , from, , the centre of dipole, the intensity is proportional to, (a), 9., , q, , (b), , d2, , qr, , (c), , d2, , An electron and a proton are at a distance of, (a), , (b), , 1.6 × 10 19, , 1 Å . The, , q, , (d), , d3, , moment of this dipole will be (C × m), (c) 3.2 × 10 19, , 1.6 × 10 −29, , qr, d3, , (d) 3.2 × 10 29, , 10. The electric field due to a dipole at a distance r on its axis is, , (a) Directly proportional to, , r3, , (b) Inversely proportional to, , r3, , (c) Directly proportional to, , r2, , (d) Inversely proportional to, , r2, , 11. Two charges + 3.2 × 10 −19 and − 3.2 × 10 −19 C placed at 2.4 Å apart form an electric dipole. It is placed in a, , uniform electric field of intensity, , 4 × 10 5 volt / m . The, , electric dipole moment is, , (a), , 15 .36 × 10 −29 coulomb × m, , (b) 15.36 × 10 −19, , (c), , 7.68 × 10 −29 coulomb × m, , (d) 7.68 × 10 −19, , coulomb × m, , coulomb × m, , 12. An electric dipole of moment p is placed at the origin along the x -axis. The electric field at a point P ,, , whose position vector makes an angle θ with the, where, (a), , tan α =, , x -axis,, , will make an angle ..... with the, , x -axis,, , 1, tan θ, 2, , (b), , α, , (c) θ + α, , θ, , (d) θ + 2α, , 13. An electric dipole is placed along the x − axis at the origin O . A point P is at a distance of 20 cm from, , this origin such that, , OP, , makes an angle, , π, 3, , with the x-axis. If the electric field at, , P, , makes an angle, , θ, , with the x-axis, the value of θ would be, (a), , π, , (b), , 3, ,  3, , + tan −1 ,  2 , 3, , , , π, ,  3, , ,  2 , , (c) 2π, , (d) tan −1 , , 3, , 14. Electric charges q, q, − 2q are placed at the corners of an equilateral triangle ABC of side l . The, , magnitude of electric dipole moment of the system is, (a), , (b), , ql, , (c), , 2ql, , (d), , 3ql, , 4 ql, , 15. The torque acting on a dipole of moment P in an electric field E is [MP PMT 1994; CPMT 2001], , (a), , (b), , P⋅ E, , (c) Zero, , P× E, , (d) E × P, , 16. The electric field at a point on equatorial line of a dipole and direction of the dipole moment, , (a) Will be parallel, , (b) Will be in opposite direction, , (c) Will be perpendicular, , (d) Are not related, , 17. Two opposite and equal charges 4 × 10 −8 coulomb when placed 2 × 10 −2 cm away, form a dipole. If this, , dipole is placed in an external electric field, the work done in rotating it through, (a), , 64 × 10 −4 Nm, , and, , (b), , 32 × 10 −4 Nm and 32 × 10 −4 J, , (c), , 64 × 10 −4 Nm, , and, , 32 × 10 −4 J, , (d), , 32 × 10 −4 Nm, , and, , 64 × 10 −4 J, , 180 °, , 4 × 10 8 newton / coulomb, , , the value of maximum torque and, , will be, , 64 × 10 −4 J, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 18. If Ea be the electric field strength of a short dipole at a point on its axial line and Ee that on the, , equatorial line at the same distance, then, (a) Ee = 2Ea, (b) Ea = 2Ee, (c) Ea = Ee, (d) None of the above, 19. An electric dipole is placed in an electric field generated by a point charge, (a) The net electric force on the dipole must be zero, (b) The net electric force on the dipole may be zero, (c) The torque on the dipole due to the field must be zero, (d) The torque on the dipole due to the field may be zero, 20. A point Q lies on the perpendicular bisector of an electrical dipole of dipole moment p . If the, , distance of, , Q, , from the dipole is, , (much larger than the size of the dipole), then electric field at, , r, , Q, , is, , proportional to, (a) p −1 and r −2, (b) p and r −2, (c) p 2 and r −3, (d) p and r −3, 21. If the magnitude of intensity of electric field at a distance x on axial line and at a distance, equatorial line on a given dipole are equal, then, (a), , (b), , 1:1, , x:y, , on, , is, (c) 1 : 2, , 1: 2, , y, , (d) 3 2 : 1, , 22. An electric dipole in a uniform electric field experiences (When it is placed at an angle θ with the field), , (a) Force and torque both, , (b) Force but no torque, , (c)Torque but no force, , (d) No force and no torque, , 23. The electric intensity due to a dipole of length 10 cm and having a charge of 500 µC , at a point on the, , axis at a distance 20 cm from one of the charges in air, is, (a), , 6.25 × 10 7, , N/C, , (b), , 9.28 × 10 7, , (b), , P, 4πε 0r 2, , N/C, , (c) 13.1 × 1111 N/C, , (d) 20.5 × 10 7 N/C, , 24. Electric potential at an equatorial point of a small dipole with dipole moment P (r, distance from the dipole) is, , (a) Zero, , (c), , P, 4πε 0r 3, , (d), , 2P, 4πε 0r 3, , 25. The distance between H + and Cl − ions in HCl molecule is 1.28 Å. What will be the potential due to, , this dipole at a distance of 12 Å on the axis of dipole, (a) 0.13 V, , (b) 1.3 V, , (c)13 V, , (d)130 V, , 26. The potential at a point due to an electric dipole will be maximum and minimum when the angles, , between the axis of the dipole and the line joining the point to the dipole are respectively, (a), , 90 o, , and, , 180 o, , (b), , 0o, , and, , (c) 90 o and, , 90 o, , 0o, , (d) 0o and, , 180 o, , 27. The value of electric potential at any point due to any electric dipole is, , (a), , k., , p×r, r2, , (b), , k., , p×r, r3, , (c) k. p ⋅2r, r, , (d) k. p 3⋅ r, r, , 28. An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a, , uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its, potential energy are respectively, (a), , 2q ⋅ E, , and minimum, , (b) q ⋅ E and, , p⋅ E, , (c)Zero and minimum, , (d) q ⋅ E and maximum, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 29. The electric field E due to a dipole, depends on distance r as, , (a), , E∝, , 1, r4, , (b), , E∝, , 1, r3, , (c) E ∝, , 1, r2, , (d) E ∝ 1, r, , 30. The ratio of electric fields on the axis and at equator of an electric dipole will be, , (a) 1 : 1, , (b) 2 : 1, , (c) 4 : 1, , (d)None of these, , 31. For a dipole q = 2 × 10 −6 C and d = 0.01 m . Calculate the maximum torque for this dipole if E = 5 × 10 5 N / C, , (a), , 1 × 10 −3 Nm −1, , (b), , 10 × 10 −3 Nm −1, , (c) 10 × 10 −3 Nm, , (d) 1 × 10 2 Nm 2, , 32. A molecule with a dipole moment p is placed in an electric field of strength E. Initially the dipole is, , aligned parallel to the field. If the dipole is to be rotated to be anti-parallel to the field, the work, required to be done by an external agency is, (b) – pE, , (a) – 2pE, , (c)pE, , (d)2pE, , 33. An electric dipole of moment p placed in a uniform electric field E has minimum potential energy, , when the angle between, (a) Zero, , p, , (b), , and, , E, , is, , π, , (c) π, , 2, , (d) 3π, 2, , 34. A region surrounding a stationary electric dipoles has, , (a) Magnetic field only, , (b)Electric field only, , (c)Both electric and magnetic fields, , (d)No electric and magnetic fields, , 35. Two electric dipoles of moment P and 64 P are placed in opposite direction on a line at a distance of, , 25 cm. The electric field will be zero at point between the dipoles whose distance from the dipole of, moment P is, (a) 5 cm, , (b), , 25, 9, , cm, , (c) 10 cm, , (d), , 4, 13, , cm, , 36. When an electric dipole P is placed in a uniform electric field E then at what angle between P and, E, , the value of torque will be maximum, , (a), , (b), , 90 o, , 0o, , (c) 180 o, , (d) 45 o, , 37. Two charges + 3.2 × 10 −19 C and − 3.2 × 10 −9 C kept 2.4 Å apart forms a dipole. If it is kept in uniform, , electric field of intensity, (a), , + 3 × 10 −23 J, , 4 × 10 5 volt/m, , (b), , − 3 × 10 −23 J, , then what will be its electrical energy in equilibrium, (c) − 6 × 10 −23 J, , (d) − 2 × 10 −23 J, , 38. What is the angle between the electric dipole moment and the electric field strength due to it on the, , equatorial line, (a) 0o, , (b) 90o, , (c)180o, , (d) 60o, , 39. The electric