PHYS102 Previous Exam Problems CHAPTER 24 Electric Potential Electric potential energy of a point charge Calculating electric potential from electric field Electric potential of point charges Calculating electric field form electric potential Work & Electric potential energy of a system Conservation of energy Conductors General 1. Two points A (2.0 m, 3.0 m) and B (5.0 m, 7.0 m) are located in a region where there is a uniform electric field that is given by E = 4.0 î + 3.0 ĵ (N/C). What is potential difference (V A-V B)? (Ans: 24 V) 2. Eight isolated identical spherical raindrops are each at a potential of 100 V at the surface, relative to the potential at infinity. They are combined together to make one spherical raindrop. What is the potential at the surface of the combined raindrop? (Ans: 400 V) 3. Point charges q and Q are placed as shown in figure 1. If q = +2.0 nc and Q = -2.0 nc, a = 3.0 m, and b = 4.0 m, what is the electric potential difference (V A-V B)? (Ans: 4.8 V) 4. Two identical and isolated 8.0-μC point charges are positioned on the x axis, one is at x = +1.0 m and the other is at x = -1.0 m. They are released from rest simultaneously. What is the kinetic energy of either of the charges after it has moved 2.0 m along the x axis? (Ans: 96 mj) 5. In figure 2, two particles with charges Q and Q are fixed at two vertices of an equilateral triangle with sides of length a. What is the work required to move a particle with charge q from point i to point f? (Ans: 0) 6. Over a certain region of space, the electric potential is give by: V(x,y) = x 2 + y 2 + 2xy, where V is in volts and x and y are in meters. Find the magnitude of the electric field at the point P (1.0, 2.0). (Ans: 8.5 N/C) 7. A charge q 1 = -5.0 μc and a charge q 2 = 6.0 μc are located at (8.0 cm, 0.0) and (0.0 cm, 6.0 cm) respectively in the xy plane. How much work was done, by an external agent, to bring these charges to their final positions starting from infinite separation? [consider V = 0 at infinity] (Ans: 2.7 J) 8. A particle, with a mass of 9.0 10-9 kg and a charge of +8 nc, has a kinetic energy of 36 μj at point A and moves to point B where the potential is 3.0 10 3 V greater than that at point A. What is the particle's kinetic energy at point B? (Ans: 12 μj) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 1
9. What is the external work required to bring four 3.0 10-9 C positive point charges from infinity and place them at the corners of a square of side 0.12 m? (Ans: +3.7 μj) 10. A point charge q 1 = + 2.4 μc is held stationary at the origin. A second point charge q 2 = - 4.3 μc moves from x 1 = 0.15 m, y 1 = 0 to a point x 2 = 0.25 m, y 2 = 0.25 m. How much work is done by the electric force on q 2? (Ans: - 0.36 J) 11. An electron is accelerated from a speed of 3 10 6 m/s to 8 10 6 m/s. Calculate the electric potential through which electron has to pass to gain this acceleration? (Ans: 157 V) 12. A conducting sphere with a radius of 10 cm, has a surface charge density of 4 10 6 C/m 2. What is the electric potential, at r = 5 cm from the center of the sphere? [assume V = 0 at infinity] (Ans: 4.5 10 4 V) 13. Calculate the ratio of the speed of a proton to that of an electron, both accelerated through the same potential difference. (Ans: 0.023) 14. Two charged spherical conductors having radii 4.0 cm and 6.0 cm are connected by a long conducting wire. A total charge of 20 μc is placed on this combination of two spheres. Find the charges on each sphere (smaller first). (Ans: 8 μc and 12 μc) 15. Consider the parallel conducting plates shown in figure 4. The distance between the equipotential surfaces A and B is 1.00 cm, and the electric potential on surface A is - 280 V. What is the electric potential on the equipotential surface B? (Ans: -220 V) 16. A point charge of 5.0 10-9 C is transferred, by an external agent, from infinity to the surface of a ball of radius 5.0 cm. If the ball has a charge density of 5.0 10-4 C/m 2, what is the amount of work done, by the external agent, in the process? [assume V = 0 at infinity] (Ans: 1.4 10-2 J) 17. A particle with a charge of 5.5 10-8 C is fixed at the origin. How much work is done by external agent to move a charge of -2.3 10-8 C from point A to point B shown in figure 6? (Ans: 6.0 10-5 J) 18. Two electrons are initially far away. Each electron is initially moving toward the other one with a speed of 500 m/s. Find the closest distance they can get to each other. (Ans: 1.01 mm) 19. In a certain region of the xy plane, the electric potential is given by V (x,y) = 2xy 3x 2 + 5y, where V is in volts, and x and y are in meters. At which point is the electric field equal to zero? (Ans: 2.5, 7.5 m) 20. A charged solid