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Objective Problems, [ Level 1], Charge and Electrostatic Force, i. When 10* electrons are removed from a neutral metal, sphere, the charge on the sphere becomes, a) 16 uC, (c) 32 µC, 9. The force between two charges 0.06 m apart is 5 N. If, each charge is moved towards the other by 0.01 m, then, the force between them will become, (d) -32 µC, (a) 7.20 N, (b) 11.25 N (c) 22.50 N (d) 45.00 N, 2. A conductor has 14.4 x 10-1C positive charge. The, conductor has (charge on electron = 1.6x 10-19, 10. 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), C), Xa) 9 electrons in excess, (b) 27 electrons in short, (c) 27 electrons in excess, (d) 9 electrons in short, (а), 2, (Ъ) F, (c) 2F, (d) 4F, 3. Charge on a-particle is, (a) 4.8 x10-19 c, 11. Electric charges of 1µC,-1uC 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) 1.6 x 10-19 C, (d) 6.4 x 10-19 C, (c) 3.2 x 10-19 c, 4. When a glass rod is rubbed with silk, it, (b) 1.8 N, C) 2.7 N, (d) 3.6 N, (a) gains electrons from silk, b) gives electrons to silk, (c) gains protons from silk, (d) gives protons to silk, 12. Two small conducting spheres of equal radius have, charges +10uC and -20uC respectively and placed at a, distance R from each other. They experience force F1. If, they are brought in contact and separated to the same, distance, they experience force F2. The ratio of F, to F, is, (a) 1:8, (c) 1:2, 5. When a body is earth connected, electrons from the earth, flow into the body. This means the body is, (b) -8:1, (d) -2:1, fa) uncharged, (b) charged positively, C) charged negatively, (d) an insulator, 13. Equal charges Q are placed at the four corners A, B,C, and D of a square of length a. The magnitude of the force, on the charge at B will be, 302, 6. There are two charges +1 uC and +5 µC. The ratio of the, forces acting on them will be, (a) 1:5, (c) 5:1, (a), (b), 4 TE a?, (b) 1:1, d) 1:25, 1+ 2/2 Q?, (d), 2, 7. F and F, represents gravitational and electrostatic force, respectively between electrons situated at a distance, 10 cm. The ratio of F,IF, is of the order of, (a) 1042, (c) 1024, 8. Two similar small 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 small sphere, having +q charge is kept, then it will experience a force in, magnitude and direction as, (a) zero having no direction, (b) 8F towards +g charge, (c) 8F towards -q charge, (d) 4F towards +q charge, 14. 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, (b) 10-21, (d) 1043, (a) F, O F2, (b) F14, (d) 4F, 15. Two charges +4e and +e are at a distance x apart. At what, distance, a charge q must be placed from charge +e, so, that it is in equilibrium?, (b) 2x/3, d) x/4, (a) x/2, Scanned by CamScanner, POCO F1

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58, Objective Physics Vol. 2, 16, A charge Q is placed at each of the two opposite corners, of a square. A charge q is placed at each of the other two, corners. If the resultant force on Q is zero, then, (a) Q = V29, (c) Q = 2/29, Electric Field Strength and Electric, Potential, (b) Q = - Jzg, - 2/29, 23. Figure shows the electric lines of force emerging from a, charged body. If the electric field at A and B are E and, E, respectively and if the distance between A and B is r,, then, (d) Q = -, 17. A charge q is lying at mid-point of the line joining the, two similar charges Q. The system will be in equilibrium, if the value of q is, (a) Q/2, (c) Q/4, (b) - Q/2, (d) - Q/4, A, 18. Two point charges +2 C and +6 C repel each other with a, force of 12 N. If a charge of-4 C is given to each of these, charges, the force now is, (a) 4 N (repulsive), (b) 4 N (attractive), (c) 12 N (attractive), (d) 8 N (repulsive), (a) E, > E,, Eg, (с) Е, %3, (b) E, < Eg, (d) E, =, %3D, 19. A charge q, exerts some force on a second charge q2., If a, 24. ABC is an equilateral triangle. Charges +q are placed at, third charge q, is brought near q,2, the force exerted by q,, on 72, (a) decreases, (b) increases, (c) remains the same, (d) increases if q, is of same sign as q, and decreases if q, is of, opposite sign as 91, each corner. Tlhe electric intensity at O will be, +g, 20. Three equal charges are placed on the three corners of a, square. If the force between q and q2 is F2 and that, between q, and q3 is F13, then the ratio of magnitudes, (F12/F13 ) is, (a) 1/2, (c) 1//2, B, (b) 2, (d) V2, (a), 4TEO, 1, (b), 4TE, r, 1 39, Sorzero, (d), 4πεο, 21. The centres of two identical small conducting spheres are, I mapart. They carry charges of opposite kind and attract, each other