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ELECTROSTATICS, (EXCLUDED CAPACITANCE), , charge, , conductor, & insulatot, , Electric field & Force, Charge, Coulomb’s law, , examples on, coulambs, , 1. When a glass rod is rubbed with silk it gains positive, charge, because, (a) electrons are removed from it, (b) protons are removed from it, (c) protons are added to it, (d) electrons are added to it, Resultant, 2. Dielectric constant is, of force, (a) dimensionless quantity (b) universal constant, (c) conversion factor, (d) none of the above, 3. Fg and Fe represent the gravitational and electrostatic, force respectively between electrons situated at some, distance. The ratio of Fg to Fe is of the order of :, (a) 1043, (b) 101, 0, (c) 10, (d) 10-43, 4.Two equal and opposite charges are placed a certain, distance apart and force between them in F. If 20% of, charge on one is transferred to another, then the force, between them will become, (a) F, (b) 9/16 F, (c) 15/16 F, (d) 16/25 F, , 5. Two point charges q1 and q2 are placed at a distance of, 50 cm from each other in air, and interact with a, certain force. Now the same charges are put in an oil, whose relative permittivity is 5. If the interacting force, between them is still the same, their separation, between now is, (a) 16.6 cm (b) 22.4 cm (c) 28.4 cm (d) 30.4 cm, 6. The numbers of electrons removed from a body in order, to produce positive charge of 5x1019 coulomb on it,, will be, (a) 3, (b) 5, (c) 7, (d) 9, 7. The coulomb’s law is valid for the charges which are, (a) stationary and point charges, (b) both of above, (c)moving and point charges, (d) none of the above, 8. If one electron is removed from an isolated body, then, the charge remaining on the body will be, (a) zero, (b) 1.6x109 Coulomb, 19, (c) 1.6x10 Coulomb, (d) 3.2x1019 Coulomb, 9. Three similar charges are lying on the corners of a, square. If the force between q1 and q2 is F12 and that, between q1 and q3 is F13 then the value of F12/F13 will, be, (a) 2, (b) 3, (c) ½, (d) 1/2, 10. Two points charges of 2 Coulomb and 6 Coulomb repel, each other with a force of 12 Newton. If each charge is, given an additional charge of 2 Coulomb then the, force between them will become, (a) 4 N attractive, (b) 4 N repulsive, (c) 8N attractive, (d) zero, 11. An electric charge q1 exerts some force on another, charge q2. If a third charge q3 is brought near q2, then, the force exerted by q1 and q2 will, (a) remains unchanged (b) increase in magnitude, (c) decrease in magnitude

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(d) increase when q2 and q1 are of same sign and, will decrease if q3 is of opposite sign., 12. In 1 g of a solid, there are 5 x 1021 atoms. If one, electron is removed from everyone of 0.01% atoms of, the solid, the charge gained by the solid is (given that, electronic charge is 1.6 1019 C ) :, (a) +0.08 C, (b) +0.8 C, (c) – 0.08 C, (d) – 0.8 C, 13. Two point charges of +2 micro-coulombs and +6, micro-coulombs repel each other with a force of 12, newton. If a charge of – 2 micro-coulombs is given to, each of these charges, what will be the force now:, (a) Zero, (b) 4 N (attractive), (c) 8 N (repulsive), (d) 4 N (repulsive), 4.Two equal and opposite charges are placed a certain, distance apart and force between them in F. If 20% of, charge on one is transferred to another, then the force, between them will become, (a) F, (b) 9/16 F, (c) 15/16 F, (d) 16/25 F, 15. Two points charges + 8q and – 2q are located at x = 0, and x = L respectively. The location of a point on the x, axis at which the net electric force due to these two, point charges is zero on a test charge placed on x axis, is, (a), , L, 4, , (b) 2 L, , (c) 4 L, , (a), , 4  Fd 2, e2, , (b), , 4 0 Fd 2, q2, , (c), , 4 0 Fd 2, e2, , (d), , 4  0 Fd 2, q2, , Level 1, 18. A charge Q is placed at each of the opposite corners of, a square. A charge q is placed at each of the other two, corners. If the net electrical force on Q is zero, then, Q/q equals, (b) 1, , (c) - , , 1, , (d) -2 2, , 2, , q 2 q3, cos , b2 a2, q, q, (b) 22 + 32 sin , b, a, , (a), , -q3, , Y, , a, , θ, , (d), , q 2 q3, sin , b2 a2, , 2, ,  2r , (b) , ,  3, ,  1 , (d) , ,  2, , 2, , 22. A negative point charge of magnitude q is located on, the Y-axis at a point y = +a and a positive charge of, the same magnitude is located at y = a. A third, positive charge of the same magnitude is located at a, distance x from the origin. The force on the third, charge is, q 2a, q 2a, (a), (b), 2o (a 2  x 2 )3 2, 4o (a 2  x 2 )1 2, , q 2a 2, , (c), , (d), , q2, , 2o (a 2  x 2 )3 2, 4o (a 2  x 2 )1 2, 23. Five balls, numbered 1 to 5 are suspended using, separate threads. Pairs (1, 2) (2, 4) (4, 1) show, electrostatic attraction, while pairs (2, 3) and (4, 5), show repulsion ,, There, ball 1 must be:, (a) Positively charged (b) negatively charged, (c) Neutral, (d) Made of metal, 24. A certain charge Q is divided at first into two parts, q, and Q – q. later on the charges are placed at a certain, distance. If the force of interaction between two, changes is maximum, than:, , Q 4, , q 1, Q 3, , (c), q 1, , Q 2, , q 1, Q 1, , (d), q 3, (b), , 25. A charge q1 exerts some force on a second charge q2. If, a third charge q3 is brought near, then force of q1, exerted on q2:, (a) Will decreases is magnitude, (b) Will increase in magnitude, (c) Will remain unchanged, , b, -q1, , r, 1/ 3, ,  2r , (c)  ,  3 , , (a), , 19. Three charges –q1 , +q2 and –q3 are place as shown in, the figure. The x – component of the force on –q1 is, proportional to, (a), , q, q2, + 32 cos , 2, a, b, , 20.Four equal charges q are lying at the corners A, B,C and, D of square of side a. The resultant force on charge at, D will be, Kq² [2 2  1], 3Kq², Kq ², (a) zero (b), (c), (d), a², 2, a², a², 21. Two pith balls carrying equal charges are suspended, from a common point strings of equal length, the, equilibrium separation between them is r. Now the, strings are rigidly clamped at half the height. The, equilibrium separation between the balls now become:, , (d) 8 L, , 16. A body can be negatively change by:, (a) Removing some neutrons form it, (b) Giving excess electrons to it, (c) Removing some protons form it., (d) Removing some electrons from it., 17. Two positive ions, each carrying a change q, are, separated by a distance d. if F is the force of repulsion, between the ions, the number of electrons missing, from each ion will be (e being the charge on an, electron):, , (a) -1, , (c), , +q2, , X

