Physics Question bank

(1)

Chapter 23—Electric Fields

MULTIPLE CHOICE

1. Each of two small non-conducting spheres is charged positively, the combined charge being 40 C. When the two spheres are 50 cm apart, each sphere is repelled from the other by a force of magnitude 2.0 N. Determine the magnitude of the smaller of the two charges.

a. 1.4 C b. 1.1 C c. 2.0 C d. 3.3 C e. 17 C

ANS: A PTS: 3 DIF: Challenging

2. A particle (charge = +40 C) is located on the x axis at the point x = 20 cm, and a second particle (charge = 50 C) is placed on the x axis at x = +30 cm. What is the magnitude of the total

electrostatic force on a third particle (charge = 4.0 C) placed at the origin (x = 0)? a. 41 N

b. 16 N c. 56 N d. 35 N e. 72 N

ANS: C PTS: 2 DIF: Average

3. In the figure, if Q = 30 C, q = 5.0 C, and d = 30 cm, what is the magnitude of the electrostatic force on q? a. 15 N b. 23 N c. zero d. 7.5 N e. 38 N

ANS: D PTS: 2 DIF: Average

4. A charge of +80 C is placed on the x axis at x = 0. A second charge of 50 C is placed on the x axis at x = 50 cm. What is the magnitude of the electrostatic force on a third charge of 4.0 C placed on the

x axis at x = 30 cm? a. 13 N b. 77 N c. 39 N d. 25 N e. 45 N

(2)

5. Three point charges are positioned on the x axis. If the charges and corresponding positions are +32 C at x = 0, +20 C at x = 40 cm, and 60 C at x = 60 cm, what is the magnitude of the electrostatic force on the +32-C charge?

a. 84 N b. 12 N c. 36 N d. 50 N e. 48 N

ANS: B PTS: 2 DIF: Average

6. A particle (m = 50 g, q = 5.0 C) is released from rest when it is 50 cm from a second particle (Q = 20 C). Determine the magnitude of the initial acceleration of the 50-g particle.

a. 54 m/s2 b. 90 m/s2 c. 72 m/s2 d. 65 m/s2 e. 36 m/s2

7. A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, Q, is placed at x = 3.0

m. If Q = 40 C, what is the magnitude of the electrostatic force on a 30-C charge placed at the origin? a. 7.2 N b. 3.9 N c. 1.5 N d. 14 N e. 8.1 N

8. A point charge Q is placed on the x axis at x = 2.0 m. A second point charge, Q, is placed at x = 1.0

m. If Q = 60 C, what is the magnitude of the electrostatic force on a 40-C charge placed at the origin? a. 16 N b. 27 N c. 32 N d. 11 N e. 3.0 N

9. A point charge Q is placed on the x axis at the origin. An identical point charge is placed on the x axis at x = 1.0 m and another at x = +1.0 m. If Q = 40 C, what is the magnitude of the electrostatic force on the charge at x = +1.0 m? a. 29 N b. 14 N c. 11 N d. 18 N e. 7.0 N

(3)

10. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 36 nC in the figure, what is the

magnitude of the electric force on q?

a. 5.0 N b. 4.4 N c. 3.8 N d. 5.7 N e. 0.60 N

11. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 30 nC in the figure, what is the

magnitude of the electric force on q?

a. 1.4 N b. 1.0 N c. 1.7 N d. 2.0 N e. 0.50 N

12. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 24 nC in the figure, what is the magnitude

of the electric force on q?

a. 2.7 N b. 1.9 N c. 2.3 N d. 1.5 N e. 0.52 N

13. If a = 3.0 mm, b = 4.0 mm, Q1 = 60 nC, Q2 = 80 nC, and q = 32 nC in the figure, what is the magnitude

(4)

a. 1.6 N b. 1.3 N c. 1.9 N d. 2.2 N e. 0.040 N

14. Three point charges, two positive and one negative, each having a magnitude of 20 C are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on the negative charge?

a. 80 N b. 40 N c. 69 N d. 57 N e. 75 N

15. Three point charges, two positive and one negative, each having a magnitude of 20 C are placed at the vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic force on one of the positive charges?

a. 69 N b. 40 N c. 80 N d. 57 N e. 20 N

16. A point charge Q is placed at the origin. A second charge, 2Q, is placed on the x axis at x = 3.0 m. If

Q = 50 C, what is the magnitude of the electrostatic force on a third point charge, Q, placed on the y

axis at y = +4.0 m? a. 2.5 N b. 3.0 N c. 3.7 N d. 4.4 N e. 1.8 N

ANS: B PTS: 3 DIF: Challenging

17. Three identical point charges Q are placed at the vertices of an equilateral triangle (length of each side = 2.0 m). If Q = 60 C, what is the magnitude of the electrostatic force on any one of the charges? a. 25 N

(5)

b. 19 N c. 14 N d. 22 N e. 16 N

18. Identical point charges Q are placed at each of the four corners of a 3.0 m  4.0 m rectangle. If Q = 40 C, what is the magnitude of the electrostatic force on any one of the charges?

a. 3.0 N b. 2.4 N c. 1.8 N d. 3.7 N e. 2.0 N

19. A point charge (5.0 C) is placed on the x axis at x = 4.0 cm, and a second charge (+5.0 C) is placed on the x axis at x = 4.0 cm. What is the magnitude of the electric force on a third charge (+2.5 C) placed on the y axis at y = 3.0 cm?

a. 90 N b. 45 N c. 54 N d. 72 N e. 36 N

20. If Q = 25 C, q = 10 C, and L = 40 cm in the figure, what is the magnitude of the electrostatic force on q? a. 28 N b. 22 N c. 20 N d. 14 N e. 10 N

21. If Q = 20 C and L = 60 cm, what is the magnitude of the electrostatic force on any one of the charges shown?

(6)

a. 25 N b. 19 N c. 15 N d. 9.1 N e. 14 N

ANS: D PTS: 3 DIF: Challenging

22. If a = 60 cm, b = 80 cm, Q = 4.0 nC, and q = 1.5 nC, what is the magnitude of the electric field at point P? a. 68 N/C b. 72 N/C c. 77 N/C d. 82 N/C e. 120 N/C

ANS: A PTS: 2 DIF: Average

23. If a = 60 cm, b = 80 cm, Q = 6.0 nC, and q = 4.0 nC, what is the magnitude of the electric field at point P?

a. 35 N/C b. 42 N/C c. 52 N/C d. 64 N/C

(7)

e. 104 N/C

24. If a = 60 cm, b = 80 cm, Q = 6.0 nC, and q = 6.0 nC, what is the magnitude of the electric field at point P in the figure?

a. 65 N/C b. 55 N/C c. 60 N/C d. 52 N/C e. 67 N/C

25. If a = 60 cm, b = 80 cm, Q = 6.0 nC, and q = 3.0 nC in the figure, what is the magnitude of the electric field at point P?