with a force F. When they are connected by a, conducting thin wire they repel each other with a force, F/3. What is the ratio of magnitude of charges carried by, the spheres initially?, (a) 1:1, (c) 3:1, 2od, 25. The insulation property of air breaks down at, E = 3x 10° V/m The maximum charge that can be given, to a sphere of diameter 5 m is approximately (in, coulombs), (a) 2x 10-2, (b) 2:1, (d) 4:1, (b) 2x 10-3, (d) 2x105, (c) 2x104, 26. The distance between the two charges 25µCand 36µCis, 11cm At what point on the line joining the two, the, intensity will be zero?, 22. A metallic sphere having no net charge is placed near a, finite metal plate carrying a positive charge. The electric, force on the sphere will be, (a) towards the plate, (b) away from the plate, (c) parallel to the plate, (d) 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 4 cm from 25 µC, (d) At a distance of 4 cm from 36 µC, Scanned by CamScanner

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Electrostatics, 59, 27, The clectric field near a conducting surface having a, uniform surface charge density o is given by, 34. Figures below show regular hexagons, with charges at, the verticés. In which of the following cases the clectric, field at the centre is not zero?, (a), and is parallel to the surface, 20, -9, (b), -and is parallel to the surface, and is normal to the surface, -9, 20, (d), and is normal to the surface, (1), (2), 29, 29, 29, 28. The unit of electric field is not equivalent to, (a) N/C, 29, 29, 29, 29, (c) V/m, (d) J/C-m, (3), (4), 29. A metallic solid sphere is placed in a uniform electric, field.The lines of force follow the path(s) shown in figure, (а) 1, (b) 2, (d) 4, 35. Electric field intensity at a point in between two parallel, sheets with like charges of same surface charge densities, (6) is, as, 1, (a), 2ɛ0, (b), 2-, S zero, 20, (d), 3, 4, 36. q, 2q, 3q and 4g charges are placed at the four corners A,, and D of a square. The field at the centre P of the, В,, square has the direction along, (a) 1, (b) 2, (c) 3, 30. The unit of intensity of electric field is, la) Newton/coulomb, (c) Volt-metre, 29, B, (b) Joule/coulomb, (d) Newton/metre, A, od, 31. The figure shows some of the electric field lines, corresponding to an electric field. The figure suggests, B., D, 49, 39, (а) АВ, (c) AC, o CB, (d) BD, (b) E, = Eg = Ec, (d) E = Ec < E,, 37. Three point charges as shown are placed at the vertices of, an isosceles right angled triangle. Which of the numbered, vectors coincides in direction with the electric field at the, (a) E, > Eg > Ec, JCE, = Ec > Eg, 32. Two spheres of radius a and b respectively are charged, and joined by a wire. The ratio of electric field of the, spheres is, mid-point M of the hypotenuse ?, Q2= +q, 3, 2, (a) alb, (c) ab?, (b) Ыа, (d) b?la?, 33. 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, 1, times, 4TEO, of this cube will be, 1= +q, Q3 = +q, (a) q/b?, (c) 32g/b?, (b) q/2b?, (a) 1, (c) 3, (b) 2, (d) 4, (d) zero, Scanned by CamScanner

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60, Objective Physics Vol. 2, 38. ABC is an equilateral triangle. Charges +q are placed at, each corner. The electric intensity at 0, the centroid of, the triangle will be, 45. Two spheres A and B of radius a and b respectively, are at, same clectric potential. The ratio of the surface charge, densities of A and B is, a, (a), b, (b), a, (c), (d)., 46. Point charge q, = 2µC and q, =-1µCare kept at points, x= 0 and x 6 respectively. Electrical potential will be, zero at points, (a) x = 2 and x = 9, (c) x = 4 andx 12, +9, 1, (a), 4πες, 3, (b), 4 TtE, r, (b) x =1 and x = 5, (d) x = - 2 and x = 2, 47. Eight small drops, each of radius r and having same, charge q are combined to form a big drop. The ratio, between the potentials of the bigger drop and the smaller, drop is, (a) 8:1, ) zero, 1, 39, (d), 4πε,, 39. Two point charges (+Q) and (-2Q) are fixed on the, X-axis at positions a and 2a from origin, respectively. At, what positions on the axis, the resultant electric field is, (b) 4:1, (c) 2:1, (d) 1:8, 48. Eight oil drops of same size are charged to a potential of, 50 V each. These oil drops are merged into one single, large drop. What will be the potential of the large drop?, (b) 100 V, (d) 400 V, zero?, (a) Only x = Za, (c) Both x = t 2a, (b) Only x = - V2a, (d) Only x = 3a/2, (a) 50 V, (c) 200 V, 40. Two point charges q and 2q are placed some distance, apart. If the electric field at the location of q be E, then, that at the location of 2q will be, 49. Electric potential