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(d) Will increase if q3 is of same sign as q1 and, will decrease if q3 is of opposite., 26. Two small balls having equal positive change Q, (coulomb) on each are suspended by two insulated, strings of equal length L meter, form a hook fixed to a, stand. The whole set up is taken in a satellite into space, where there is no gravity (state if weightlessness)., Then the angle  between the two strings is:, (a) 00, (b) 900, 0, (c) 180, (d) 00 <  < 1800, 27. In the previous question , the tension in each string is, (a) 0, , (b), , 1 Q2, 4 0 L2, , Q2, 4 0 4 L2, 28. Two equal point charge each of 3  C are separated by, (c), , Q2, 4 0 2 L2, 1, , (d), , 1, , a certain distance in metes. If they are located at, ^, , ^, , ^, , ^, , ^, , ^, , (i  j  k ) and (2 i  3 j  3 k ), then the electrostatic, force between then is:(a) 9  103 N, (b) 9  103 N, (c) 9  102 N, (d) 10 3 N, 29. Two point charges A and B, having charges + Q and –, Q respectively, are placed at certain distance apart and, force acting between them is F. If 25% charge of A is, transferred to B, then force between the charges, becomes:, , (a) F, (c), , 16 F, 9, , 9F, 16, 4F, (d), 3, , (b), , 30. There charges +Q, q, + Q are placed respectively, at, distance, 0, d/2 and d from the origin, on the x-axis. If, the net force experienced by + Q, placed at x = 0, Is, zero, then value of q is:, [JEE Mains 2019], (a) + Q/2, (b) – Q/2, (c) – Q/4, (d) +Q/4, 31. Three equal charges are placed on three corners of a, square. If the force between q1 and q2 is F12 and that, between q1 and q3 is F13, the ration of magnitudes, F12/F13 is:, (a) 1/2, (b) 2, (c) 1/ 2, (d) 2, 32. Three changes 4q, Q and q are placed in a straight line, of length 1 at points distant 0, 1/2 and 1 respectively., What should be Q in order to make the net force on q, to be zero:, (a) – q, (b) – 2q, , (c) – q/2, , (d) 4q, , Electric field (Point charge system), , electric field, , 33. The point charges – Q and 2Q are placed at a distance, R apart. Where should a third point charge be placed, so that it is equilibrium:, (a) at a point on the right of 2Q, (b) at a point on the left of – Q, (c) between – Q and 2Q, (d) at a point on a line perpendicular to line, joining – Q and 2Q., 34. q, 2q, 3q and 4q changes are placed at the four corners, A, B, C and D of a square. The field at the center P of, the square has the direction along or parallel to:, , (a) AB, (b) BC, (c) AC, (d) BD, 35. Three changes +Q each are placed at the corners A, B, and C of an equilateral triangle. At the circumcenter O,, the electric will be:, , (a), , 1 3Q, 4 r 2, , (c) Zero, , 1 3Q, 4 0 r 2, 1 Q.Q, (d), 4 0 r 2, (b), , 36. Five charges each equal to q are placed at the five, corners A, B, C, D and E of a regular hexagon ABCDF, of side a. Then the electric intensity at the center O of, the hexagon is:

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(a), , q, , along, , 4 0 a, q, (c), along, 4 0 3a 2, 2, , (b), , q, , along, , 4 0 a 2, 5q, (d), along, 4 0 a 2, , 37. In a regular polygon of n sides, each corner is at a, distance r form the center. identical charges of, magnitude Q are placed at (n - 1) corners. The field at, the center is (k = 9 x 109 N – m2/C2):, , Q, r2, n, Q, k 2, (c), (n  1) r, (a) k, , Q, r2, (n  1) Q, (d), k 2, n, r, (b) (n  1) k, , 38. In the following diagram,, A, three identical charges each, of magnitude q1 are situated, r, at the corners of an, r, O r, equilateral triangle. The, B, C, electric field intensity at O, will be, (a) zero, (b) kq1/r, (c) kq1²/r, (d) kr/q1, 39. Two point charges q and +q/2 are situated at the, origin and at the point (a, 0, 0) respectively. The point, along the X-axis where the electric field vanishes is, 2a, 2a, a, (a) x =, (b) x = 2 a (c) x =, (d) x =, 2, 2 1, 2 1, 40. Like equal charges are situated at the four corners of a, square. If the field intensity due to any one charge at, the centre of the sphere is E, then the resultant intensity, at the centre will be, (a) zero, (b) E, (c) E/4, (d) 4E, 41. The ratio of electric fields due to an electric dipole at, equal distances in its axial and equatorial positions will, be, (a) 1:2, (b) 2:1, (c) 1:4, (d) 4:1, , ^, , ^, , i j, (a) (ql), 2, , ^, , (b), , ^, , i j, 3ql, 2, , ^, , ^, , (c)  3ql j, (d) 2ql j, 44. Six charges of equal, magnitude, 3 positive and 3, negative are to be placed on, PQRSTU corners of a regular, hexagon, such that field at, P, Q, the, centre is double that of what, O, R, U, it, would have been if only one, +ve charge is placed at R., T, S, (a) +,+,+,-,-,(b) -,+,+,-,+,(c) -,+,+,-,+,(d) +,-,+,-,+,45. A charge Q is fixed at each of two opposite corners of, a square. A charge q is placed at each of the other twocorners. If the resultant force on Q is zero, then Q and, q are related as, (a) Q = 2 q, (b) Q = 2 2 q, (c) Q = 2 q², (d) Q = 2 2 q², 46. Figure shows three particles with charges q1 = +2Q, q2, = -2Q and q3 = - 4Q, each a distance d from the origin., Find the net electric field at the origin:, , level 1, 42. ABC is a right angle triangle with right angle A and, AB = AC = 30 cm. If the charge on B and C is 4x103, µC then electric field at A will be, (a) 400 NC1 parallel to BC, (b) 800 NC1 parallel to BC, (c) 400 2 NC-1 perpendicular to BC, (d) 800 NC1 perpendicular to BC, 43. Determine the electric dipole moment of the system, of three charges, placed on the vertices of a, equilateral triangles, as shown in the [JEE Mains, 2019], , 2.56Q, towards +ve x-axis, 4 0 d 2, 6.93Q, (b), toward +ve x-axis, 4 0 d 2, 6.93Q, (c), toward –ve x-axis, 4 0 d 2, (a), , (d) Zero, 47. Three charges of (+2q), (-q) and (-q)are placed at the, corners A. B and C of an equilateral triangles of sides a, as shown in the adjoining figure. Then the dipole, moment of this combination is:

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(a) 100 V/m (b) 320 V/m (c) 64 V/m (d) 32 V/m, 53. A “semi-infinite” insulatingA rod has a linear charge, +, +, +, +, +, density . The electric, 90°, field at P is, (a), , (a) q a, , (b) zero, , (c) q a 3, , (d), , , , , Q, 1 2 2, 2, Q, (c) - 1  2 2, 4, , , , , P, , AB., , 2, qa, 3, , , , , Q, 1 2 2, 4, Q, 1 2 2, (d), 2, (b), , y, , 2, (b), at an angle of 45° with AP or 135° with, 4 0 y, , , along AP., 4 0 y, , (d), at an angle of 45° with AP or 45° with, 4 0 y, (c), , 47. Four charges equal –Q are placed at the four corners of, a square and a charge q is at its centre. If the system is, in equilibrium the value of q is, (a) -, , 2, Along AP., 4 0 y, , B, , , , , 54., , 48. A charge q is placed at the centre of the line joining, two equal charges Q. The system will be in, equilibrium if q is equal to, (a) Q/2, (b) Q/4, (c) +Q/4, (d) +Q/2, 49. Two equal negative charges –q are fixed at point, (0, -  ) on y – axis. A positive charge Q is released, from rest at the point (2  ,0) on the x – axis. The, charge Q will, (a) execute simple harmonic motion about the origin, (b) move to the origin remain at the rest, (c) move to infinity, (d) execute oscillatory but not simple harmonic motion, Electric field (Continuous charge system), , A thin conducting ring of radius R is given a, charge + Q. The electric field at the center O of the, ring due to the charge on the part AKB of the ring, is E. the electric field at the center due to the, charge on the part ACDB of the ring is:, (a) 3 E along OK, (c) E along OK, , (b) 3 E along KO, (d) E along KO, , 55. The electric field at a distance, , 3R, from the center of a, 2, , charges conducting spherical shell of radius R is E., The electric field at a distance, , R, from the centers of, 2, , the sphere is:, , E, 2, (c) Zero, , (a), , 50.The intensity of electric field due to a conducting sphere, of radius R and carrying charge Q at a point distant r, from its centre (r < R) will be, (a) kq/r², (b) kQ/R², (c) zero, (d) kQr/R3, 51. Two linear charges of infinite length are situated, parallel to each other d distance apart. The linear, charge density on both is . The electric force per unit, length between them will be, 2K ², 2 K, K ², K ², (a), (b), (c), (d), d, d, d², d, 52. A semicircular ring of radius 0.5 m is uniformly, charged with a total charge of 1.4x109C. The electric, field intensity at the centre of curvature of this ring is, , (b), , E, 3, , (d) E, , 56. A rod lie along the x-axis with one end at the origin, and the other at x   . it earries a uniform charge, c / m . The electric field at the point x = - a on the, axis will be., , (a), (c), , ^, , ( i ), 4 0 a, ^, , ( i ), =, 2 0 a, , (b), (d), ,  ^, (i ), 4 0 a,  ^, (i ), 2 0 a, , 57. A thin glass rod is bent into a semicircle of radius r. A, charge +q is uniformly distributed along the upper half, and a charge –q is uniformly, + +q, +, distributed along the lower half,, +, as shown in the figure. The, +, magnitude and direction of the +, P, electric field, produced at P, , r, , , , ,  q