(8)

26. If Q = 16 nC, a = 3.0 m, and b = 4.0 m, what is the magnitude of the electric field at point P? a. 33 N/C b. 31 N/C c. 24 N/C d. 19 N/C e. 13 N/C

27. If Q = 80 nC, a = 3.0 m, and b = 4.0 m in the figure, what is the magnitude of the electric field at point P? a. 45 N/C b. 70 N/C c. 29 N/C d. 47 N/C e. 92 N/C

28. A +2.0-nC point charge is placed at one corner of a square (1.5 m on a side), and a 3.0-nC charge is placed on a corner diagonally away from the first charge. What is the magnitude of the electric field at either of the two unoccupied corners?

a. 20 N/C b. 14 N/C c. 4.0 N/C d. 12 N/C e. 8.0 N/C

29. A +15-nC point charge is placed on the x axis at x = 1.5 m, and a 20-nC charge is placed on the y axis at y = 2.0m. What is the magnitude of the electric field at the origin?

(9)

30. A +20-nC point charge is placed on the x axis at x = 2.0 m, and a 25-nC point charge is placed on the

y axis at y = 3.0 m. What is the direction of the electric field at the origin?

a. 209 b. 61 c. 29 d. 241 e. 151

31. A charge Q is placed on the x axis at x = +4.0 m. A second charge q is located at the origin. If Q = +75 nC and q = 8.0 nC, what is the magnitude of the electric field on the y axis at y = +3.0 m?

32. A 40-C charge is positioned on the x axis at x = 4.0 cm. Where should a 60-C charge be placed to produce a net electric field of zero at the origin?

a. 5.3 cm b. 5.7 cm c. 4.9 cm d. 6.0 cm e. +6.0 cm

33. A charge of 80 nC is uniformly distributed along the x axis from x = 0 to x = 2.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 8.0 m.

34. A charge (uniform linear density = 9.0 nC/m) is distributed along the x axis from x = 0 to x = 3.0 m. Determine the magnitude of the electric field at a point on the x axis with x = 4.0 m.

(10)

35. A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a 90-degree angle. What is the magnitude of the electric field at the center of the circle along which the arc lies? a. 81 N/C b. 61 N/C c. 71 N/C d. 51 N/C e. 25 N/C

36. Charge of uniform density 4.0 nC/m is distributed along the x axis from x = 2.0 m to x = +3.0 m. What is the magnitude of the electric field at the point x = +5.0 m on the x axis?

a. 16 N/C b. 13 N/C c. 19 N/C d. 26 N/C e. 5.0 N/C

37. A uniformly charged rod (length = 2.0 m, charge per unit length = 5.0 nC/m) is bent to form one quadrant of a circle. What is the magnitude of the electric field at the center of the circle? a. 62 N/C

b. 56 N/C c. 50 N/C d. 44 N/C e. 25 N/C

ANS: C PTS: 3 DIF: Challenging

38. A uniformly charged rod (length = 2.0 m, charge per unit length = 3.0 nC/m) is bent to form a semicircle. What is the magnitude of the electric field at the center of the circle?

39. A 16-nC charge is distributed uniformly along the x axis from x = 0 to x = 4 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +10 m on the x axis?

a.

b.

(11)

d.

e. none of these

40. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the y component of the electric field at y = 4 m on the y axis?

a.

b.

c.

d.

e. none of these

41. A 12-nC charge is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of the following integrals is correct for the x component of the electric field at x = 2 m on the x axis?

a.

b.

c.

d.

e. none of these

42. A uniform linear charge of 3.0 nC/m is distributed along the y axis from y = 3 m to y = 2m. Which of the following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis? a.

b.

c.

d.

(12)

43. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Which of the following integrals is correct for the x component of the electric field at y = 2 m on the y axis?

a.

b.

c.

d.

e. none of these

44. A rod (length = 2.0 m) is uniformly charged and has a total charge of 40 nC. What is the magnitude of the electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the rod? a. 40 N/C

b. 45 N/C c. 24 N/C d. 90 N/C e. 36 N/C

45. A charge of 50 nC is uniformly distributed along the y axis from y = 3.0 m to y = 5.0 m. What is the magnitude of the electric field at the origin?

46. A 24-nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at x = +8 m on the x axis? a.

b.

c.

d.

e. none of these

(13)

47. A uniform linear charge density of 7.0 nC/m is distributed along the y axis from y = 2 m to y = 5 m. Which of the following integrals is correct for the magnitude (in N/C) of the electric field at y = 0 on the y axis? a. b. c. d. e. none of these

48. A uniform linear charge of 2.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. What is the x component of the electric field at y = 2 m on the y axis?

a. 5.0 N/C b. 4.0 N/C c. 5.7 N/C d. 6.2 N/C e. 9.0 N/C

49. A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field is uniform and is given by Ex = 2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vx = 80 m/s, vy = vz = 0, what is the speed of the particle at t = 2.0 s?

a. 40 m/s b. 20 m/s c. 60 m/s d. 80 m/s e. 180 m/s

50. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is

uniform and is given by Ex = 2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vy =

50 m/s, vx = vz = 0, what is the speed of the particle at t = 2.0 s? a. 81 m/s

b. 72 m/s c. 64 m/s d. 89 m/s e. 25 m/s

(14)

51. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = 5.5 N/C, Ey = Ez = 0. If the position and velocity of the particle at t = 0

are given by x = y = z = 0 and vx = 50 m/s, vy = vz = 0, what is the distance from the origin to the particle at t = 2.0 s? a. 60 m b. 28 m c. 44 m d. 12 m e. 88 m

52. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field is uniform and is given by Ex = 2.3 N/C, Ey = Ez = 0. If the position and velocity of the particle at t = 0 are given by x = y = z = 0 and vz = 20 m/s, vx = vy = 0, what is the distance from the origin to the particle at t = 2.0 s? a. 60 m b. 54 m c. 69 m d. 78 m e. 3.2 m

53. A particle (q = 3.0 mC, m = 20 g) has a speed of 20 m/s when it enters a region where the electric field has a constant magnitude of 80 N/C and a direction which is the same as the velocity of the particle. What is the speed of the particle 3.0 s after it enters this region?

54. A particle (q = 4.0 mC, m = 50 g) has a velocity of 25 m/s in the positive x direction when it first enters a region where the electric field is uniform (60 N/C in the positive y direction). What is the speed of the particle 5.0 s after it enters this region?