conducting sphere has a radius of 20 cm and a potential of 400 V on its surface. Calculate the magnitude of the electric field 40 cm from the center of the sphere. (Ans: 500 V/m) 21. A proton moves in a uniform electric field of 2.5 10 7 N/C from point A to point B by traveling a distance of 1.5 m. Find the magnitudes of the work done and the potential difference between points A and B. (Ans: 6 10-12 J, 3.75 10 7 V) 22. The electric potential at point in an xy plane is given by V = 3x 2 4y 2. What are the magnitude and direction of the electric field at the point (4.0, 2.0) m? (Ans: E = 29 N/C at an angle of 146 o counterclockwise from the + x axis) 23. What is the net electric potential at point P due to the four point charges arranged in the configuration shown in figure 7? [Take q = 36 nc, d = 0.5 m] ( Ans: V p = 324 V) 24. Two oppositely charged parallel plates, 0.02 m apart, produce a uniform electric field between the plates. The potential energy U of an electron in the field varies with displacement x from one of the plates as shown in figure 8. What is the magnitude of the force on the electron? (Ans: 7.5 10-15 N) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 2
25. Two protons, p, are fixed 6.0 m apart, as shown in figure 10. An electron, e, is released from point A. Find its speed at point O, midway between the protons. (Ans: 11.6 m/s) 26. Over a certain region of space, the electric potential is give by: V(x,y) = x 2 +y 2 +2xy, where V is in volts, and x and y are in meters. Find the angle that the electric field vector makes with z axis at the point P (1.0, 2.0, 0.0). (Ans: 90 o ) 27. In figure 12, two large horizontal metal plates are separated by 4 mm. The lower plate is at a potential of -6.0 V. What potential should be applied to the upper plate to create an electric field of strength 4000 V/m upwards in the space between the plates? (Ans: -22 V) 28. 1.0 mj of work is required to move two identical positive charges +q from infinite separation so that they are separated by a distance a. How much work is required to move four identical positive charges +q from infinite separation so that they are arranged at the corner of a square with edge length a? [consider V = 0 at infinity] (Ans: 5.4 mj) 29. Find the electric potential at x = 0 for the following distribution of charges: -2q at x = 10 cm and -2q at x = -10 cm. [Take q = 1.0 10-9 C, and the electrostatic potential at infinity = 0] (Ans: -360 V) 30. Three point charges are initially infinitely far apart. Two of the point charges are identical and have charge Q. If zero net work is required to assemble the three charges at the corners of an equilateral triangle of side d, what is the value of the third charge? (Ans: - Q/2) 31. Consider two concentric conducting shells of radii a and b, b > a. The smaller (inner) shell has a positive charge q and the larger (outer) shell has a charge Q. If the potential at the surface of the inner shell is zero, what is the value of Q? (Ans: Q = -bq/a) 32. In figure 14, two equal positive charges, each of magnitude 5.0 10-5 C, are fixed at points A and B separated by a distance of 6 m. An equal and opposite charge moves towards them along the line CO. At point C, 4.0 m from O, the kinetic energy of the moving charge is 4.0 J. What is the kinetic energy of this charge when it passes point O? (Ans:10.0 J) 33. In figure 15, what is the net electric potential at point P due to the four point charges if V = 0 at infinity? [Take d = 2 cm, q = 1.0 μc] (Ans: 9.0 10 5 V) 34. Two balls with charges 5.0 μc and 10 μc are at a distance of 1.0 m from each other. In order to reduce the distance between them to 0.5 m, what amount of work needs to be performed? (Ans: 0.45 J) 35. In figure 18, Q 1 = 2.0 10-6 C and Q 2 = - 2.0 10-6 C. What is the external work needed to move a charge Q = - 4.0 10-6 C at constant speed from point A at the center of the square to point B at the corner? (Ans: zero) 36. Consider a metallic sphere carrying a charge of 4.0 10-8 C and having a potential of 400 V. Find the diameter of the sphere. (Ans: 1.8 m) 37. Two equal charges, each of 0.12 C, are separated by a distance of 1.8 m. What is the work done, by an external agent, to bring a charge of 0.15 C from infinity to the midpoint between the two charges? (Ans: 3.6 10 8 J) 38. What is the electric potential energy of an electron at a distance r = 2.40 10-10 m from the nucleus of a hydrogen atom? [the nucleus consists of a single proton, 1 ev = 1.6 10-19 J] (Ans: -6.0 ev) 39. A 2-meter conducting rod is fixed perpendicularly to a uniform 200-N/C electric field. What is the potential difference between its ends? (Ans: zero) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 3