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the center of the circle, will be., (a), , (b), , (a) 0, (b), , q, ,  0 2 r 2, , perpendicular to the line OP and, , directed downward, (c), , q, ,  0 r 2, , perpendicular to the line OP and, , E, E, , directed downward, (d), , q, ,  0 r 2, , (c), , Along the axis OP, , r, , 58. An infinite line charge wire produces a field of, 9 104 N / C at a distance of 2 cm. calculate the linear, charge density., (a) 100  C / m, (b) 10  C / m, (c), , (d), , 1, C / m, 10, , (d), , r, , Electric field lines, , 1, C / m, 100, , 59. A ring of radius R is charged uniformly with a charge, +Q. the electric field at a point on its axis at a distance, r from any point on the ring will be:-, , KQ, (r  R 2 ), KQ, (c) 3 (r 2  R 2 )1/2, r, (a), , 2, , KQ, r2, KOr, (d), R3, (b), , 60. A hollow metal sphere of radius R is uniformly, charged. The electric field due to the sphere at a, distance r from the center:, (a) increases as r increases for r < R and for r > R, (b) zero as r increases for r < R, decreases as r, increases for r > R, (c) zero as r increases for r < R, increases as r, increases for r > R, (d) decreases as r increases for r < R and for r > R, 61. Two parallel infinite line charge wit linear change, densities C / m and C / m are placed at a, distance of 2R in free space. What is the electric field, mid-way between the two line charges?, (a) Zero, (c), , ,  0 R, , (b), , N /C, , (d), , 2, N /C,  0 R, , , , 2 0 R, , R, (b) R (c), 2, , (a), , (b), , N /C, , 62. For a uniformly charged ring of radius R, the electric, field on its axis the largest magnitude at a distance, from its center. then value of h is:, [JEE Main 2019], , R, (a), 5, , 66. Figure shows some of the, electric field lines, B, C, A, corresponding to an electric, field. The figure suggests, that, (a) EA > EB > EC, (b) EA = EB = EC, (c) EA = EC > EB, (d) EA = EC < EB, 67. Three positive charges of equal value q are placed at, the vertices of an equilateral triangle. The resulting, lines of force should be sketched as in., , (d)R 2, , (c), , (d), , 68. A metallic shell has a point charge ‘q’ kept inside its, cavity. Which one of the following diagrams correctly, represents the electric lines of forces., , 65. The E-r curve for an infinite linear charge distribution, will be, E, , E, , (a), , (b)

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71. The figure given below is a plot of lines of force due to, two charges q1 and q2. Find out the sign of the charges:, (c), (d), 69. In the following diagram, the electric lines of force, from a charged body are shown. If the electric fields at, the points A and B are EA and EB respectively and, distance, between, them, is, r,, then, , (a) both negative, (b) upper negative and lower positive, (c) both positive, (d) upper positive and lower negative., , (a) EA = EB (b) EA < EB (c) EA > EB (d) EA = EB, 70. Electric lines of force:, (a) are always parallel, (b) never intersect each other, (c) are always perpendicular to each other, (d) terminate at positive charges., , Gauss Law, , 1.A cylinder of radius R and length L is placed in a, uniform electric field. The net flux emanating out of the, cylinder will be, (a) R²E (b) 2R²E, (c) zero, (d) 2R²/E, 2 .Six dipoles are enclosed by a cube. The electric flux, coming out of will be, q, q, q, (a), (b), (c) zero (d), 24  o, 6 o, 4 o, 3. A point charge q is lying the centre of a cube of side L., The flux emanating out of the cube will be, (a) zero (b) q/6L²o, (c) q/o, (d) 6L²o/q, 4. If the flux entering and leaving an enclosed surface, respectively is 1 and 2 , the electric charge inside, the surface will be, (a) ( 2  1 )  0, (b) 1   2  /  0, (c)  2  1  /  0, (d) 1   2  /  0, 5. An electric charge q is lying at the open end, q, of a cylindrical vessel as shown in the

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figure. The flux emanating out of the cylinder will be, (a) zero, (b) q/o (c) q/2o (d) 2q/o, 6.A metallic particle having no net charge is placed near a, finite metal plate carrying a positive charge. The, electric force on the particle will be, (a) towards the plate (b) away from the plate, (c) parallel to the plat, (d) zero, 7.Gauss’s law is valid for the fields which, (a) obey the inverse square law, (b) for all types of fields, (c) do not obey the inverse square law, (d) none of the above, 8.A charge is q is lying at the centre of the face of cube., The electric flux passing through the cube will be, (a) q/o (b) q/2o, (c) q/4o, (d) q/8o, 9. A point of charge q is placed at distance s above a flat, plane of radius R, q, as shown. When, s, the, distance, between the point, R, charge and the, flat plane is very, small (s < < < R) then the magnitude of the electric, flux through the flat plane is, (a) Ф = q/2εo, (b) Ф = q/εo, (c) Ф = q/4εo, (d) Ф = q/3εo, 10. Two conducting spheres of radii R1 and R2 are charged, to same surface charge density. The ratio of electric, fields near their surface will be, (a) 1, (b) R1²/R2², (c) R2/R1, (d) R1/R2, 11. Two metallic plates, each of area A and bearing, charges q and q respectively, are placed at distance d, apart. The electric field between the plates will be, , A o, qA, q, (b), (c), (d) zero, o, A o, q, 12. A hemispherical surface of, E, radius R is placed with its, cross-section perpendicular to, a uniform electric field E as, R, shown in fig. flux linked with, its curved surface is, 2, 2, (a)zero, (b)2 πR E (c) πR E (d) (E/2 π), 13. A sphere of radius ‘R’ has a uniform distribution of, electric charge in its volume. At a distance x from its, center for x < R, the electric field is directly, proportional to:, (a) 1/x2, (b) 1/x, (c) x, (d) x2, 14. A charge Q is kept at the corner of a cube electric flux, passing through one of those faces not touching that, charge is, , sphere of radius 10 cm is E. Then at a distance 5 cm, from the center it will be, (a) 16 E, (b) 4E, (c) 2 E, (d) Zero, 16. As one penetrates a uniformly charged dielectric, sphere the electric field strength E:, (a) Increases, (b) decreases, (c) Remains the same as at the surface, (d) Is zero at all points., 17. A sphere encloses an electric dipole with charge, 3 106 C . What is the electric flux across the, sphere?, (a) 3 106 Nm 2 / C (b) Zero, (c) 3 106 Nm2 / C, (d) 6 106 Nm 2 / C, , Conductor properties, , 18. In a region with uniform electric field number of lines, of force for unit area is E. If a spherical metallic, conductor is placed in this region, the number of lines, of force per unit area inside the conductor will be:, (a) E, (b) more than E., (c) less than E, (d) zero, 19. A metallic sphere is placed in a uniform electric field., The lines of force follow the path (s) shown in the, figure as:, , (a), , Q, 24 0, Q, (c), 8 0, (a), , Q, 3 0, Q, (d), 6 0, , (a) 1, (c) 3, , (b) 2, (d) 4, , 20. If the surface density of charge be  , electric field, near the surface of spherical conductor would be:, (a) 2 /  0, (b)  /  0, (c)  / 2 0, (d) 3 / 2 0, 21. The adjacent diagram shows a charge + Q held on an, insulating support S and enclose by a hollow spherical, conductor. O represent the center of the of the, spherical conductor and P is a point such that OP = x, and SP = r. the electric field at point P will be:, , (b), , 15. The electric field at 20 cm from the center of a, uniformly charged non-conducting sphere of radius, , (a), , Q, 4 0 x, , 2, , (b), , Q, 4 0 r 2