55. A charge of 50-C is placed on the y axis at y = 3.0 cm and a 77-C charge is placed on the x axis at x = 4.0 cm. If both charges are held fixed, what is the magnitude of the initial acceleration of an electron released from rest at the origin?

a. 1.2  1020 m/s2 b. 1.5  1020 m/s2 c. 1.0  1020 m/s2 d. 1.8  1020 m/s2 e. 2.0  1020 m/s2

(15)

56. The velocity of a particle (m = 10 mg, q = 4.0 C) at t = 0 is 20 m/s in the positive x direction. If the particle moves in a uniform electric field of 20 N/C in the positive x direction, what is the particle's speed at t = 5.0 s? a. 60 m/s b. 20 m/s c. 45 m/s d. 40 m/s e. 70 m/s

57. A particle (m = 20 mg, q = 5.0 C) moves in a uniform electric field of 60 N/C in the positive x direction. At t = 0, the particle is moving 25 m/s in the positive x direction and is passing through the origin. How far is the particle from the origin at t = 2.0 s?

a. 80 m b. 20 m c. 58 m d. 10 m e. 30 m

58. A particle (m = 20 mg, q = 5.0 C) moves in a uniform electric field of 60 N/C in the positive x direction. At t = 0, the particle is moving 30 m/s in the positive x direction and is passing through the origin. Determine the maximum distance beyond x = 0 the particle travels in the positive x direction. a. 25 m

b. 20 m c. 15 m d. 30 m e. 60 m

59. Charge Q is distributed uniformly along a semicircle of radius a. Which formula below gives the correct magnitude of the electric field at the center of the circle?

a. . b. . c. . d. . e. .

60. Charge Q is distributed uniformly along a semicircle of radius a. Which formula below gives the correct magnitude of the force on a particle of charge q located at the center of the circle?

(16)

a. . b. . c. . d. . e. .

61. Charge Q is uniformly distributed over a line segment of length 2L, as shown below. When the x-coordinate of point P is x, the magnitude of the y-component of the electric field at point P is

a. 0. b. . c. . d. . e. .

ANS: A PTS: 1 DIF: Easy

62. When gravitational, magnetic and any forces other than static electric forces are not present, electric field lines in the space surrounding a charge distribution show

a. the directions of the forces that exist in space at all times.

b. only the directions in which static charges would accelerate when at points on those lines c. only the directions in which moving charges would accelerate when at points on those

lines.

d. tangents to the directions in which either static or moving charges would accelerate when passing through points on those lines.

e. the paths static or moving charges would take.

(17)

63. When a positive charge q is placed in the field created by two other charges Q1 and Q2, each a distance

r away from q, the acceleration of q is

a. in the direction of the charge Q1 or Q2 of smaller magnitude.

b. in the direction of the charge Q1 or Q2 of greater magnitude.

c. in the direction of the negative charge if Q1 and Q2 are of opposite sign.

d. in the direction of the positive charge if Q1 and Q2 are of opposite sign.

e. in a direction determined by the vector sum of the electric fields of Q1 and Q2.

ANS: E PTS: 1 DIF: Easy

64. Two charged particles, Q1 and Q2, are a distance r apart with Q2 = 5Q1. Compare the forces they exert

on one another when is the force Q2 exerts on Q1 and is the force Q1 exerts on Q2.

a. _{= 5} _.

b. _{= 5} _.

c. ₌ _.

d. _{= } _.

e. 5 = .

ANS: D PTS: 1 DIF: Easy

65. Rubber rods charged by rubbing with cat fur repel each other. Glass rods charged by rubbing with silk repel each other. A rubber rod and a glass rod charged respectively as above attract each other. A possible explanation is that

a. Any two rubber rods charged this way have opposite charges on them. b. Any two glass rods charged this way have opposite charges on them.

c. A rubber rod and a glass rod charged this way have opposite charges on them. d. All rubber rods always have an excess of positive charge on them.

e. All glass rods always have an excess of negative charge on them.

ANS: C PTS: 1 DIF: Easy

66. Which one of the diagrams below is not a possible electric field configuration for a region of space which does not contain any charges?

a. b. c. d. e.

67. A positively charged particle is moving in the +y-direction when it enters a region with a uniform electric field pointing in the +x-direction. Which of the diagrams below shows its path while it is in the region where the electric field exists. The region with the field is the region between the plates

bounding each figure. The field lines always point to the right. The x-direction is to the right; the y-direction is up.

a. b. c. d. e.

(18)

68. A negatively charged particle is moving in the +x-direction when it enters a region with a uniform electric field pointing in the +x-direction. Which graph gives its position as a function of time correctly? (Its initial position is x = 0 at t = 0.)

a. b. c. d. e.

69. The symbol appears in Coulomb's law because we use independently defined units for a. force and distance.

b. charge and distance. c. distance and force.

d. force, distance and electric charge. e. charge.

70. Three pith balls supported by insulating threads hang from a support. We know that ball X is

positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that

a. Y has a negative charge. b. Z has a negative charge. c. Y has a positive charge. d. Z has a positive charge.

e. Z is neutral (has no net charge.)

71. Three pith balls supported by insulating threads hang from a support. We know that ball X is

positively charged. When ball X is brought near balls Y and Z without touching them, it attracts Y and repels Z. Since pith is an insulating material, we can conclude that

a. Y has a negative charge. b. Z has a negative charge. c. Y has a positive charge.

d. Z is neutral (has no net charge.)

e. Y is negatively charged or neutral (has no net charge.)

72. Two identical pith balls supported by insulating threads hang side by side and close together, as shown below.

One is positively charged; the other is neutral. We can conclude that

(19)

b. some of the field lines leaving the positively charged pith ball end on the neutral pith ball. c. none of the field lines leaving the positively charged pith ball end on the neutral pith ball. d. positive charge is transferred along the field lines until both balls have equal charges. e. positive charge is transferred along the field lines until both balls hang along vertical lines.

ANS: B PTS: 1 DIF: Easy

73. Two imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the concentric spheres. When compared to the number of field lines N1 going

through the sphere of radius R, the number of electric field lines N2 going through the sphere of radius

2R is a. . b. . c. N2 = N1. d. N2 = 2N1. e. N2 = 4N1.

74. Two tiny metal spheres are fixed to the ends of a non-conducting string of length . Equal charges, +q, are placed on the metal spheres. Randall says that the force on the string has magnitude .

Tilden says that the tension in the string has magnitude . Which one, if either, is correct? a.

Randall, because both charges exert forces on the string, but the tension is . b.

Tilden, because both charges exert forces on the string, but the net force is . c. Both are correct, because both charges exert forces on the string.

d.

Neither is correct, because both the tension and the force have magnitude . e.

Neither is correct, because the tension is , but the net force is 0.

75. Enrico says that positive charge is created when you rub a glass rod with silk, and that negative charge is simply the absence of positive charge. Rosetta says that negative charge is created and that positive charge is the absence of positive charge. (She has heard that Ben Franklin should have reversed the signs he associated with the charges.) Which one, if either, is correct?

a. Enrico, because there really is only one kind of charge. b. Rosetta, because there really is only one kind of charge.

c. Neither: although no charge is present originally, both types of charge are created through friction.

d. Both: only one type of charge is created by friction at any one time.

e. Neither: both negative and positive charge are present simultaneously in all solid materials on Earth and the process described involves a transfer of charge, not the creation of charge.

(20)

76. Three 2.50 C charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120 angles as shown below. The magnitude, in N, of the force on any one of the charges is a. 1.88  102 . b. 3.25  102 . c. 3.73  102 . d. 6.50  102 . e. 7.50  102 .

77. Three 2.50 C charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120 angles as shown below. The magnitude, in N, of the tension in any one of the strings is a. 1.88  102 . b. 3.25  102 . c. 3.75  102 . d. 6.50  102 . e. 7.50  102 .