40. Two conducting spheres are very far apart. The smaller sphere carries a total charge of 6 μc. The larger sphere has a radius twice that of the smaller sphere and is neutral (Q = 0). After the two spheres are connected by a thin conducting wire, what are the charges on the smaller and the larger spheres, respectively? (Ans: 2 μc and 4 μc) 41. An electron is accelerated by a potential difference of 2000 V. If this potential difference is increased to 8000 V, by what factor will the speed of the electron increase? (Ans: 2) 42. An electron is moving parallel to the x axis under the influence of a uniform electric field directed along the positive x axis. The electron has an initial velocity of 3.0 10 6 m/s at point A and its velocity is reduced to 2.0 10 6 m/s at point B. Calculate the potential difference (V B-V A). (Ans: -14 V) 43. The electric field in a region of space is E x = 5000 x (V/m), where x is in meters. Find an expression for the electric potential V at point x. As a reference, let V = 0 at the origin. (Ans: -2500 x 2 ) 44. Figure 22 shows two equipotential (dashed) surfaces such that V A = -5.0 V and V B = -15 V. What is the external work needed to move a -2.0 μc charge at constant speed from A to B along the indicated path? (Ans: 20 μj) 45. A charge of +28 nc is placed at the origin in a uniform electric field that is directed along the positive y axis and has a magnitude of 4.0 10 4 V/m. What is the work done by the electric field when the charge moves to the point (3.0 m, 4.0 m)? (Ans: +4.5 mj) 46. An electron is placed in an xy plane where the electric potential depends on x and y as shown in figure 23 (the potential does not depend on z). What is the electric field (in units of kv/m)? (Ans: 5 î 2 ĵ ) 47. An isolated conducting sphere has radius R = 0.20 m and a charge of +20 μc. Point A is at a distance of 3R from the center of the sphere. If V C is the electric potential at the center of the sphere, what is the electric potential difference V C V A? (Ans: +6.0 10 5 V) 48. An electron is projected with an initial kinetic energy of 3.6 10-24 J toward a fixed proton. If the electron is initially infinitely far from the proton, at what distance from the proton is its speed equal to twice its initial speed? (Ans: 21 μm) 49. Two charges q = + 2.0 μc are fixed a distance 2d = 2.0 cm apart (see figure 25). With V = 0 at infinity, how much work needs to be done by an external agent to move one of the charges to point C? (Ans: + 0.75 J) 50. Four equal positive charges, each 3.2 μc, are held at the four corners of a square of edge 0.50 m. How much work is required to move one of those charges far away from other three? (Ans: 0.50 J) 51. A non-conducting solid sphere of radius R = 10.0 cm has a uniformly distributed charge Q = +1.50 μc. Find the magnitude of the potential difference between a point at r = 50.0 cm and a point on the surface of the sphere. (Ans: 108 kv) 52. A proton is released from rest in a uniform electric field of magnitude 8.0 10 4 V/m directed along the positive x axis. The proton undergoes a displacement of 0.50 m along the direction of the field. Calculate the change in the potential energy of the proton. [1 ev = 1.6 10-19 J] (Ans: -40 kev) 53. In figure 29, a proton s speed as it passes point A is 5.0 10 4 m/s. It follows the trajectory shown in the figure. What is the proton s speed at point B? [mass of the proton = 1.67 10-27 kg] (Ans: 1.2 10 5 m/s) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 4
54. Two large, parallel, conducting plates are 20 cm apart and have charges of equal magnitude but opposite signs on their facing surfaces. An electron, placed anywhere between the two plates experiences an electrostatic force of 1.6 10-15 N. Find the magnitude of the potential difference between the two plates. (Ans: 2.0 kv) 55. In figure 30, point P is at the center of the square. Find the net electric potential at point P. Assume V = 0 at infinity. (Ans: - 2.8 kq/d) 56. Find the electric potential at the center of a charged metal sphere of radius 15 cm if the electric field at its surface is 1.2 10 4 N/C. (Ans: 1.8 kv) 57. Two electrons are fixed 2.0 cm apart. Another electron is shot from infinity with speed v and comes to rest at a point midway between the two electrons. Find v. (Ans: 318 m/s) 58. How much work is required to move the charge q 2 from the initial position i to the final position f, as shown in figure 31? [q 1 = -60 μc and q 2 = 20 μc] (Ans: 5.4 J) 59. As shown in figure 32, two particle with charge Q = 10 μc each are fixed at the vertices of an equilateral triangle with sides of length a = 0.30 m. How much work is required to move a particle with a charge q = 1 μc from point A at the other vertex to