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(c) 0, (d) none of the above, 22. A spherical conducting shell of inner radius r 1 and, outer radius r2 has a charge Q. A charge – q is placed, at the center of the shell. The surface charge density on, the inner and outer surfaces of the shell will be., , q, Q, and, 2, 4 r1, 4 r22, Qq, q, (c), and, 2, 4 r1, 4 r22, (a), , q, Qq, and, 2, 4 r1, 4 r22, Qq, (d) 0 and, 4 r22, (b), , 23. A non conducting sphere of radius ‘a’ has a net charge, ‘+q’ uniformly distributed throughout its volume A, spherical conducting having inner and outer, radii ‘b’, and ‘c’ and a net change ‘-q’ is concentric with the, sphere (see the figure). Read the following statements., , (i) the electric field at distance r for the center of the, sphere for, (ii) the electric field at distance r for a < r < b = 0, (iii) the electric field at distance r for b < r < c = 0, (iv) The charge on the inner surface of the spherical, shell = - q, (v) The charge on the outer surface of the spherical, shell = + q, Which of the above statements are true?, (a) (i), (ii) and (v), (b)(i),(iii) and (iv), (c) (ii), (iii) and (iv), (d) (ii), (iii), and (v), 24. An uncharged sphere of metal is placed inside a, charged parallel plate capacitor. The lines of force look, like:, , 25.A thin metallic spherical shell, Q, contains a charge Q on it. A point, charge q is placed at the centre of, the shell and another charge q1 is, q, placed outside it as shown in the, figure. All the three charges are, positive. The force on the charge at the centre is, (a) towards left, (c) towards right, , (b) upward, (d) zero, , 26.Consider the situation of the previous problem., The force on the central charge due to the shell is, (a) towards left, (b) towards right, (c) upward, (d) zero, 27. As shown in the figure, a closed surface intersects a, spherical, conductor. If a, P, positive charge is, placed at point P closed surface, conductor, then the electric flux coming out of the closed surface, will be, (a) zero (c) negative (b) positive, (d) nothing can be said, , Force & Torque in field field lines, 28 An electron is moving in a uniform horizontal electric, field. If the acceleration of electron is at 45° from the, horizontal the intensity of electric field will be, (a) 55.8x1011 N/C, (b) 5.58x1011 N/C, 11, (c) 558x10 N/C, (d) 0.558x1011 N/C, 29. A charged ball B hangs from a slik thread S, which, makes an angle  with, large charged conducting, +, P+, sheet P, as shown in the, +θ, figure. The surface charge, + S, density  Of the sheet is, +, +, proportional to, +, (a) cot , (b) cot , +, +, (c) tan , (d) sin , +, B, , 30. An electron and a proton are in a uniform electric field., The ratio of their acceleration will be:, (a) zero, (b) one, (c) ratio of mass of proton and electron., (d) ratio of mass of electron and proton., , , 31. An electron (mass = 9 1031 kg ) is sent in an electric, field of intensity 1106 volts/m. If the weight of the, electron is negligible, its acceleration will be:, (a) 1.7 1018 m / s 2, (b) 1.7  1017 m / s 2, (c) 1.7  1021 m / s 2, (d) 1.7  1025 m / s 2, 32. A pendulum bob of mass 80 mg and carrying a charge, of 2  10 8 C is at rest in a horizontal uniform electric, field of 20,000 V/m. The tension in the thread of, pendulum is:, (a) 2.2 104 N, (b) 4.4 104 N, (c) 8.8  104 N, (d) 17.6 104 N, 33. An electron having a charge e moves with a velocity V, in X-direction. An electric field acts on it in Ydirection. The force on the electron acts in:, (a) positive direction Y-axis, (b) negative direction of Y-axis, (c) positive direction of Z-axis, (d) negative direction of Z-axis, 34. An electric dipole is placed in a uniform electric field, E. The dipole will experience:, (a) a net force along E, (b) a torque, (c) a net force opposite to E

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(d) all the three above unit it comes in equilibrium, 35. An electron of mass me, initially at rest, moves through, a certain distance in a uniform electric field in time t 1., A proton of mass mp, also initially at ret takes time t 2, to move through an equal distance inn this uniform, electric field. Neglecting effect of gravity, the ratio t 1/t2, is nearly equal to :, (a) 1, , (b), , me, mp, , (c), , mp, me, , (d) 1836, , 36. An electron is released from the bottom plate A as, shows in the figure (E = 104 N/C). The velocity of the, electron when it reaches plate B will be nearly equal, to: [AMU 2009], , sheet P, as shown in the figure. The surface charge, density  of the sheet is proportional to, , (a) tan , (b) sin , (c) cot , (d) cos , 41. An electric dipole is placed at an angle of 300 with an, electric field intensity 2 105 N / C . It experiences a, torque equal to 4 N m. the charge on the dipole if the, dipole length is 2 cm, is, (a) 7  C, (b) 8  C, , (c) 2mC, , (d) 5mC, , 42. An electric dipole is formed by two equal and opposite, charges q with separation d. the charges have same, mass m. It is kept in a uniform electric field E. If it is, slightly rotated from its equilibrium orientation, then, its angular frequency  is [JEE Mains 2019], (a) 0.85 107 m / s, (b) 1.0  107 m / s, (c) 1.25 107 m / s, (d) 1.65 107 m / s, 37. The electric force on a point charge situated on the axis, of a short dipole is F. If the charge is shifted along the, axis to double the distance, the electric force acting, will be, (a) 4F, (c), , F, 4, , F, 2, F, (d), 8, (b), , 38. An electron falls from rest through a vertical distance h, in a uniform and vertically upward direction electric, field E. The direction of electrical field is now reversed, keeping magnitude the same. A proton is allowed to, fall from rest in through the same vertical distance h., The time fall of the electron, in comparison to the time, fall of the proton is:-, , (a) Smaller, (c)10 times greater, , (c), , qE, 2md, 2qE, md, , (b) 2, (d), , (b) 1m/s, 3m/s, (d) 1.5 m/s, 3 m/s, , 40. A charged ball B hangs from a silk thread S, which, makes an angle  with a large charged conducting, , qE, md, qE, md, , 43. The bob of a simple pendulum has mass 2g and a, charge of 5.0  C . It is at rest in a uniform horizontal, electric field of intensity 2000 V/m. at equilibrium, the, angle that the pendulum makes with the vertical is:, (take g = 10 m/s2), [JEE Mains 2019], , (a) tan 1 (5.0), , (b) tan 1 (2.0), , (c) tan 1 (0.5), , (d) tan 1 (0.2), , 44. A simple pendulum of length L is placed between the, plates of a parallel plates capacitor having electric field, E, as shows in figure. Its bob has mass m and charge q., The time period of the pendulum is given by:, [JEE Mains 2019], , (b) 5 times greater, (d) equal, , 39. A toy car with charge q moves on a frictionless, horizontal plane surface under the influence of a, uniform electric field . Due to the force q .its, velocity increases from 0 to 6 m/s in one second, duration. At that instant the direction of the field is, reversed. The car continues to move for two more, seconds under the influence of this field. The average, velocity and the average speed of the toy car between 0, to 3 second are respectively:-, , (a) 2m/s, 4m/s, (c) 1 m/s, 3.5 m/s, , (a), , (a) 2, , L,  qE , g , ,  m, 2, , (b) 2, , L,  qE , g , ,  m, , 2