78. Three 2.50 C charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings that are connected at 120 angles as shown below. The magnitude, in N, of the force on the knot at the center is

(21)

a. 0. b. 3.75  102 . c. 5.63  102 . d. 6.50  102 . e. 7.50  102 .

79. Suppose a uniform electric field of 4 N/C is in the positive x direction. When a charge is placed at and fixed to the origin, the resulting electric field on the x axis at x = 2 m becomes zero. What is the magnitude of the electric field at x = 4 m on the x axis at this time?

a. 0 b. 1 N/C c. 2 N/C d. 4 N/C

e. More information is needed to find the resulting field magnitude at this position.

80. In a diagram of charges and electric field lines charge has twelve field lines going outward from it and charge has three field lines going into it. If one of the charges is 100 nC, what is the other one? a. 25 nC

b. 100 nC c. –25 nC d. –100 nC

e. Both answers b and c can be correct.

81. Two uniform rods, each of length 2.0 m, are bent to form semicircles. One rod has a charger per unit lent of 1.5 nC/m, and the other has a charge per unit length of –1.5 nC/m. The semicircles are joined to make a circle. What is the magnitude of the electric field at the center of the circle?

a. 42 N/C b. 84 N/C c. 34 N/C d. 68 N/C e. 0

PROBLEM

82. The electron gun in a television tube accelerates electrons (mass = 9.11  1031_{kg, charge = 1.60 }

(22)

ANS: 128 000 N/C

PTS: 2 DIF: Average

83. An alpha particle (charge = +2e) is sent at high speed toward a gold nucleus (charge +79e). What is the electrical force acting on the alpha particle when it is at a distance of 2  1014

m away from the gold nucleus? (e = 1.6  1019

C) ANS:

91 N

PTS: 2 DIF: Average

84. A proton moving at 3  104_{m/s is projected at an angle of 30 above a horizontal plane. If an electric}

field of 400 N/C is directed downwards, how long does it take the proton to return to the horizontal plane? (HINT: Ignore gravity.) [mProton = 1.67  10

27 kg, qProton = +1.6  10 19 C.] ANS: 7.8  107 s PTS: 2 DIF: Average

85. Imagine for a minute that the Moon is held in its orbit about the Earth by electrical forces rather than by gravitation. What electrical charges Q on the Earth and +Q on the Moon are necessary to hold the

Moon in a circular orbit with a period of 27.3 days? The Earth-Moon distance is 384 000 km and the mass of the Moon is 7.35  1022

kg. ANS:

Q = 5.73  1013 C

PTS: 3 DIF: Challenging

Chapter 24—Gauss's Law

MULTIPLE CHOICE

1. Two charges of 15 pC and 40 pC are inside a cube with sides that are of 0.40-m length. Determine the net electric flux through the surface of the cube.

a. +2.8 N  m2 /C b. 1.1 N  m2 /C c. +1.1 N  m2 /C d. 2.8 N  m2 /C e. 0.47 N  m2 /C

2. The total electric flux through a closed cylindrical (length = 1.2 m, diameter = 0.20 m) surface is equal to 5.0 N  m2

/C. Determine the net charge within the cylinder.

a. 62 pC

b. 53 pC

(23)

d. 71 pC

e. 16 pC

3. Charges q and Q are placed on the x axis at x = 0 and x = 2.0 m, respectively. If q = 40 pC and Q = +30 pC, determine the net flux through a spherical surface (radius = 1.0 m) centered on the origin. a. 9.6 N  m2 /C b. 6.8 N  m2/C c. 8.5 N  m2 /C d. 4.5 N  m2 /C e. 1.1 N  m2 /C

4. A uniform linear charge density of 4.0 nC/m is distributed along the entire x axis. Consider a spherical (radius = 5.0 cm) surface centered on the origin. Determine the electric flux through this surface. a. 68 N  m2 /C b. 62 N  m2 /C c. 45 N  m2 /C d. 79 N  m2 /C e. 23 N  m2 /C

5. A uniform charge density of 500 nC/m3 is distributed throughout a spherical volume (radius = 16 cm). Consider a cubical (4.0 cm along the edge) surface completely inside the sphere. Determine the electric flux through this surface.

a. 7.1 N  m2 /C b. 3.6 N  m2 /C c. 12 N  m2 /C d. 19 N  m2 /C e. 970 N  m2 /C

6. A point charge +Q is located on the x axis at x = a, and a second point charge Q is located on the x

axis at x = a. A Gaussian surface with radius r = 2a is centered at the origin. The flux through this

Gaussian surface is

a. zero because the negative flux over one hemisphere is equal to the positive flux over the other.

b. greater than zero.

c. zero because at every point on the surface the electric field has no component perpendicular to the surface.

d. zero because the electric field is zero at every point on the surface. e. none of the above.

7. The xy plane is "painted" with a uniform surface charge density which is equal to 40 nC/m2. Consider a spherical surface with a 4.0-cm radius that has a point in the xy plane as its center. What is the electric flux through that part of the spherical surface for which z > 0?

a. 14 N  m2

/C b. 11 N  m2

(24)

c. 17 N  m2 /C d. 20 N  m2 /C e. 23 N  m2 /C

8. A long cylinder (radius = 3.0 cm) is filled with a nonconducting material which carries a uniform charge density of 1.3 C/m3. Determine the electric flux through a spherical surface (radius = 2.0 cm) which has a point on the axis of the cylinder as its center.

a. 5.7 N  m2 /C b. 4.9 N  m2 /C c. 6.4 N  m2 /C d. 7.2 N  m2 /C e. 15 N  m2 /C

9. Charge of uniform surface density (4.0 nC/m2) is distributed on a spherical surface (radius = 2.0 cm). What is the total electric flux through a concentric spherical surface with a radius of 4.0 cm?

a. 2.8 N  m2 /C b. 1.7 N  m2 /C c. 2.3 N  m2 /C d. 4.0 N  m2 /C e. 9.1 N  m2 /C

10. A charge of uniform volume density (40 nC/m3) fills a cube with 8.0-cm edges. What is the total electric flux through the surface of this cube?

a. 2.9 N  m2 /C b. 2.0 N  m2 /C c. 2.6 N  m2 /C d. 2.3 N  m2 /C e. 1.8 N  m2 /C

11. A charge of 0.80 nC is placed at the center of a cube that measures 4.0 m along each edge. What is the electric flux through one face of the cube?

a. 90 N  m2 /C b. 15 N  m2 /C c. 45 N  m2 /C d. 23 N  m2 /C e. 64 N  m2 /C

12. A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field of magnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric flux through the hemisphere surface?

a. R2E

b. 4R2E/3

c. 2R2E/3

(25)

e. R2E/3

13. The electric field in the region of space shown is given by N/C where y is in m. What is the magnitude of the electric flux through the top face of the cube shown?

a. 90 N  m2 /C b. 6.0 N  m2 /C c. 54 N  m2 /C d. 12 N  m2 /C e. 126 N  m2 /C

14. Charge of uniform surface density (0.20 nC/m2) is distributed over the entire xy plane. Determine the magnitude of the electric field at any point having z = 2.0 m.

15. Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m2 and 0.60 nC/m2. What is the magnitude of the electric field at a point between the two surfaces?

16. Two infinite, uniformly charged, flat surfaces are mutually perpendicular. One of the sheets has a charge density of +60 pC/m2, and the other carries a charge density of 80 pC/m2. What is the magnitude of the electric field at any point not on either surface?

a. 1.1 N/C b. 5.6 N/C c. 7.9 N/C

(26)

d. 3.8 N/C e. 4.0 N/C

17. Charge of a uniform density (8.0 nC/m2) is distributed over the entire xy plane. A charge of uniform density (3.0 nC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 3.0 m.

a. 0.79 kN/C b. 0.17 kN/C c. 0.62 kN/C d. 0.34 kN/C e. 0.28 kN/C

18. Charge of a uniform density (8.0 nC/m2) is distributed over the entire xy plane. A charge of uniform density (5.0 nC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 1.0 m.

19. Charge of uniform density (0.30 nC/m2) is distributed over the xy plane, and charge of uniform density (0.40 nC/m2

) is distributed over the yz plane. What is the magnitude of the resulting electric field at any point not in either of the two charged planes?

a. 40 N/C b. 34 N/C c. 28 N/C d. 46 N/C e. 6.0 N/C

20. A long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m3)

distributed throughout its column. Determine the magnitude of the electric field 5.0 cm from the axis of the cylinder. a. 25 N/C b. 20 N/C c. 14 N/C d. 31 N/C e. 34 N/C

21. A long nonconducting cylinder (radius = 12 cm) has a charge of uniform density (5.0 nC/m3)

distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the axis of the cylinder.

a. 20 N/C b. 27 N/C c. 16 N/C

(27)

d. 12 N/C e. 54 N/C

22. Each 2.0-m length of a long cylinder (radius = 4.0 mm) has a charge of 4.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point 5.0 mm from the axis of the cylinder? a. 9.9 kN/C b. 8.1 kN/C c. 9.0 kN/C d. 7.2 kN/C e. 18 kN/C

23. A long nonconducting cylinder (radius = 6.0 mm) has a nonuniform volume charge density given by r2, where  = 6.2 mC/m5 and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis?

a. 1.4 N/C b. 1.6 N/C c. 1.8 N/C d. 2.0 N/C e. 5.4 N/C

24. A long cylindrical shell (radius = 2.0 cm) has a charge uniformly distributed on its surface. If the magnitude of the electric field at a point 8.0 cm radially outward from the axis of the shell is 85 N/C, how much charge is distributed on a 2.0-m length of the charged cylindrical surface?

a. 0.38 nC b. 0.76 nC c. 0.19 nC d. 0.57 nC e. 0.98 nC

25. Charge of uniform linear density (4.0 nC/m) is distributed along the entire x axis. Determine the magnitude of the electric field on the y axis at y = 2.5 m.

26. Charge of uniform density (80 nC/m3) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 2.0 mm from the symmetry axis.

a. 7.9 N/C b. 9.0 N/C c. 5.9 N/C d. 6.8 N/C

(28)

e. 18 N/C

27. Charge of uniform density (80 nC/m3) is distributed throughout a hollow cylindrical region formed by two coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electric field at a point which is 4.0 mm from the symmetry axis.

a. 7.9 N/C b. 10 N/C c. 9.0 N/C d. 8.9 N/C e. 17 N/C

ANS: C PTS: 3 DIF: Challenging

28. Charge of uniform density (20 nC/m2) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of 12 nC/m2

. Determine the magnitude of the electric field at a point 2.0 cm from the symmetry axis of the two surfaces.

29. Charge of uniform density (20 nC/m2) is distributed over a cylindrical surface (radius = 1.0 cm), and a second coaxial surface (radius = 3.0 cm) carries a uniform charge density of 12 nC/m2

. Determine the magnitude of the electric field at a point 4.0 cm from the symmetry axis of the two surfaces.

30. Charge of uniform density (40 pC/m2) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m2. What is the magnitude of the electric field at a point 4.0 cm from the center of the two surfaces? a. 3.8 N/C

b. 4.1 N/C c. 3.5 N/C d. 3.2 N/C e. 0.28 N/C

31. A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m3) distributed throughout its volume. Determine the magnitude of the electric field 15 cm from the center of the sphere.

a. 22 N/C b. 49 N/C c. 31 N/C d. 87 N/C

(29)

e. 26 N/C

32. A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) which has a charge of 8.0 nC distributed uniformly throughout its volume. What is the magnitude of the electric field at a point that is 1.0 cm from the center of the sphere?

a. 1.8  105 N/C b. 9.0  104 N/C c. 3.6  105 N/C d. 2.7  105 N/C e. 7.2  105 N/C

33. A charge of 5.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of 2.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 3.0 cm from the center of the two surfaces. a. 30 N/C

b. 50 N/C c. 40 N/C d. 20 N/C e. 70 N/C

34. A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a second charge of 3.0 pC is distributed uniformly on a concentric spherical surface (radius = 4.0 cm). Determine the magnitude of the electric field 5.0 cm from the center of the two surfaces. a. 14 N/C

b. 11 N/C c. 22 N/C d. 18 N/C e. 40 N/C

35. A point charge (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm), and a charge of 3.0 pC is spread uniformly upon this surface. Determine the magnitude of the electric field 1.0 cm from the point charge.

36. Charge of uniform density (40 pC/m2) is distributed on a spherical surface (radius = 1.0 cm), and a second concentric spherical surface (radius = 3.0 cm) carries a uniform charge density of 60 pC/m2. What is the magnitude of the electric field at a point 2.0 cm from the center of the two surfaces? a. 1.1 N/C

b. 4.5 N/C c. 1.4 N/C d. 5.6 N/C

(30)

e. 0.50 N/C

37. A 4.0-pC point charge is placed at the center of a hollow (inner radius = 2.0 cm, outer radius = 4.0 cm) conducting sphere which has a net charge of 4.0 pC. Determine the magnitude of the electric field at a point which is 6.0 cm from the point charge.

38. The axis of a long hollow metallic cylinder (inner radius = 1.0 cm, outer radius = 2.0 cm) coincides with a long wire. The wire has a linear charge density of 8.0 pC/m, and the cylinder has a net charge per unit length of 4.0 pC/m. Determine the magnitude of the electric field 3.0 cm from the axis. a. 5.4 N/C

b. 7.2 N/C c. 4.3 N/C d. 3.6 N/C e. 2.4 N/C

39. A long straight metal rod has a radius of 2.0 mm and a surface charge of density 0.40 nC/m2. Determine the magnitude of the electric field 3.0 mm from the axis.