point B at the center of the line joining the fixed charges? (Ans: 0.6 J) 60. A metallic sphere, of radius 8 cm, is charged to a potential of 500 V (take V = 0 at infinity). An electron is initially 15 cm from the center of the sphere. What must be the initial speed of the electron to barely hit the sphere (v f = 0)? (Ans: 9.1 10 6 m/s) 61. Consider two point charges: one is q 1 = 6 μc and is located at (0, 12 cm), and the other is q 2 = 6 μc and is located at (0, -12 cm). How much work must be done by an external agent to move a third charge q 3 = 6 μc from the origin to (5 cm, 0)? (Ans: 415 mj) 62. Consider an insulating infinite plane sheet of uniform charge density σ. The electric potential at point A is 200 V and at point B is 350 V (see figure 33). What is the charge density on the sheet? (Ans: -1.33 nc/m 2 ) 63. If the electric field has magnitude of 200 V/m and makes an angle of 30 with the positive x-axis, what is the potential difference V B-V A between point A (0, 0) and point B (3.0 m, 0 m)? (Ans: - 520 V) 64. Three point charges 2.00 μc, Q, and + 6.00 μc are fixed along the x-axis as shown in figure 34. If the net electric potential at point P due to these charges is zero, what is the charge Q? (Ans: - 2.83 μc) 65. Figure 35 shows the x component of the electric field as a function of x in a region. The y and z components of the electric field are zero in this region. If the electric potential at x = 0 is 10 V, what is the electric potential at x = 3 m? (Ans: +40 V) 66. A particle of charge 2 10-3 C is placed in an xy plane where the electric potential depends on x and y as shown in figure 23. The potential does not depend on z. What is the electric force on the particle? (Ans: 10 î 4 ĵ N) 67. Two point charges of equal magnitude (50 nc) and opposite signs are placed on diagonally opposite corners of a (60 cm 80 cm) rectangle, as shown in figure 37. Determine the potential difference V B V A. (Ans: 375 V) 68. In a certain region of space, the electric potential is given by V (x,y,z) = 2xy-x 2 +5y, where x and y are in cm. Determine the x and y coordinates of a point in space where the electric field is E = ( 4 î 3 ĵ ) V/cm. (Ans: x = 1.0 cm, y = + 1.0 cm) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 5
69. A +1.0-μC point charge moves from point A to point B in the uniform electric field shown in figure 38. What is the change in the potential energy of the charge? (Ans: It decreases by 9.0 10-6 J) 70. A conducting sphere of radius 15 cm has a net positive charge of 3.0 10-8 C. At what distance from the surface of the sphere has the electric potential decreased by 500 V? (Ans: 5.8 cm) 71. A particle with mass m = 6.7 10-27 kg and charge q = + 3.2 10-19 C has a speed of 20 km/s at point A and moves to point B where it momentarily stops. Only electric forces act on the particle during the motion. Determine the electric potential difference V A V B. (Ans: 4.2 V) 72. Two positive charges, separated by a distance d, have an electric potential energy of 70 μj. The magnitude of the electrostatic force between the charges is 10-3 N, find the separation d between them. (Ans: 7.0 cm) 73. A proton of kinetic energy 4.8 10 6 ev travels (from infinity) head-on toward a lead nucleus (with 82 protons). Assuming that the proton does not penetrate the nucleus and that the only force between the proton and the nucleus is the electric force, calculate the smallest separation between the proton and the nucleus when the proton comes momentarily to rest. (Ans: 2.5 10-14 m) 74. Figure 39 shows an electron moving to the right between two parallel charged plates. The electric potentials of the plates are V 1 = 70 V and V 2 = 50 V. What is the change in the kinetic energy of the electron as it moves from the left to the right plate? (Ans: +3.2 10-18 J) 75. Two point charges are fixed along the x axis as follows: q 1 = +2.0µC at x 1 = 0, and q 2 = -5.0 µc at x 2 = 1.0 m. At what value of x (on the + x-axis) is the electric potential equal to zero? (Ans: 0.29 m) 76. An electron is released from rest at the origin in a uniform electric field that points in the positive x direction and has a magnitude of 850 N/C. What is the change in the electric potential energy of the electronfield system when the electron moves a distance of 2.5 m? (Ans: 3.4 10-16 J) 77. Two point charges QA = + 2 μc and QB = 6 μc are located on the x-axis at xa = 1 cm and xb = + 2 cm. Where should a third charge, QC = + 3μC, be placed on the positive x-axis so that the net electric potential at the origin is equal to zero? (Ans: x = 3 cm) 78. Four identical point charges, each with charge q = + 30 µc, are placed at the corners of a rectangle, as shown in figure 42. How much work must