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(c) 2, , (d) 2, , L, qE , , g, , m, , , (a) 100 V/m upwards, (b) 10 V/m, downwards, (c) 0.1 V/m downwards, (d), 0.1 V/m upwards, Dipole in field, , L, q2 E 2, g  2, m, , 46. Two equal negative charges –q are fixed at point, (0, -  ) on y – axis. A positive charge Q is released, from rest at the point (2  ,0) on the x – axis. The, charge Q will, (a) execute simple harmonic motion about the origin, (b) move to the origin remain at the rest, (c) move to infinity, (d) execute oscillatory but not simple harmonic, Motion, 47. A drop of water mass 106 kg has an electric charge of, 100 nC. What electric field will balance the drop in air, , 48. An electric dipole is placed in a uniform electric field., The net electric force on the dipole., (a) is always zero, (b) can never be zero, (c) depends on the orientation of the dipole, (d) depends on the strength of the dipole, 49. An electric dipole consists of two equal and opposite, chares of magnitude 2 µC placed 0.03 m apart. It is, lying in an electric field of intensity 2x105 N/C. The, maximum torque acting on the dipole will be, (a) 2.4 N-m, (b) 1.2 N-m, (c) 1.2x102 N-m, (d) 2.4x102 N-m., , Electric potential & Potential energy, , Electric potential & potential energy concept, , 1. On moving a charge of 20 coulomb by 2 cm, 2 J of, work is done, then the potential difference between the, points is, (a) 0.1 V, (b) 8 V, (c) 2 V, (d) 0.5V., 2. The intensity of electric field in a region of space is, represented by E = 100/x² V/m. The potential, difference between the points x = 10 m and x = 20 m, will be, (a) 15 V, (b) 10 V, (c) 5 V, (d) 1 V, 3. Two point P and Q are maintained at the potentials of, 10 V and – 4 V, respectively. The work done in, moving 100 electrons from P to Q is, (a) 9.60 × 10- 17 J, (b) -2.24 × 10- 16 J, - 16, (c) 2.24 × 10 J, (d) -9.60 × 10- 17 J

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15. A point charge q moves from point P to a point S along, a path PQRS in a uniform y, electric field E pointing, , P, E, parallel to the Xaxis., The coordinates of P, Q,, 2Q, Q, x, R and S are (a,b,0), (2a, S, 0,0), (a,b,0) and (0,0,0)., The work done by the, R, field in the above process, is, (a) zero, (b) qEab, (c) qEa, (d) qEa, 16.Two points A and B lying on Y-axis at distances 12.3, cm and 12.5 cm from the origin. The potentials at these, points are 56 V and 54.8 V respectively, then the, component of force on a charge of 4µC placed at A, along Y-axis will be, (a) 0.12 N, (b) 4.8x103 N, (c) 24x104 N, (d) 96x102 N, 17 The variation of, potential, with 5, distance R from a, fixed point is as, shown in the figure., 0 1 2 3 4 5 6 R(m), The electric field at, R = 5 m is:, (a) 2.5 volts/m, (b) –2.5 volts/m, (b) 2/5 volts/m, (d) –2/5 volt/m, 18.An electron in an electric field moves, (a) from low potential to high potential, (b) cannot be predicted, (c) from high potential to low potential, (d) none of the above, 19. An electric charge 10-3  C is placed at the origin (0,, 0) of X–Y co-ordinate system. Two points A and B are, Situated at 2 , 2 and (2, 0) respectively. The, potential difference between the points A and B will be, (a) 4.5 volts (b) 9 Volts, (c) Zero (d) 2 Volt, , 20. Charge Q is give a displacement r  aî  bĵ in an, , electric field E  E1î  E 2 ĵ . The work done is, V(volts), , 4. The potential at a point x (measured in  m) due to some, charges situated on the x-axis is given by V(x) = 20/(x2, -4) volt The electric field E at x = 4  m is given by, (a) (10/9) volt/  m and in the +ve x direction, (b) (5/3) volt/  m and in the -ve x direction, (c) (5/3) volt/  m and in the +ve x direction, (d) (10/9) volt/  m and in the -ve x direction, 5. A uniform electric field pointing in positive x –, direction exists in a region. Let A be the origin, B be, the point on the x-axis at x = +1 cm and C be the, point on the y-axis at y = +1 cm. Then the potentials, at the points A,B and C satisfy:, (a) VA < VB (b) VA > VB (c) VA < VC (d) VA > VC, 6. The electric potential while moving along the lines of, force, (a) Decreases, (b) increases, (c) remains constant, (d) becomes infinite, 7. a charged particles was initially in position 1. They are, free to move and they come in position 2 after some, time. Let U1 and U2 be the electrostatic potential, energies in position 1 and 2. Then, (a) U1 > U2 (b) U2 > U1 (c) U1 = U2 (d) U2  U1, 8. The equipotential surfaces for a point charge and a linear, charge will respectively be, (a) spherical and cylindrical, (b) plane and cylindrical, (c) cylindrical and spherical (d) spherical and plane, 9. Potential at any point can be defined as, (a) work done by agent to move a unit charge from, infinity to that point in all cases, (b) –ve of work done by electric field, (c) both are true, (d) None of these, 10 The magnitude of the force on a charge of 12 µC, placed at a point where the potential gradient has a, magnitude of 6x105 V/m is, (a) 14.4 N (b) 21.6 N (c) 7.2 N, (d) 3.6 N, 11.The potential function of an electric field is defined by, the relation V = 5 x + 3y + 15 z. The intensity of, electric field at point (x,y,z) in M.K.S. units will be, (a) 32, (b) 42, (c) 52, (d) 7, , 12 An electric field is given by E  ( yî  xĵ) N/C. The, work done in moving a 1C change from, , , rA  (2î  2 ĵ) m to rB  ( 4î  ĵ) m is, (a) + 4J, (b) 4J, (c) +8J, (d) zero, 13.An electric field E = 50 i + 75 j N/C exists in a certain, region of space. Presuming the potential at the origin, to be zero, the potential at point P (1 m, 2 m) will be, (a) 100 V, (b) 100 V (c) 200 V (d) 200V, 14. A test charge qo is moved, C, without acceleration from point, A to B through a path A  C  d, 45°, B. The potential difference q1, , A, between A and B is, E, (a) E (AC cos45° + BC), (b) E (AC + BC), (c)Ed cos45°, (d) Ed, , , , (a) Q(E1a + E2b), , , , (b) Q (E1a )2  (E2b)2, , (c)Q(E1+E2) a 2  b 2 (d) Q  E12  E 22  a 2  b 2, , , 21. In the region of an electric field a charge is moved, from point A to B via three different paths as shown in, figure W1 W2 and W3 denote the work done along the, three paths. Then :, , (a) W1 < W2 < W3, (b) W1 = W2 > W3, (c) W1 < W2 < W3, (d) W1 = W2 = W3, 22. There is an electric field E in x-direction. If the work, done in moving a charge 0.2 C though a distance of 2, meters along a line making an angle 60 0 with the xaxis is 4 J, what is the value of E:, (a) 4 N/C, (b) 8 N/C