40. If the electric field just outside a thin conducting sheet is equal to 1.5 N/C, determine the surface charge density on the conductor.

a. 53 pC/m2 b. 27 pC/m2 c. 35 pC/m2 d. 13 pC/m2 e. 6.6 pC/m2

41. The field just outside the surface of a long conducting cylinder which has a 2.0-cm radius points radially outward and has a magnitude of 200 N/C. What is the charge density on the surface of the cylinder? a. 2.7 nC/m2 b. 1.8 nC/m2 c. 3.5 nC/m2 d. 4.4 nC/m2 e. 0.90 nC/m2

(31)

42. A spherical conductor (radius = 1.0 cm) with a charge of 2.0 pC is within a concentric hollow

spherical conductor (inner radius = 3.0 cm, outer radius = 4.0 cm) which has a total charge of 3.0 pC. What is the magnitude of the electric field 2.0 cm from the center of these conductors?

a. 23 N/C b. zero c. 45 N/C d. 90 N/C e. 110 N/C

43. A long cylindrical conductor (radius = 1.0 mm) carries a charge density of 4.0 pC/m and is inside a coaxial, hollow, cylindrical conductor (inner radius = 3.0 mm, outer radius = 4.0 mm) that has a total charge of 8.0 pC/m. What is the magnitude of the electric field 2.0 mm from the axis of these conductors? a. 24 N/C b. 18 N/C c. zero d. 36 N/C e. 226 N/C

44. The electric field just outside the surface of a hollow conducting sphere of radius 20 cm has a

magnitude of 500 N/C and is directed outward. An unknown charge Q is introduced into the center of the sphere and it is noted that the electric field is still directed outward but has decreased to 100 N/C. What is the magnitude of the charge Q?

a. 1.5 nC b. 1.8 nC c. 1.3 nC d. 1.1 nC e. 2.7 nC

45. A point charge of 6.0 nC is placed at the center of a hollow spherical conductor (inner radius = 1.0 cm, outer radius = 2.0 cm) which has a net charge of 4.0 nC. Determine the resulting charge density on the inner surface of the conducting sphere.

a. +4.8 C/m2 b. 4.8 C/m2 c. 9.5 C/m2 d. +9.5 C/m2 e. 8.0 C/m2

46. An astronaut is in an all-metal chamber outside the space station when a solar storm results in the deposit of a large positive charge on the station. Which statement is correct?

a. The astronaut must abandon the chamber immediately to avoid being electrocuted. b. The astronaut will be safe only if she is wearing a spacesuit made of non-conducting

materials.

c. The astronaut does not need to worry: the charge will remain on the outside surface. d. The astronaut must abandon the chamber if the electric field on the outside surface

(32)

becomes greater than the breakdown field of air.

e. The astronaut must abandon the chamber immediately because the electric field inside the chamber is non-uniform.

47. A small metal sphere is suspended from the conducting cover of a conducting metal ice bucket by a non-conducting thread. The sphere is given a negative charge before the cover is placed on the bucket. The bucket is tilted by means of a non-conducting material so that the charged sphere touches the inside of the bucket. Which statement is correct?

a. The negative charge remains on the metal sphere.

b. The negative charge spreads over the outside surface of the bucket and cover. c. The negative charge spreads over the inside surface of the bucket and cover.

d. The negative charge spreads equally over the inside and outside surfaces of the bucket and cover.

e. The negative charge spreads equally over the sphere and the inside and outside surfaces of the bucket and cover.

48. A positive point charge q is placed off center inside an uncharged metal sphere insulated from the ground as shown. Where is the induced charge density greatest in magnitude and what is its sign?

a. A; negative. b. A; positive. c. B; negative. d. B; positive. e. C; negative.

49. A positive point charge q is placed at the center of an uncharged metal sphere insulated from the ground. The outside of the sphere is then grounded as shown. Then the ground wire is removed. A is the inner surface and B is the outer surface. Which statement is correct?

a. The charge on A is q; that on B is +q.

b. The charge on B is q; that on A is +q.

c.

The charge is on A and on B. d. There is no charge on either A or B.

(33)

50. An uncharged metal sphere is placed on an insulating puck on a frictionless table. While being held parallel to the table, a rod with a charge q is brought close to the sphere, but does not touch it. As the rod is brought in, the sphere

a. remains at rest. b. moves toward the rod. c. moves away from the rod.

d. moves perpendicular to the velocity vector of the rod. e. moves upward off the puck.

51. Three originally uncharged infinite parallel planes are arranged as shown. Then the upper plate has surface charge density  placed on it while the lower plate receives surface charge density . The net charge induced on the center plate is

a. 0. b. /2. c. +/2. d. . e. +.

52. Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces. When compared to the electric flux 1 through the

surface of radius R, the electric flux 2 through the surface of radius 2R is

a. . b. . c. 2 = 1. d. 2 = 21. e. 2 = 41.

53. Two concentric imaginary spherical surfaces of radius R and 2R respectively surround a positive point charge Q located at the center of the surfaces. When compared to the electric flux 1 through the

surface of radius R, the electric flux 2 through the surface of radius 2R is

a.

. b.

. c. 2 = 1.

(34)

d. 2 = 21.

e. 2 = 41.

54. When a cube is inscribed in a sphere of radius r, the length L of a side of the cube is . If a positive point charge Q is placed at the center of the spherical surface, the ratio of the electric flux sphere at the spherical surface to the flux cube at the surface of the cube is

a. . b. . c. 1. d. . e. .

55. The electric flux through the two adjacent spherical surfaces shown below is known to be the same.

It is also known that there is no charge inside either spherical surface. We can conclude that a. there is no electric field present in this region of space.

b. there is a constant E field present in this region of space. c. the electric flux has a constant value of zero.

d. any of the above may be correct. e. only (a) and (b) above may be correct.

56. Which one of the following cannot be a statement of Gauss's Law for some physical situation? a. 4r20E = Q.

b. 2rL0E = Q.

c. _.

d. _.

e. _.

57. Which one of the following is not an expression for electric charge? a.

(35)

b.

c.

d.

e.

58. An uncharged spherical conducting shell surrounds a charge q at the center of the shell. The charges

on the inner and outer surfaces of the shell are respectively a. q, q.

b. q, +q.

c. +q, q.

d. +q, +q. e. +q, 0.

59. An uncharged spherical conducting shell surrounds a charge q at the center of the shell. Then charge

+3q is placed on the outside of the shell. When static equilibrium is reached, the charges on the inner and outer surfaces of the shell are respectively

a. +q, q.

b. q, +q.

c. +q, +2q. d. +2q, +q. e. +3q, 0.

60. A constant electric field is present throughout a region of space that includes the plane bounded by the x and y axes and the lines x = 30 cm and y = 50 cm. The electric flux through the plane's surface, in N  m2 /C, is a. 0. b. 0.25. c. 25. d. 50. e. 100.

61. A constant electric field is present throughout a region of space that includes the plane bounded by the y and z axes and the lines y = 50 cm and z = 50 cm. The electric flux through the plane's surface, in N  m2 /C, is a. 0. b. 0.25. c. 25. d. 50.

(36)

e. 100.