be done by an external agent to bring a charge Q = +56 µc from infinity to point P, located at the midpoint of one of the 6.0-m long sides of the rectangle? (Ans: +16 J) 79. Two concentric conducting spherical shells are shown in figure 43. The outer sphere has charge of qb = 5.0 μc and radius RB = 5.0 m. The inner sphere has charge qa = + 2.0 μc and radius RA = 2.0 m. What is the electric potential at r = 3.0 m, where r is the distance from the center. Take V = 0 at infinity. (Ans: 3.0 kv) 80. A particle of charge +2.0 mc moves in a region where only electric forces act on it. The particle has a kinetic energy of 5.0 J at point A. The particle then passes through point B, which has an electric potential of +1.5 kv relative to A. What is the kinetic energy of the particle as it passes through point B? (Ans: 2.0 J) 81. Point A is inside a charged conducting sphere and is a distance of 5.0 cm from the center of the sphere. Point B is outside the sphere at a distance of 15 cm from the center. If V = 0, VA = 150 V, and VB = 80 V, what is the radius of the sphere? (Ans: 8.0 cm) 82. In figure 46, particles with charges q 1 = + 10 µc and q 2 = 30 µc are fixed in place with separation d. What is the value of Q that will make the potential equal to zero at point P? (Ans: + 7.1 μc) Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 6
83. In a certain region of space, the electric field is given by E = 0.40 x î (N/C). If the electric potential at the origin is + 5.0 V, what is the electric potential at the point (3.0, 0, 0) m? (Ans: + 3.2 V) 84. A metallic isolated sphere of diameter 3.5 cm, fixed in space, carries +9.0 nc charge. A proton was released from rest at the sphere s surface. Determine the maximum speed of the proton. (Assume V=0 at infinity) (Ans: 9.4 10 5 m/s) 85. Two metal spheres 1 and 2 with radii r 1= 1.0 cm and r 2=2.0 cm carry charges q 1 = +22 nc, and q 2 = 10 nc, respectively. Initially both spheres are far apart. Then the spheres are connected by a thin wire, how much charge is lost by sphere 1 when the electrostatic equilibrium is reached? (Ans: +18 nc) A B C D E Conceptual Problems 1. Conducting sphere 1 with radius R has a positive charge Q. Another conducting sphere 2 with radius 2R is far from sphere 1 and initially uncharged. After the separated spheres are connected with a thin conducting wire, the two spheres end up with charges q 1 and q 2. Which of the following statements is correct? A. Both spheres are at same potential. B. The amount of charge on each sphere is Q/2. C. The electric field at the surfaces of the two spheres is equal. D. The potential of the spheres are in the ratio V2/V1 = q2/q1. E. The potential of the spheres are in the ratio V2/V1 = 2. 2. In figure 3, two conducting spheres, one having twice the diameter of the other, are separated by a distance large compared to their diameters. Initially, the smaller sphere (1) has charge q and the larger sphere (2) is uncharged. If the spheres are then connected by a long thin conducting wire: A. 1 and 2 have the same potential B. 2 has twice the potential of 1 C. 2 has half the potential of 1 D. 1 and 2 have the same charge E. 1 has twice the charge of 2 3. The diagram in figure 5 shows four pairs of identical large parallel conducting plates. The value of the electric potential is given for each plate. Rank the pairs according to the magnitude of the electric field between them, least to greatest. A. 2, 4, 1, 3 B. 1, 2, 3, 4 C. 4, 3, 2, 1 D. 2, 3, 1, 4 E. 3, 2, 4, 1 4. Which one of the following statements is true? A. The electric field lines are perpendicular to the equipotential surfaces. B. We have to do work to move a charged particle along an equipotential surface. C. The electric field is a scalar quantity. D. The electric potential is a vector quantity. E. Any two equipotential surfaces are always parallel. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 7
5. A point charge, Q, at the center of a circle, is surrounded by six charges each of magnitude q at a distance r, as shown in figure 9. How much work is done by an external agent to remove the charge Q from the center to infinity? A. zero B. 6kQq/r 2 C. 6kq/r D. 6kq/r 2 E. 3kQq/r 6. Figure 11 shows three points X, Y and Z forming an equilateral triangle of side S in a uniform electric field of strength E. A unit positive test charge is moved from X to Y, then from Y to Z, and from Z back to X. Which one of the following correctly gives the work done by an external agent in moving the charge along the various parts of the path? A. 0, -E.S sin60 O, +E.S sin60 O B. 0, -E.S cos60 O, +E.S cos60 O C. E.S, -E.S sin60 O, +E.S cos60 O D. 0, -E.S cos60 O, +E.S sin60 O E. E.S, -E.S tan60 O, +E.S sin60 O 7. In