field due to an electric dipole at a distance r from its centre in axial position is E. If the, , dipole is rotated through an angle of 90° about its perpendicular axis, the electric field at the same, point will be, (a) E, , (b) E / 4, , (c)E / 2, , (d)2E, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, ELECTRIC FLUX AND GAUSS'S LAW, 1., , A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis., The total flux for the surface of the cylinder is given by, (a), , 2., , 3., , (b), , 2πR 2 E, , (c), , πR 2 / E, , Electric field at a point varies as, , r0, , (πR 2 − πR) / E, , (d)Zero, , for, , (a) An electric dipole, , (b)A point charge, , (c)A plane infinite sheet of charge, , (d)A line charge of infinite length, , An electric charge, , q is, , placed at the centre of a cube of side, , α, , . The electric flux on one of its faces, , will be, (a), 4., , (b), , q, , (c), , ε 0 a2, , (b), , ε0, , (c) (4 pε 0 )−1, , ε 0−1, , For a given surface the Gauss's law is stated as, (a), , E, , is necessarily zero on the surface, , q, , ε0, , (b), , (d)The flux is only going out of the surface, E, , , where, , E = Eˆi, , (c) 4l 2 E, , l 2E, , Eight dipoles of charges of magnitude, , (d) 4πε 0, , (b) E is perpendicular to the surface at every point, , A cube of side l is placed in a uniform field, (a) Zero, , 7., , (d), , ∫ E ⋅ ds = 0 . From this we can conclude that, , (c) The total flux through the surface is zero, 6., , q, 4πε 0 a 2, , Total electric flux coming out of a unit positive charge put in air is, (a), , 5., , q, 6ε 0, , e, , . The net electric flux through the cube is, (d) 6l 2 E, , are placed inside a cube. The total electric flux coming out of, , the cube will be, (a), 8., , (b), , 16 e, , ε0, , (c), , e, , (d)Zero, , ε0, , A point charge +q is placed at the centre of a cube of side L . The electric flux emerging from the cube is, , (a), 9., , 8e, , ε0, , q, , (b) Zero, , ε0, , A charge, , q, , (c) 6qL, , 2, , ε0, , (d), , q, 6 L2 ε 0, , is placed at the centre of the open end of cylindrical vessel. The flux of the electric field, , through the surface of the vessel is, (a) Zero, , (b), , q, , ε0, , (c), , (d) 2q, , q, 2ε 0, , ε0, , 10. It is not convenient to use a spherical Gaussian surface to find the electric field due to an electric, , dipole using Gauss’s theorem because, (a) Gauss’s law fails in this case, (b)This problem does not have spherical symmetry, (c) Coulomb’s law is more fundamental than Gauss’s law, (d)Spherical Gaussian surface will alter the dipole moment, 11. According to Gauss’ Theorem, electric field of an infinitely long straight wire is proportional to, , (a) r, , (b), , 1, r, , 2, , (c), , 1, r3, , (d) 1, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR, , r

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Electrostatics : Electric charge, Electric Field and Electric potential, 12. Electric charge is uniformly distributed along a long straight wire of radius 1mm. The charge per cm, , length of the wire is Q coulomb. Another cylindrical surface of radius 50 cm and length 1m, symmetrically encloses the wire as shown in the figure. The total electric flux passing through the, +, +, +, , cylindrical surface is, (a), (c), , Q, , ε0, 10 Q, (πε 0 ), , (b), , 100 Q, , (d), , 100 Q, (πε 0 ), , ε0, , 1m, , +, +, +, , 13. The S.I. unit of electric flux is, , (a) weber, , (b) newton per coulomb, , (c)volt × metre, , 50cm, , (d)joule per coulomb, , 14. q1 , q 2 , q 3 and q4 are point charges located at points as shown in the figure and S is a spherical, , Gaussian surface of radius R. Which of the following is true according to the Gauss’s law, (a), (c), , , , ∫ (E, s, , ∫, , 1, ,  q +q +q, , , 2, 3, + E2 + E3 ).dA = 1, 2ε 0, , , , , , , , (q1 + q 2 + q 3 ), , ε0, , S, , ε0, , s, ,  (q + q + q + q ), , , , 2, 3, 4, (E1 + E2 + E3 ).dA = 1, , s, , , , (b) ∫ (E1 + E2 + E3 ).dA =, , q1, , (d) None of the above, , R, q4, , q2, , 15. Gauss’s law should be invalid if, , q3, , (a) There were magnetic monopoles, (b) The inverse square law were not exactly true, (c) The velocity of light were not a universal constant, (d) None of these, 16. The inward and outward electric flux for a closed surface in units of N - m2 / C are respectively 8 × 10 3, and 4 × 10 3. Then the total charge inside the surface is [where ε 0 = permittivity constant], , (a), , 4 × 10 3, , C, , (b), , − 4 × 10 3, , C, , (c) (−4 × 10, ε, , 3, , ), , C, , (d) − 4 × 10 3 ε 0 C, , 17. A charge q is placed at the centre of a cube. Then the flux passing through one face of cube will be, , (a), , q, , (b), , ε0, , q, 2ε 0, , (c), , q, 4ε 0, , (d), , q, 6ε 0, , 18. If a spherical conductor comes out from the closed surface of the sphere then total flux emitted from, , the surface will be, (a), (c), , 1, , ε0, , ×, , (the charge enclosed by surface), , 1, ×, 4πε 0, , (charge enclosed by surface), , (b) ε 0 × (charge enclosed by surface), (d) 0, , 19. If the electric flux entering and leaving an enclosed surface respectively is φ1 and φ 2 the electric, , charge inside the surface will be, (a), , (φ1 + φ 2 )ε 0, , (b), , (φ 2 − φ 1 )ε 0, , (c), , (φ 1 + φ 2 ) / ε 0, , (d) (φ2 − φ1) / ε 0, , 20. A charge q is located at the centre of a cube. The electric flux through any face is, , (a), , 4πq, 6(4πε 0 ), , (b), , πq, 6(4πε 0 ), , (c), , q, 6(4πε 0 ), , (d), , 2πq, 6(4πε 0 ), , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR

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Electrostatics : Electric charge, Electric Field and Electric potential, 21. Shown below is a distribution of charges. The flux of electric field due to, , these charges through the surface S is, (a), , 3q / ε 0, , (b), , (c), , q /ε0, , (d) Zero, , +q, , +q, , S, , 2q / ε 0, +q, , 22. Consider the charge configuration and spherical Gaussian surface as shown in the figure. When, , calculating the flux of the electric field over the spherical surface the electric field will be due to, (a), , (b)Only the positive charges, , q2, , (c) All the charges, , (d) +q1 and, , +q, , −q1, , –q, , q, , 2, , 1, , 1, , 23. Gauss’s law is true only if force due to a charge varies as, , (a), , (b), , r −1, , (c) r −3, , r −2, , (d) r −4, , 24. An electric dipole is put in north-south direction in a sphere filled with water. Which statement is, , correct, (a) Electric flux is coming towards sphere, (b) Electric flux is coming out of sphere, (c) Electric flux entering into sphere and leaving the sphere are same, (d) Water does not permit electric flux to enter into sphere, 25. Two infinite plane parallel sheets separated by a distance d have equal and opposite uniform charge, , densities, , σ, , . Electric field at a point between the sheets is, , (a) Zero, (c), , (b), , σ, , σ, ε0, , (d)Depends upon the location of the point, , 2ε 0, , 26. The electric flux for Gaussian surface A that enclose the charged particles in free space is (given q1 = –14, , nC, q2 = 78.85 nC, q3 = – 56 nC), (a) 103 Nm2 C–1, , q3, , q1, , (b) 103 CN-1 m–2, , q2, , (c) 6.32 × 103 Nm2 C–1, , Gaussian, surface A, Gaussian, surface B, , (d) 6.32 × 103 CN-1 m–2, 27. The electric intensity due to an infinite cylinder of radius R and having charge q per unit length at a, , distance, , r (r > R) from, , its axis is, , (a) Directly proportional to, , r2, , (b) Directly proportional to, , r3, , (c) Inversely proportional to r, (d) Inversely proportional to, , r2, , 28. A sphere of radius R has a uniform distribution of electric charge in its volume. At a distance x from, , its centre, for, (a), , 1, x, , 2, , x < R,, , the electric field is directly proportional to, (b), , 1, x, , (c) x, , (d) x 2, , SHREENIVASA M BHAT, Lecturer in PHYSICS, GPUC, KARWAR