62. A spaceship encounters a single plane of charged particles, with the charge per unit area equal to . The electric field a short distance above the plane has magnitude ____ and is directed ____ to the plane. a. , parallel b. , perpendicular c. , parallel d. , perpendicular e. , parallel

63. You are told that summed over both the surface areas of sphere A and sphere B below totals to . You can conclude that

a. Sphere A contains charge qin = Q.

b. Sphere B contains charge qin = Q.

c. Sphere B contains charge qin = +Q. d.

Each sphere contains charge .

e. The sum of the charges contained in both spheres is Q.

64. If we define the gravitational field , where is a unit radial vector, then Gauss's Law for gravity is a. _. b. _. c. _. d. _. e. _.

(37)

65. Gino says that the analog of Gauss's law for the flow of an incompressible fluid of density  at constant velocity is for an imaginary surface within the fluid. Lorenzo says that it is true only if the area where the fluid enters the surface and the area where it leaves the surface are both perpendicular to the velocity of the fluid. Which one, if either, is correct?

a. Gino, because as much fluid leaves as enters.

b. Lorenzo, because is not equal to zero if the fluid enters or exits at angles other than 90.

c. Lorenzo, because this is true only when the fluid executes rotational motion.

d. Gino, because it is true only when the fluid is enclosed on all sides, not when it is flowing. e. Lorenzo, because it is true only when the fluid is enclosed on all sides, not when it is

flowing.

66. A beam of electrons moves at velocity . The number of particles per unit volume in the beam of area A is . If we imagine a cylindrical Gaussian surface of radius r and length centered on the beam, the electron flux through the surface is

a. 0. b. vfA. c. vfA. d. vf(A+2r ).

e. vf(A+r ).

67. A student has made the statement that the electric flux through one half of a Gaussian surface is always equal and opposite to the flux through the other half of the Gaussian surface. This is a. never true.

b. never false.

c. true whenever enclosed charge is symmetrically located at a center point, or on a center line or centrally placed plane.

d. true whenever no charge is enclosed within the Gaussian surface. e. true only when no charge is enclosed within the Gaussian surface.

68. A student has made the statement that the electric flux through one half of a Gaussian surface is always equal to the flux through the other half of the Gaussian surface. This is

a. never true. b. never false.

c. true whenever enclosed charge is symmetrically located at a center point, on a center line, or on a centrally placed plane.

d. true whenever no charge is enclosed within the Gaussian surface. e. true only when no charge is enclosed within the Gaussian surface.

(38)

69. Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in the region between the two planes has magnitude . The electric field in the region to the left of A and the electric field in the region to the right of B may have the magnitudes

a. 0, 0. b.

, . c.

, .

d. given in any answer above.

e. given only in answer (a) or (b) above.

70. Two planes of charge with no thickness, A and B, are parallel and vertical. The electric field in region I to the left of plane A has magnitude and points to the left. The electric field in the region to the right of B has magnitude and points to the right. The electric field in the region between the two planes has magnitude and points to the right. The surface charge density on planes A and B respectively is a. , . b. ,  c. _ , . d. _ , . e. 2, .

ANS: E PTS: 2 DIF: Average

71. Whitney says that Gauss's Law can be used to find the electric field of a sufficiently symmetrical distribution of charge as long as over the whole Gaussian surface. Algie says that the electric field must be a constant vector over the entire Gaussian surface. Which one, if either, is correct?

a. Whitney, because that means no charge is enclosed within the Gaussian surface. b. Algie, because a constant electric field means that .

c. Both, because the conditions in (a) and (b) are equivalent.

d. Neither, because the electric field can be found from Gauss's law only if holds only over a portion of the Gaussian surface.

e. Neither, because the charge distribution must be symmetric if anywhere on the surface.

(39)

72. A uniform electric field is present in the region between the infinite parallel planes of charge A and B, and a uniform electric field is present in the region between the infinite parallel planes of charge B and C. When the planes are vertical and the fields are both non-zero,

a. _and _{are both directed to the right.} b. _and _{are both directed to the left.} c. _{points to the right and} _{to the left.} d. _{points to the left and} _{to the right.} e. Any one of the above is possible.

73. A uniform electric field is present in the region between infinite parallel plane plates A and B and a uniform electric field is present in the region between infinite parallel plane plates B and C. When the plates are vertical, is directed to the right and to the left. The signs of the charges on plates A, B and C may be

a. , , . b. +, , . c. +, , +. d. +, +, +.

e. any one of the above.

74. Three infinite planes of charge, A, B and C, are vertical and parallel to one another. There is a uniform electric field to the left of plane A and a uniform electric field to the right of plane C. The field points to the left and the field points to the right. The signs of the charges on plates A, B and C may be

a. , , . b. +, , . c. +, , +. d. +, +, +.

e. any one of the above.

75. An constant electric field, N/C, goes through a surface with area m2.

(This surface can also be expressed as an area of 10 m2 with the direction of the unit vector ( ). What is the magnitude of the electric flux through this area?

a. 24 N  m2 /C b. 48 N  m2 /C c. 0.24 N  m2 /C d. 0.48 N  m2 /C e. 0

(40)

76. A point charge is located at the origin. Centered along the x axis is a cylindrical closed surface of radius 10 cm with one end surface located at x = 2 m and the other end surface located at x = 4 m. If the magnitude of the electric flux through the surface at x = 2 m is 4 N  m2

/C, what is the magnitude of the electric flux through the surface at x = 4 m?

a. 1 N  m2 /C b. 2 N  m2 /C c. 4 N  m2 /C d. 16 N  m2 /C

e. The correct value is not given.

PROBLEM

77. The nucleus of lead-208, , has 82 protons within a sphere of radius 6.34  1015. Each electric charge has a value of 1.60  1019

C. Assuming that the protons create a spherically symmetric distribution of charge, calculate the electric field at the surface of the nucleus.

ANS: 2.94  1021

N/C

PTS: 2 DIF: Average

78. At the point of fission, a nucleus of U-238, with 92 protons is divided into two smaller spheres each with 46 protons and a radius of 5.9  1015

m. What is the repulsive force pushing the two spheres apart when they are just touching one another? (The mass of the U-238 nucleus is 3.98  1025

kg.) ANS:

3 500 N

PTS: 2 DIF: Average

79. The nucleus of a hydrogen atom, a proton, sets up an electric field. The distance between the proton and electron is about 5.1  1011

m. What is the magnitude of the electric field at this distance from the proton? [The charge on the proton is +1.6  1019

C.] ANS:

5.5  1011

N/C

PTS: 2 DIF: Average

80. A Geiger counter is like an electroscope that discharges whenever ions formed by a radioactive particle produce a conducting path. A typical Geiger counter consists of a thin conducting wire of radius 0.002 cm stretched along the axis of a conducting cylinder of radius 2.0 cm. The wire and the cylinder carry equal and opposites charges of 8.0  1010

C all along their length of 10.0 cm. What is the magnitude of the electric field at the surface of the wire?