figure 13, the point charge Q 1 causes an electric potential of 60 V and an electric field strength of 30 V/m at P, and the point charge Q 2, separately, causes an electric potential of 120 V and electric field strength of 40 V/m at P. Which of the following gives possible values of potential and field strength at P due to the joint action of Q 1 and Q 2? A. 180 V, 50 V/m B. 180 V, 70 V/m C. 135 V, 50 V/m D. -600 V, 10 V/m E. 135 V, 70 V/m 8. In figure 16, an electron moves from point I to point F in a uniform electric field directed as shown in the figure. Which of the following statements is incorrect? A. The electric field does positive work on the electron. B. The electric field does negative work on the electron. C. The electric potential energy of the electron increases. D. The electron moves to a lower potential. E. An external force is required to move the electron from I to F. 9. In figure 17, a hollow sphere, of radius r that carries a negative charge -q, is put inside another hollow sphere, of radius R, that carries a positive charge Q. At a distance x from the common center, such that r < x < R, the electric potential is: A. k[(q/r)-(q/x)] B. k[(q/r)-(q/r)] C. k[(q/r)+(q/x)] D. k[(q/r)+(q/r)] E. k[(q/x)-(q/r)] Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 8
10. In figure 19, four charges are fixed at the corners of a square whose sides are of length d. The work done by an external agent to bring a fifth charge, Q, from infinity to the center of the square is: A. - 2.8kqQ/d B. 1.4kqQ/d C. 2.8kqQ/d D. 1.4kqQ/d E. 3.4kqQ/d 11. A charge q is located at the center of a circle with a large radius R, as shown in figure 20. Another charge Q is located on the circumference of the circle at the x axis. What is the work needed to move Q from its location to point F, on the x axis, along the circumference? A. Zero B. kqq(2r) C. kqq/r D. 2kqQ/R E. kq/2r) 12. Which of the following statements are correct? 1. Electric charge is quantized. 2. The potential at the center of a charged conductor is zero. 3. If E = 0 at a point P then V must be zero at P. 4. The electric field inside a charged conductor is zero. 5. If V = 0 at a point P then E must be zero at P. A. 1 and 4. B. 2 and 4. C. 1, 2 and 3. D. 1, 2, and 5. E. 3 and 5. 13. Which of the following statements are correct? 1. The electric flux through a Gaussian surface depends on the shape of the surface. 2. The electric flux through a closed surface depends on the net charge enclosed by the surface. 3. The electric field inside a uniformly charged solid conducting sphere in electrostatic equilibrium is zero. 4. The electric potential inside a uniformly charged solid conducting sphere in electrostatic equilibrium is zero. A. 2 and 3 only B. 1 and 2 only C. 1, 2, 3, and 4 D. 3 and 4 only E. 4 only 14. Which of the following statements is correct? A. The electric field inside a uniformly charged solid conducting sphere in electrostatic equilibrium is zero. B. The electric flux through a Gaussian surface depends on the shape of the surface. C. The electric flux through a closed surface does not depend on the net charge inside the surface. D. The electric potential inside a uniformly charged sphere in electrostatic equilibrium is zero if the potential at infinity is zero. E. The electric field lines are always parallel to Gaussian surface. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 9
15. Three concentric spherical shells A, B and C, of radii a, b and c (a < b < c), have charges q, -q and q respectively. What is the potential of C? 16. Two charges, q 1 = +2.0 μc and q 2 = -2.0 μc, are placed as shown in figure 21. At the midpoint between the charges, which one of the following statements correctly describes the electric field (E.F.) and the electric potential (E.P.)? A. E.F. is directed toward q2 and the E.P. is zero. B. E.F. is directed toward q1 and the E.P. is zero. C. E.F. is directed toward q2 and the E.P. is negative. D. E.F. is directed toward q1 and the E.P. is negative. E. E.F. is directed toward q2 and the E.P. is positive. 17. If the electric field is 12 V/m in the positive x-direction, what is the potential difference between the origin, (0, 0), and the point (3m, 4m)? A. 36 V with the origin at the higher potential B. 48 V with the origin at the higher potential C. 48 V with the origin at the lower potential D. 36 V with the origin at the lower potential E. 100 V with the origin at the lower potential 18. In figure 24, particles of charges q 1 = + 5e and q 2 = 15e are fixed in place with separation d. With V = 0 at infinity, at what point between the two particles and on the x axis is the net electric potential zero? A. x = d/4 B. x = 3d/4 C. x = d/8 D. x = 3d/8 E. x = d/2 19. In a certain region of space the electric potential increases uniformly from east to west, and does not vary in any other direction. The electric field: A. points east and does not vary with position. B. points east and varies with position. C. points west and varies with position. D. points west and does not vary with position. E. points north and does not vary with position. 