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(c) 3 N/C, (d) 20 N/C, 23. It requires 4 joules of work to move a charge of 20 C, from point A to point B, separated by a distance of 0.2, m. the potential difference between the points A and B,, in volts is:, (a) 80, (b) 16, (c) 5, (d) 0.2, 24. A uniform electric field pointing in positive x-direction, exists in a region. Let A be the origin, B be the point, on the x-axis at x = + 1 cm and C be the point on the yaxis at y = + 1 cm. Then the potentials at the points A,, B and C satisfy:, (a) VA < VB, (b) VA > VB, (c) VA < VC, (d) VA > VC, 25. Let V0 be the potential at the origin in an electric field, ^, , (a) V0  xEx  yE y, , (b) V0  xEx  yE y, , (c) xEx  yE y  V0, , , , 31. In a region, the potential is represented by V (x, y, z) =, 6x – 8xy – 8y + 6yz, where V is volts and x, y, z are in, meters. The electric force experienced by a charge of 2, coulomb situated at point (1, 1, 1) is:, , x2  y 2, , , , Ex2  E y2  V0, , (b) 4 35N, , (a) 24 N, , (c) 6 5N, (d) 30 N, 32. If potential (in volts) in a region is expressed as V (x,, y, z) = 6xy – y + 2yz, the electric field (in N/C) at, point (1, 1, 0) is:, ^, , ^, , ^, , ^, , ^, , (a) (6 i  9 j  k ), ^, , (c) (6 i  5 j  2 k ), , ^, , = (E x i  E x j ) `. The potential at the point (x, y) is :, , (d), , (a) Maximum at B, (b) Maximum at C, (c) Same at all the three points A, B and C, (d) Maximum at A, , ^, , ^, , ^, , ^, , ^, , (b) (3 i  5 j  3 k ), ^, , (d) (2 i  3 j  k ), , 33. n a region of space, the variation of the electric, potential  with distance from the origin is shown in, the figure., The electric field strength is zero at:, , 26. The electric potential at a point (x, y, z) is given by: V, 2, 3, =  x y  xz  4, The electric field, , at that point is:, , ^, , ^, , ^, , = i (2 xy z3 )  j x 2  k 3xz 2, , (a), , ^, , ^, , ^, , = i 2 xy j ( x 2  y 2 )  k (3xz  y 2 ), , (b), , ^, , ^, , ^, , = i z 3  j xyz  k z 2, , (c), ^, , ^, , = (A x + B), , ^, , i , where E is in NC-1 and x is in meters. The values of, ^, , (d) i (2 xy z3 )  j xy 2  k 3z 2 x, 27. The mean free path of electrons in a metal is, 4  108 m . The electric field which can give on an, average 2V energy to an electron in the metal will be, in units of V/m, (a) 8  10 2, (b) 5 1011, (c) 8 1011, (d) 5  107, 28. The electric potential V at any point (x, y, y), all in, meters in space is given by V = 4x2 volt. The electric, field at the point (1, 0, 2) in volt/meter, is:, (a) 8 along positive X-axis, (b) 16 along negative X-axis, (c) 16 along positive X-axis, (d) 8 along negative X-axis, 29. The electric field in a certain region is given by =, ^, , (a) point A, (b) point B, (c) point C, (d) point D, 34. The electric field in a region is given by, , constants are A = 20 SI unit and B = 10 SI unit. If the, potential at x = 1 is V1 and that at x = - 5 is V2 then V1, – V2 is, [JEE Mains, 2019], (a) – 48 V, (b) – 520 V, (c) 180 V, (d) 320 V, 35. When a charge of 3 coulombs is placed in a uniform, electric field, it experiences a force of 3000 newtons, within this filed, potential difference between two, points separated by a distance of 1 cm is:, (a) 10 volts, (b) 90 volts, (c) 1000 volts, (d) 3000 volts., 36. The figure shows the lines of constant potential in a, region in which an electric field is maximum at:, , ^, , 5 i  3 j KV/m. The potential difference VB – VA, between points A and B, having coordinates (4, 0, 3) m, and (10, 3, 0) m respectively, is equal to., (a) 21 kV, (b) – 21 kV, (c) 39 kV, (d) – 39 kV, 30. A, B and C are three points in a uniform electric field., The electric potential is:, , (a) A, (c) C, 37., , (b) B, (d) equal at A, B and C, , The diagram below shows region of equipotential :-

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40V, 20V, , 10V, , 40V, , 30V, , (a), , 20V, , 10V, (b), , 40V, , 10V, , 30V, , 20V, , 30V, , 20V, , 10V, 40V, , (c), , 30V, (d), , A positive charge is moved from A to B in, each diagram., (a) In all the four cases the work done is the same, (b) Minimum work is required to move q in figure, (a), (c) Maximum work is required to move q in figure, (b), (d) Maximum work is required to move q in figure, (c), 38. Figure shows a set of equipotent surface. the, magnitude and direction of electric field that, exists in the region is, , 2 V/m at 450 with x-axis, (b) 10 2 V/m at – 450 with x-axis, (c) 5 2 V/m at 450 with x-axis, (d) 5 2 V/m at 450 with x-axis, (a) 10, , 39. Select the correct statement., (a) potential obeys law of super position, (b) potential is the negative of work done by electric, field in order to shift a unit charge from reference point, to that point, , (c) both, , (d) None of these, 40. The charge on a drop of water is 3 108 C . If its, potential on the surface is 500 volts, its radius is:, (a) 18 cm, (b) 36 cm, (c) 45 cm, (d) 54 cm, 41. A hollow metal sphere of radius 5 cm is charged such, that the potential on its surface is 10 volts. The, potential at the center of the sphere is:, (a) Zero, (b) 10 V, (c) Same as at a point 5 cm away the surface, (d) Same as at a point 25 cm away from the, surface, 42. In the electric field of a point charge q, a certain charge, is carried from point A to B, C, D and E. the work, done, , Electric potential due to point & continuous, charge, equipotential surface, (a) Is the least along the path AB, (b) Is the least along the path AD, (c) Is zero along any one of the path AB, AC, AD, and AE, (d) Is the least along AE., 43. In the electric field on a point charge q shown, a, charge is carried from A to B and from A to C., compare the work done:, , (a) Work done is greater along the path AC than, along AB, (b) Work done is the same in both the cases

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(c) Work done is greater along the path AB than, along AC, (d) Work done is zero in both the cases., 44. and V represent the electric field and electric, potential at a point in space:, (a) If V = 0, E must be zero, (b) If E = 0, must be zero, (c) Id E = 0, V is zero or constant at all points in, its neighborhood, (d) None of the above statements is true., 45. A hollow charged metal sphere has radius r. If the, potential difference between its surface and a point at, distance 3 r from the center is V, then the electric field, intensity at distance 3 r from the center, is:, (a) V/6r, (b) V/4r, (c) V/3r, (d) V/2r, 46. Consider the situation of figure. The work done in, taking a point charge from P to A is WA, from P to B is, WB and from P to C WC:, , (a) WA < WB < WC, (c) WA = WB = WC, , 47., , 49., , A soap bubble is charged to a potential of 16 V. its, radius is them doubled. The potential of the bubble, now will be, (a) 16 V, (b) 8 V, (c) 4 V, (d) 2 V, 50. Choose the correct relation regarding potential., Hence A, B, C and D all are at equal distance from, point O. Then, , (a) VA = VB > VC = VD, (b) VC = VD> VA = VB, (c) VA> VC = VD > VB, (d) VB > VC =VD >VA, 51. An electric charge 10-3  C is placed at the origin (0,, 0) of X – Y co-ordinates system. Two points is A and, B are situated at ( 2, 2) and (2, 0) respectively. The, potential difference between the points A and B will be, (a) 4.5 volt, (b) 9 volt, (c) Zero, (d) 2 volt, , (b) WA > WB > WC, (d) none of these, , 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 centers of the two, rings is:, , 52., , Q, 4 0 (a  b  c), Q(a  b  c), (b), 4 0 (a 2  b 2  c 2 ), Q ab  be  cn, (c), 12 0, abc, , , Q 1, 1, (a),  , , 2, 2, 4 0  R, R d , , (a), , (b) Zero, , , Q 1, 1,  , , 2 0  R, R2  d 2 , QR, (d), 2 0 d 2, (c), , 48., , The given graph shows variation (with distance r, from center) of:, , A charge Q is distributed over three concentric, spherical shell of radii a, b, c (a < b c) such that their, surface charge densities are equal to one another. The, total potential at a point at distance r from their, common center, where r < a, would be:, , (d), , Q (a 2  b 2  c 2 ), 4 0 (a 3  b3  c3 ), , , 53., , A point dipole = - p0 x is kept at the origin. The, potential and electric field due to this this dipole on the, y-axis at a distance d are, respectively: (Take V = 0 at, infinity):, , , (a) Potential of a uniformly charged sphere, (b) Potential of a uniformly charged spherical shell, (c) Electric field of uniformly charged spherical, shell, (d) Electric field of uniformly charged sphere, , , , , , |P|, P, (c), ,, 2, 4 0 d 4 0 d 3, 54., , , , , , | p|, p, (a), ,, 2, 4 0 d 4 0 d 3, , (b) 0,, , P, 4 0 d 3, , , P, (d) 0,, ], 4 0 d 3, , There concentric spherical shells have radii a, b and, c (a<b<c) and having surface charge densities +σ,- σ ,+