ANS: 7.2  106

N/C

(41)

Chapter 25—Electric Potential

MULTIPLE CHOICE

1. A charged particle (q = 8.0 mC), which moves in a region where the only force acting on the particle is an electric force, is released from rest at point A. At point B the kinetic energy of the particle is equal to 4.8 J. What is the electric potential difference VB  VA?

a. 0.60 kV b. +0.60 kV c. +0.80 kV d. 0.80 kV e. +0.48 kV

2. A particle (charge = 50 C) moves in a region where the only force on it is an electric force. As the particle moves 25 cm from point A to point B, its kinetic energy increases by 1.5 mJ. Determine the electric potential difference, VB  VA.

a. 50 V b. 40 V c. 30 V d. 60 V e. +15 V

3. Points A [at (2, 3) m] and B [at (5, 7) m] are in a region where the electric field is uniform and given by N/C. What is the potential difference VA  VB?

a. 33 V b. 27 V c. 30 V d. 24 V e. 11 V

4. A particle (charge = +2.0 mC) moving in a region where only electric forces act on it has a kinetic energy of 5.0 J at point A. The particle subsequently passes through point B which has an electric potential of +1.5 kV relative to point A. Determine the kinetic energy of the particle as it moves through point B. a. 3.0 J b. 2.0 J c. 5.0 J d. 8.0 J e. 10.0 J

5. A particle (mass = 6.7  1027_{kg, charge = 3.2  10}19

C) moves along the positive x axis with a speed of 4.8  105

m/s. It enters a region of uniform electric field parallel to its motion and comes to rest after moving 2.0 m into the field. What is the magnitude of the electric field?

a. 2.0 kN/C b. 1.5 kN/C

(42)

c. 1.2 kN/C d. 3.5 kN/C e. 2.4 kN/C

6. A proton (mass = 1.67  1027_{kg, charge = 1.60  10}19

C) moves from point A to point B under the influence of an electrostatic force only. At point A the proton moves with a speed of 50 km/s. At point B the speed of the proton is 80 km/s. Determine the potential difference VB  VA.

a. +20 V b. 20 V c. 27 V d. +27 V e. 40 V

7. A proton (mass = 1.67  1027_{kg, charge = 1.60  10}19

C) moves from point A to point B under the influence of an electrostatic force only. At point A the proton moves with a speed of 60 km/s. At point B the speed of the proton is 80 km/s. Determine the potential difference VB  VA.

a. +15 V b. 15 V c. 33 V d. +33 V e. 20 V

8. What is the speed of a proton that has been accelerated from rest through a potential difference of 4.0 kV? a. 1.1  106 m/s b. 9.8  105 m/s c. 8.8  105 m/s d. 1.2  106 m/s e. 6.2  105 m/s

9. An electron (m = 9.1  1031_{kg, q = 1.6  10}19_{C) starts from rest at point A and has a speed of 5.0 }

106 m/s at point B. Only electric forces act on it during this motion. Determine the electric potential difference VA  VB. a. 71 V b. +71 V c. 26 V d. +26 V e. 140 V

10. A proton (m = 1.7  1027_{kg, q = +1.6  10}19

C) starts from rest at point A and has a speed of 40 km/s at point B. Only electric forces act on it during this motion. Determine the electric potential difference

VB  VA.

a. +8.5 V b. 8.5 V

(43)

c. 4.8 V d. +4.8 V e. 17 V

11. A particle (m = 2.0 g, q = 5.0 C) has a speed of 30 m/s at point A and moves (with only electric forces acting on it) to point B where its speed is 80 m/s. Determine the electric potential difference VA

 VB. a. 2.2 kV b. +1.1 kV c. 1.1 kV d. +2.2 kV e. +1.3 kV

12. An alpha particle (m = 6.7  1027_{kg, 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 this motion. Determine the electric potential difference VA  VB.

a. +4.2 V b. 4.2 V c. 9.4 V d. +9.4 V e. 8.4 V

13. Points A [at (3, 6) m] and B [at (8, 3) m] are in a region where the electric field is uniform and given by N/C. What is the electric potential difference VA  VB?

a. +60 V b. 60 V c. +80 V d. 80 V e. +50 V

14. If a = 30 cm, b = 20 cm, q = +2.0 nC, and Q = 3.0 nC in the figure, what is the potential difference

VA  VB? a. +60 V b. +72 V c. +84 V d. +96 V e. +48 V

(44)

15. Several charges in the neighborhood of point P produce an electric potential of 6.0 kV (relative to zero at infinity) and an electric field of N/C at point P. Determine the work required of an external agent to move a 3.0-C charge along the x axis from infinity to point P without any net change in the kinetic energy of the particle.

a. 21 mJ b. 18 mJ c. 24 mJ d. 27 mJ e. 12 mJ

16. Point charges q and Q are positioned as shown. If q = +2.0 nC, Q = 2.0 nC, a = 3.0 m, and b = 4.0 m, what is the electric potential difference, VA  VB?

a. 8.4 V b. 6.0 V c. 7.2 V d. 4.8 V e. 0 V

17. Three charged particles are positioned in the xy plane: a 50-nC charge at y = 6 m on the y axis, a 80-nC charge at x = 4 m on the x axis, and a 70-nc charge at y = 6 m on the y axis. What is the electric potential (relative to a zero at infinity) at the point x = 8 m on the x axis?

a. +81 V b. +48 V c. +5.8 V d. 72 V e. 18 V

18. Point charges of equal magnitudes (25 nC) and opposite signs are placed on (diagonally) opposite corners of a 60-cm  80-cm rectangle. If point A is the corner of this rectangle nearest the positive charge and point B is located at the intersection of the diagonals of the rectangle, determine the potential difference, VB  VA. a. 47 V b. +94 V c. zero d. 94 V e. +47 V

(45)

19. Identical 2.0-C charges are located on the vertices of a square with sides that are 2.0 m in length. Determine the electric potential (relative to zero at infinity) at the center of the square.

a. 38 kV b. 51 kV c. 76 kV d. 64 kV e. 13 kV

20. A +4.0-C charge is placed on the x axis at x = +3.0 m, and a 2.0-C charge is located on the y axis at y = 1.0 m. Point A is on the y axis at y = +4.0 m. Determine the electric potential at point A (relative to zero at the origin).

a. 6.0 kV b. 8.4 kV c. 9.6 kV d. 4.8 kV e. 3.6 kV

21. Identical 4.0-C charges are placed on the y axis at y = 4.0 m. Point A is on the x axis at x = +3.0 m. Determine the electric potential of point A (relative to zero at the origin).

a. 4.5 kV b. 2.7 kV c. 1.8 kV d. 3.6 kV

e. 14 kV

22. Four identical point charges (+6.0 nC) are placed at the corners of a rectangle which measures 6.0 m  8.0 m. If the electric potential is taken to be zero at infinity, what is the potential at the geometric center of this rectangle?

a. 58 V b. 63 V c. 43 V d. 84 V e. 11 V

23. Three identical point charges (+2.0 nC) are placed at the corners of an equilateral triangle with sides of 2.0-m length. If the electric potential is taken to be zero at infinity, what is the potential at the midpoint of any one of the sides of the triangle?

a. 16 V b. 10 V c. 70 V d. 46 V e. 44 V