20. Consider two concentric conducting thin spherical shells. The first one has a radius R 1 = 10.0 cm and carries a charge Q 1 = +5.00 μc and the second shell has a radius R 2 = 20.0 cm and carries a charge Q 2 = 10.0 μc. Calculate the potential at a distance of 10.0 cm from the center of the shells. A. Zero B. 900 kv C. + 900 kv D. 450 kv E. 450 kv Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 10
21. In a certain situation, the electric potential varies along an x axis as shown in figure 26. Rank the three regions, shown in the figure, according the magnitude of the x component of the electric field within them greatest first. A. 1, 3, then 2 B. 1, 2, then 3 C. 3, 1, then 2 D. 2, 3, then 1 E. 3, 2, then 1 22. An electron moves from point i to point f in figure 27, in the direction of a uniform electric field. During this displacement A. the work done by the field is negative and the electric potential energy of the electron-field system increases. B. the work done by the field is positive and the electric potential energy of the electron-field system increases. C. the work done by the field is positive and the electric potential energy of the electron-field system decreases. D. the work done by the field is negative and the electric potential energy of the electron-field system decreases. E. the work done by the field is positive and the electric potential energy of the electron-field system does not change. 23. Figure 28 shows a particle of mass m and charge q moving between two equipotential surfaces V 1 and V 2 which are separated by a distance d. If the speed of the particle at surface V 1 is v o, what is the change in the kinetic energy of the particle when it moves from surface V 1 to surface V 2? A. qv B. qv C. (½)mvo 2 D. (½)mvo 2 E. qv (½)mvo 2 24. Which one of the following statements is correct? A. All points of a conductor in electrostatic equilibrium are at the same potential. B. Electric field lines are always parallel to equipotential surfaces. C. Electric field lines are always in the direction of increasing electric potential. D. The electric field at the surface of a conductor in electrostatic equilibrium is parallel to the surface of the conductor. E. If a conducting sphere carries a net charge, the charge will be uniformly Distributed over its volume. 25. The electric potential at point A in an electric field is15 V smaller than at point B. If a charge q = -2.0 C is moved from A to B, then the electric potential energy of this charge will: A. decrease by 30 J. B. increase by 30 J. C. increase by 15 J. D. decrease by 15 J. E. increase by 25 J. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 11
26. Two hollow metal spheres of radii R 1 and R 2 carry an equal electric charge Q. The spheres have potentials V 1 and V 2 at their centers, respectively. If the ratio V 1/V 2 is equal to 3, what is the value of the ratio R 1/R 2? A. 1/3 B. 3 C. 1/9 D. 9 E. 1 27. The work required by an external agent to carry a particle with a charge of 6.0 C from a 5.0 V equipotential surface to a 6.0 V equipotential surface and back again to the 5.0 V surface is: A. 0 J B. 2.2 10-6 J C. 3.2 10-6 J D. 2.2 10-5 J E. 3.2 10-5 J 28. If the electric field is 12 V/m in the positive x-direction, what is the potential difference between the origin and the point (3.0 m, 4.0 m)? A. 36 V with the origin at the higher potential B. 48 V with the origin at the lower potential C. 36 V with the origin at the lower potential D. 48 V with the origin at the higher potential E. 40 V with the origin at the higher potential 29. A parallel-plate capacitor contains a positively charged plate on the left, and a negatively charged plate on the right. An electron in between the plates is moving to the right. Which one of the following statements is true? A. The potential energy of the electron is increasing and it is moving to a region having a lower potential. B. The potential energy of the electron is decreasing and it is moving to a region having a lower potential. C. The potential energy of the electron is increasing and it is moving to a region having a higher potential. D. The potential energy of the electron is decreasing and it is moving to a region having a higher potential. E. The potential energy of the electron is constant and it is moving to a region having a higher potential. 30. A metallic sphere, in electrostatic equilibrium, has a radius R and carries a net charge Q. Which of the following statements are true for the sphere? i- It is made of a non-conducting material. ii- The excess charge resides on its surface. iii- The electric field inside it is zero. iv- The electric potential inside it is constant. A. ii, iii, and iv only. B. i and ii only. C. i, ii, and iii only. D. iii, and iv only. E. i, ii, and iv only. Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 12