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σ respectively . if VA, VB and VC denote the potentials, of the three shells. Then for c = a+ b, we have:, (a) VC  VA  VB, (b) VC  VB  VA, , (c) VC  VB  VA, 55., , (d) VC  VB  VA, , charge q. Another charge Q is placed at the centre of, the shell. The electrostatics potential at a point P a, , R, from the centre of the shell is, 2, 2Q, 2Q, 2q, (a), (b), 40 R, 40 R 40 R, q  Q 2, 2Q, q, (c), +, (d), 40 R, 40 R, 40 R, , distance, , Four point charges – Q, - q , 2q and 2Q are placed,, one at each corner of the square. The relation between, Q and q doe which the potential at the center of the, square is zero is:, (a) Q = q, (c) Q = - q, , 1, q, 1, (d) Q = q, (b) Q =, , 56., , If the earth had a net charge equivalent to 1, electron/m2 of surface area of radius = 6.4  106 m; its, potential would be;, (a) +0.12 volts, (b) – 0.12 volts, (c) +1.2 volts, (d) – 1.2 volts, 57. A charge Q is distributed over two concentric hollow, spheres of radii r and R (> r) such that the surface, densities are equal. The potential at the common center, is:, (a), , Q(R 2  r 2 ), 4 0 (R  r), , (c) Zero, , Q, R r, Q (R  r ), (d), 4 0 (R 2  r 2 ), , 64.The electric fields near the surface of two charged, conducting spheres of radii R1 and R2 are same. The, ratio of their electric potential will be, (a) R1/R2, (b) R1²/R2² (c), R2/R1, (d) R2²/R1², 65.Equal chares q are situated on three points of a circle, such that they form an equilateral triangle of side a., The potential at the centre of the circle will be, q, (a) zero, (b), a, 3(4o ), (c), , 3q, 4o a, , (d), , 3 3q, 4o a, , (b), , 58. The potential on the surface of a charged metallic, sphere of radius 5 cm is 10 volt. The potential at the, centre of the sphere will be, (a) 10 V, (b) 5 V, (c), zero, (d) 20 V, 59. The distance between two parallel equipotent surfaces, A and B, having same potential, is r. The work done in, carrying a q charge from surface A to surface B will, be, Kq,  Kq, Kq, (a) W = 0 (b) W = 2 (c) W =, (d) W =, r, r, r, 60. E and V respectively represent electric field and, electric potential at a point, then, (a) if E = 0, V may be zero or constant, (b) if V = 0, E must be zero, (c) if E = 0, V must be zero, (d) nothing can be predicted, 61. Four charges each of magnitude q are situated at four, corners of a square of side r. The potential at the centre, of square will be, Kq, 4 2, (a) zero, (b), r, Kq, Kq, (c) 2, (d) 2 2, r, r, 62.Two conducting spheres of radii r 1 and r2 are charged, such that their charge densities are equal. The ratio of, potential, near, their, surface, will, be, 2, 2, r, r, (a) r2/r1, (b) r1/r2, (c) 22, (d) 12, r1, r2, 63. A thin spherical conducting shell of radius R has a, , 66 A conducting sphere of radius R is charged to a, potential of V volts. Then the electric field at a, distance r (> R) from the centre of the sphere would be, R 2V, RV, rV, V, (a), (b) 3, (c) 2, (d) 2, r, r, R, r, 67.Two thin concentric hollow conducting spheres of radii, R1 and R2 bear charges Q1 and Q2 respectively. If R1 > R2,, then the potential at a point distance r such that R 1 > r > R2, is:, , Q Q , . 1  2 , 4 0  r R2 , 1  Q1 Q2 , 1  Q1 Q2 , (c), .    (d), .  , 4 0  R1 R2 , 4 0  R1 r , (a), , 68., , Q1  Q2, 4 0, r, 1, , ., , 1, , (b), , Consider two point 1 and 2 in a region outside a, charged sphere two points are not very far away from, the sphere. If E and V represent the electric field vector, and the electric potential, which of the following is not, possible., , , , , , , , , (a) | E1 || E2 |, V1  V2 (b) E1  E2 , V1  V2, , , , , (b) E1  E2 , V1  V2 (d) E1  E2 , V1  V2, 69., , A charges drop of mass 3.2 x 1012 gm. Floats, between two horizontal parallel plates maintained at, potential difference of 980 V and separation between, the plates 2 cm. the number of excess or deficient, electrons on the drop is., , (a) 2, (c) 8, , (b) 4, (d) 16

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Work energy application, Mutual potential energy, , 2E 2t 2, mg, E 2 q 2t 2, (c), 2m, (a), , 75., , 70., , Four equal changes Q are placed at the four corners, of a square of side a each. Work done in removing a, charge – Q form its center to infinity is:, (a) Zero, (c), , 71., , 2Q 2, ( 0 a), , (b), (d), , Q, 4 0 r, , (c) zero, , (d), , Eqm, 2t, , 1, , Qq, 4 0 R, 1, 1, Q, q, , , (c), (d), 4 0 R, 4 0 R, Distance between two charges of 8  C and 12  C is, (b), , , , 10 cm. If distance between them is reduced to 6 cm,, work done is:, (a) 1.8 J, (b) 5.8 J, (c) 6.4 J, (d) 3.0 J, 77. Doubly ionized helium atoms and hydrogen ions are, accelerated from rest through same potential, difference. The ratio of final velocities of helium and, hydrogen ions is:, (a) 1/2, (b) 2, (c) 1/ 2, (d) 2, 78. Three charges Q, +q and +q are placed at the vertices, of a right-angled isosceles triangle as shown. The net, electrostatic energy of the configuration is zero if Q is, equal to:, , 2Q 2, (4 0 a), , Q2, (2 0 a), , A positive charge Q units is moved around another, point positive charge of Q units on a circular path. If, the radius of the circular path is r, the work done on the, charge Q in making one complete revolution is:, (a), , E 2q2m, 2t 2, , A spherical conductor of radius R is charged to Q, volts. Work done in taking a charge q from the center, of the sphere to its surface is:, (a) 0, , 76., , (b), , QQ ', 4 0 r, Q', (d), 4 0 r, (b), , An electron having charge –e located at A, in the, presence of a point charge +q located at O, is moved to, the point B such that OAB forms an equilateral, triangle. The work done in the process is equal to:, (a) q/AB, (b) eq/AB, (c) –eq/AB, (d) zero, 73. A could is at a potential of 8  106 volts relative to, the ground. A charge of 40 coulombs is transferred in, lightning stroke between the cloud and the ground. The, energy dissipated is:, (a) 5.0 106 J, (b) 3.2 107 J, (c) 3.2  108 J, (d) 3.2 108 J, 74. A charge particle of mass m and charge q is released, from rest in a electric field of constant magnitude E., the kinetic energy of the particle after a time t is:, , q, 1 2, (c) – 2q, (a), , 79., , 72., , 2q, 2 2, (d) +q, , 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 [coordinates )(0, a)] to another, point B [coordinates (a, 0)] along the straight path AB, is:, , (a) zero, ,  qQ 1 , 2a, 2 ,  4 0 a , , (c) , 80., , (b), ,  qQ 1 , 2a, 2 ,  4 0 a ,  qQ 1  2, (d) , 2., 2 ,  4 0 a , (b) , , Two charges q1 and q2 are placed 30 cm apart as, shown in the figure. A third charge q3 is moving along, the are of a circle of radius 40 cm from C to D. the