at a point x from the centre inside a, conducting sphere of radius R and carrying charge Q is, (а) ЗЕ, (c) E, (Ъ) E/2, (d) None of these, (b), 4πεο x, (a), 4πε, R, 1, (c), 41. Infinite charges of magnitude q each are lying at, x= 1, 2, 4, 8,...metre on X-axis. The value of intensity of, electric field at point x 0 due to these charges will be, (a) 12 x 10° qN/C, xQ, 4πεο, (d) zero, 50. Consider a system composed of two metallic spheres of, n connected by a thin wire and switch S as, shown in the figure. Initially, Sis in open position and the, spheres carry charges q, and q2, respectively. If the, switch is closed, then potential of the system is, radii, and, (b) zero, (c) 6 x 10° gN/C, (d) 4 x 10° qN/C, 42. Angle between equipotential surface and lines of force is, (а) zero, S, (b) 180°, (d) 45°, .06-(0, 43. 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 15 cm from the centre will be, 92, 91, 1, (a), 9192, 1, (b), 4 TE, 2, (a) v, (b), V, 1, (c), 4πεο η, 1, (d), 92, (c), V, (d) 3 V, 2, 51. Two equal positive charges are kept at points A and B., The electric potential at the points between A and B, (excluding these points) is studied while moving from A, to B. The potential, (a) continuously increases, (b) continuously decreases, (c) increases then decreases, (d) decreases then increases, 44. Two unlike charges of magnitude q are separated by a, distance 2d. The potential at a point mid-way between, them is, (a) zero, (b), 4 TEO, 1, (c), 4 TEO, 29, (d), 4 TEO, d, d, Scanned by CamScanner

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Electrostatics, 61, 52. A uniform electric field having a magnitude E, and, direction along the positive .X-axis exists. If the potential, V is zero at r Q then its value at X = +x will be, (a) +xE, (c) +x'E, Potential Energy, Work done,, Kinetic Energy and Speed of, Charged Particle in Electric Field, (b) -xE, (d) -x'E,, 60. 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 work, done, 53. 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, 1 cm?, (a) 10 V, (c) 1000 V, (b) 250 V, (d) 2500 V, 54. The electric potentialV is given as a function of distance.x, (metre) by V (5r + 10x-9) volt. The value of electric, field at x l is, E, (a) - 20 V/m, (c) 11 V/m, (b) 6 V/m, (d) -23 V/m, D, 55. 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) is least along the path AB, (b) is least along the path AD, (c) is zero along all the paths AB, AC, AD and AE, (d) is least along AE, (a) 2000 V/m, (c) 500 V/m, (b) 1000 V/m, (d) 3000 V/m, 61. If E is the clectric field intensity of an electrostatic field,, then the electrostatic energy density is proportional to, (c) 1/E?, 56. Charges 2q,- q and - q lie at the vertices of an equilateral, triangle. The value of E and V at the centroid of the, triangle will be, (a) E 0 andV 0, (c) E * 0 and V = 0, (a) E, (b) E?, (d) E, 62. A particle A has charge +q and a particle B has charge, (b) E = 0 and V = 0, (d) E = 0 and V 0, +4g with each of them having the same mass m. When, allowed to fall from rest through the same electric, VA, potential difference, the ratio of their speed, will, 57. In a uniform electric field a charge of 3 C experiences a, force of 3000 N. The potential difference between two, points 1 cm apart along the electric lines of force will be, (b) 100 V, (d) 300 V, VB, become, (a) 10 V, (c) 30 V, (а) 2:1, (c) 1:4, (b) 1:2, (d) 4:1, 63. Three particles, each having a charge of 10 µCare placed, 58. From a point charge there is a fixed point A. At that point, there is an electric field of 500 V/m and potential of, 3000 V. Then, the distance of A from the point charge is, (а) 6 m, (c) 36 m, at the corners of an equilateral triangle of side 10 cm. The, electrostatic potential energy of the system is (given, 1, (b) 12 m, (d) 144 m, -= 9x 10° N-m2/C), 4πεο, (a) zero, (c) 27 J, (b) infinite, (d) 100 J, 59. Two point charges are kept at a certain distance from one, another. The graph represents the variation of the, potential along the straight line connecting the two, charges. At what point is the electric field zero?, 64. A mass m= 20g has a charge q = 3.0mC. 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 s in this region is, (a) 80 m/s, (c) 44 m/s, (b) 56 m/s, (d) 40 m/s, 3, 2, 65. Four identical charges +50 µC each are placed, one at, each corner of a square of side 2 m. How much extermal, energy is required to bring another charge of + 50 µC, from infinity to the centre of the square?, (a) 1, (c) 3, (b) 2, (d) None of these, (а) 64 J, (c) 16 J, (b) 41 J, (d) 10 J, Scanned by CamScanner