31. Which of the following statements is correct regarding a metallic conductor in static equilibrium? A. If it carries a net charge, the charge must be distributed on its surface. B. If it carries a net charge, the charge must be uniformly distributed throughout its volume. C. If it carries a net charge, the charge has to be positive. D. The potential inside the conductor is smaller than that at the surface. E. It cannot carry a net charge. 32. A system consists of a negatively-charged particle moving in an electric field. When the charged particle moves in the direction of the electric field A. The electric potential energy increases. B. The work done by the electric force on the particle is positive. C. The electric potential energy decreases. D. The kinetic energy of the particle increases. E. The particle acceleration is in the direction of the electric field. 33. Figure 36 shows two different arrangements of 12 electrons fixed in space. In the arrangement (a) they are uniformly spaced around a circle of radius R and in (b) they are non-uniformly spaced along an arc of the original circle. Which of the following statements is TRUE? A. The electric potential at the center C is the same in both (a) and (b). B. The electric potential at the center C is larger in (b) than that in (a). C. The magnitude of electric field at the center C is the same in both (a) and (b). D. The magnitude of electric field at the center C is smaller in (b) than that in (a). E. The electric potential and the electric field at the center C are both zero in (a). 34. Two point charges (+q and q) are placed as shown in figure 40. Consider the points 1, 2, 3, and 4 that are shown on the figure. At which point is the net electric potential HIGHEST? Take V = 0 at infinity. A. 4 B. 3 C. 2 D. 1 E. All points have the same potential 35. Four point charges are placed at the corners of a square, as shown in figure 41. The magnitudes of the charges are equal. What is the electric potential energy of the system? A. zero B. +5.4 kq 2 /d C. +2.6 kq 2 /d D. 2.6 kq 2 /d E. +0.71 kq 2 /d 36. Suppose that a region of space has a uniform electric field, directed towards the right, as shown in figure 44. Which one of the following statements is CORRECT? A. VA = VB and VA > VC B. VA = VB = VC C. VA = VB and VA < VC D. VA > VB > VC E. None of the other choices Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 13
45. Figure 45 shows a system of two charged particles. Let W AB, W AC, W AD be the work done by an external agent to move the charge +q from A to B, from A to C, or from A to D, respectively. Which of the following statements is true? A) WAB > WAC > WAD B) WAB < WAC < WAD C) WAB > WAC = WAD D) WAB = WAC < WAD E) WAB < WAC = WAD 46. Electric charge is uniformly distributed throughout the volume of a solid insulating sphere. Let r be the distance from the center of the sphere. Which of the following quantities varies as r 2 inside the sphere? A. The electric potential B. The electric field C. The electric charge D. The electric flux E. The product of charge and flux 47. A charged particle is released in a uniform external electric field. Which of the following statements is CORRECT? A. The electric potential energy of the particle always decreases. B. The electric potential energy of the particle always increases. C. The electric potential energy of the particle does not change. D. The electric potential energy increases if the particle has positive charge. E. The electric potential energy increases if the particle has negative charge. 48. Two point charges (+q and q) are fixed on a line, as shown in figure 47. Rank the electric potentials at points 1, 2, 3; greatest first. A) 1, 2, 3 B) (1 and 3) tie, then 2 C) 3, 2, 1 D) 2, then (1 and 3 tie) E) 2, 3, 1 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 14
Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 15
Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 16
Figure 32 Figure 33 Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Figure 39 Figure 40 Figure 41 Figure 42 Figure 43 Figure 44 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 17
Figure 45 Figure 46 Figure 47 Dr. M. F. Al-Kuhaili PHYS 102 Chapter 24 Page 18