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charge in the potential energy of the system is, , q3, , 4 0, , k, , (d), 84., , where K is:, , (a) 8 q1, (b) 6 q1, (a) (c) 8 q2, (d) 6 q2, (b) Its passes through the frame only once, 81. Charges +q and –q are placed at points A and B, respectively which are a distance 2L apart, C is the, midpoint between A and B. the work done in moving a, charge +Q along the semicircle CRD is:, , An electric field of 1000 V/m is applied to an, electric dipole at angle of 450. The value of electric, dipole moment is 10-29 C.m. what is the potential, energy of the electric dipole?, [JEE Mains 2019], 20, (a) 9 10 J, (b) 7  1027 J, (c) 10 1029 J, (d) 20 1018 J, 85. Four equal point charges Q each are placed in the xy, plane at (0, 2), (4, 2), (4, -2) and (0, -2). The work, required to put a fifth charge Q at the origin of the, coordinate system will be:, [JEE Mains 2019], (a), , qQ, 6 0 L, qQ, (c), 2 0 L, 82., , qQ, 4 0 L, qQ, (d), 6 0 L, (b), , Three charges, each +q are placed at the corners of, an isosceles triangle ABC of sides BC and AC, 2a. D, and E are the mid points of BC and CA. The work, done in taking a charge Q from D to E is., , (b), , Q2 , 1 , (c), 1, , , 4 0 , 3, , 86., , (a) , , Q2, 2 2 0, , [Take, , 1, 4 0, ,  9 109 NmC 2 ], , [JEE Mains 2019], 4, (a) 2.0  10 m / s, (b) 3.0 10 m / s, 3, , (c) 1.5  102 m / s, 87., , (c) zero, 83., , A particle of positive charge Q is fixed at point P.A, second particle of mass m and negative charge –q, moves at constant speed in a circle of radius r 1,, centered at P. the work W that must be done by an, external agent on the second particle to increase the, radius of the motion to r2 is given by, (a) W =, (b) W =, (c) W =, , (d) 1.0 m / s, , A uniformly charged ring of radius 3a and total, charge q is placed in xy-plane centered at origin. A, point charge q is moving towards the ring along the zaxis and has speed u at z = 4a. the minimum value of u, such that it crosses the origin is:, [JEE Mains, 2019], (a), , qQ, (b), 4 0 a, 3qQ, (d), 4 0 a, , Q2, (d), 4 0, , In free space, a particle A of charge 1  C is held, fixed at a point P. another particle B of the same, charge and mas 4 mg is kept at a distance of 1 mm, form P. if B is released then its velocity at a distance of, 9 mm from P is:, , 1/2, , 3qQ, (a), 8 0 a, , Q2 , 1 , 1, , , 4 0 , 5, , 2  1 q2 , , , m  15 4 0 a , 1/2, , 2  4 q2 , , , m  15 4 0 a , , 1/2, , 2  2 q2 , (b), , , m  15 4 0 a , , (c), , 1/2, , 2  1 q2 , (d), , , m  5 4 0 a , , In a field free region, two electron are released to move, on a line towards each other with velocities 1016 m/s., the distance of their closest approach will be nearer to., 10, , 10, , (a) 1.28  10 m, (b) 1.92  10 m, 10, 10, (c) 2.56 10 m, (d) 3.84 10 m, 88. An electric dipole of moment p is placed in the, position of stable equilibrium in uniform electric field, of intensity E. this is rotated through an angle θ from, the initial the final position is find work done, (a) pE cos , (b) pE sin , (c)  pE cos , (d) pE (1  cos  ), 86. Positive and negative point charge of equal

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, , , a, 2, , , , , magnitude are kept at  0,0,  and  0,0,, , a, ,, 2 , , respectively. The work done by the electric field, when another positive point charge is moved from, (- a, 0, 0) to (0, a, 0) is, (A) positive, (B) negative, (C) zero, (D) depends on the path connecting the initial, and final positions, 91.Two charges +q and q are arranged as shown in the, figure. The, a, r, a, work done +q, q, B, X, Y, by, in, A, carrying a test charge q from X to Y will be, kqq, kqq, (a), (b), r  2a, r, 2kqqr, 2kqqa, (c), (d), r (r  a ), a (a  r ), , 92 An electric dipole of moment p is located in a region, , of constant electric field E at an angle  to the field., The dipole is to be rotated by 180° about an axis, passing through its centre of mass and perpendicular to, , p . The work required to achieve this is, (a) pE cos, (b) 2pE sin (c), 2pE cosn (d)  pE sin, 93. An electric dipole of moment ‘p’ is placed in an, electric field of intensity ‘E’. The dipole acquires a, position such that the axis of the dipole makes an angle,  with the direction of the field. Assuming that the, potential energy of the dipole to be zero when  = 900,, the torque and the potential energy of the dipole will, respectively be:, (a) p E sin  , 2p E cos , (b) p E cos  , - p E sin , (c) p E sin  ,-p E cos , (d) p E sin  , - 2p E cos , 93 If an electron is accelerated through a potential, difference of V volt then its momentum will be, 2 eV, (a) 2 meV (b), (c) meV, (d) meV, m, 94 The charge and mass of particle are 2 times and 4000, times the charge and mass of an electron respectively., This particle is accelerated through a potential, difference of 5 V. If initially the particle was at rest, then it final kinetic energy will be, (a) 10 eV (b) 5 eV (c) 100 eV, (d)2x103 eV, , Charge distribution,Connection & Earthing, , 95., , Two identical conduction spheres, fixed in place,, attract each other with an electrostatic force of 0.108 N, when separated by 50.0 cm, center to center. the, spheres are then connected by a thin conducting wire,, when the wire is removed, the spheres repel each other, with an electrostatic force of 0.0360 N. the initial, charges on the spheres were., 6, 6, (a) 9 10 C, 3 10 C, 6, 6, (b) 110 C , 3 10 C, 6, 6, (c) 3 10 C, 2 10 C, 6, , 6, , (d) 110 C , 2 10 C, 96. Two metal spheres, one of radius R and the other of, radius 2R respectively have the same surface charge, density  . They are brought in contact and separated., What will be the new surface charge densities on, them?, , , 5, , 6, 2, , 5, (b)  1   ,  2  , 2, 6, , 5, (c)  1   ,  2  , 2, 3, , 5, (d)  1   ,  2  , 3, 6, (a)  1   ,  2 , , 97.The charge given to any conductor resides on its outer, surface, because, (a) The free charge tends to be in its minimum, potential energy state., (b) The free charge tends to be in its minimum, kinetic energy state., (c) The free charge tends to be in its maximum, kinetic energy state., (d) The free charge tends to be in its maximum, potential energy state, 98. A solid conducting sphere, 1mving a charge Q, is, surrounded by an uncharged conducting hollow, spherical shell let. The potential difference between the, surface of the solid sphere and that of the outer surface, of the hollow shell be V. if the shell is now given n, change of – 4 Q, the new potential difference between, the same two surface is:, [JEE Mains 2019], (a) V, (b) 2V, (c) – 2 V, (d) 4V

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Miscellaneous, 99., , The insulation property of air breaks down at E = 3x, 106 volts per meter. The maximum charge that can be, given to a sphere of diameter 5 meters is, approximately:, (a) 2  10 2 C, (b) 2  10 3 C, (c) 2  10 4 C, (d) 2  10 5 C, 100. Two identical conducting spheres carrying different, charges attract each other with a force F when placed, in air medium at a distance ‘d’ apart. The spheres are, brought into contact an then taken to their original, positions. Now the two spheres repel each other with a, force whose magnitude is equal to that of the initial, attractive force. The ratio between initial charge on the, spheres is, (b) 3  8 only, , (a) (3  8) only, , (c) (3  8) or (3  8) (d)  3, 101. Consider the following statements about electric, dipole and select the correct ones:, , , S1: Electric dipole moment vector P is directed, form the negative charge to the positive charge, S2: The electric field of a dipole at a point with, , , , , , S3: The electric dipole potential falls as, , , , , , (a) S2, S3 and S4, , (b) S3 and S4, , (c) S2 and S3, , (d) All four, , 102. A conducting sphere of radius R is given a charge Q., The electric potential and the electric field at the center, of the sphere respectively are:, , Q, Q, and, 4 0 R, 4 0 R 2, , (b) Both are zero, (c) Zero and, (d), , (b) 4  0Q x10, , 22, , volt/m, , (c) 12  0Q x10 volt/m, (d) 4  0Q x10 volt/m, , ….By Praveen Gupta, , 1, r, , r  p E, , (a), , 105. The electric potential at a point in free space due to a, charge Q coulomb is Q 1011 volts. The electric field at, that point is, 22, (a) 12  0Q x10 volt/m, , 1, and, r2, , S4: In a uniform electric field, the electric dipole, experience no net forces but a torque, , , It moves slowly towards the frame and stays in the, plane of the frame, , 20, , angle between r and P ., , not as, , (c) –ve charge oscillates along the Z-axis, (d) It moves away from the frame, , 20, , position vector r depends on r as well as the, , , 104. 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 Zaxis. If a –ve point charge is placed at a distance z, away from the above frame (z < <L) the, , Q, 4 0 R 2, , Q, and Zero, 4 0 R, , 103. A soap bubble is given a negative charge. Then its, radius:, (a) Decreases, (b) Increase, (c) Remain unchanged, (d) Nothing can be said because sufficient, information is not available.