Physics Question bank

7/22/2019 Physics Question bank

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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 magnitude2.0 N. Determine the magnitude of the smaller of the two charges.

a. 1.4 C b. 1.1 Cc. 2.0 Cd. 3.3 Ce. 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 totalelectrostatic force on a third particle (charge =4.0 C) placed at the origin ( x = 0)?a. 41 N

b. 16 Nc. 56 Nd. 35 Ne. 72 N

ANS: C PTS: 2 DIF: Average

3. In the figure, ifQ = 30 C, q = 5.0 C, andd = 30 cm, what is the magnitude of the electrostatic forceon q?

a. 15 N b. 23 Nc. zerod. 7.5 Ne. 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 axisat 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 Nc. 39 Nd. 25 Ne. 45 N

ANS: B PTS: 2 DIF: Average


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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 electrostaticforce on the +32- C charge?a. 84 N b. 12 Nc. 36 Nd. 50 Ne. 48 N


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 chargeQ is placed on the x axis at x = 2.0 m. A second point charge,Q, is placed at x = 3.0m. IfQ = 40 C, what is the magnitude of the electrostatic force on a 30- C charge placed at theorigin?a. 7.2 N b. 3.9 Nc. 1.5 Nd. 14 Ne. 8.1 N


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

m. IfQ = 60 C, what is the magnitude of the electrostatic force on a 40- C charge placed at theorigin?a. 16 N b. 27 Nc. 32 Nd. 11 Ne. 3.0 N


9. A point chargeQ is placed on the x axis at the origin. An identical point charge is placed on the x axisat x = 1.0 m and another at x = +1.0 m. IfQ = 40 C, what is the magnitude of the electrostatic forceon the charge at x = +1.0 m?a. 29 N b. 14 Nc. 11 Nd. 18 Ne. 7.0 N



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10. Ifa = 3.0 mm,b = 4.0 mm,Q1 = 60 nC,Q2 = 80 nC, andq = 36 nC in the figure, what is themagnitude of the electric force onq?

a. 5.0 N b. 4.4 Nc. 3.8 Nd. 5.7 Ne. 0.60 N


11. If a = 3.0 mm,b = 4.0 mm,Q1 = 60 nC,Q2 = 80 nC, andq = 30 nC in the figure, what is themagnitude of the electric force onq?

a. 1.4 N b. 1.0 Nc. 1.7 Nd. 2.0 Ne. 0.50 N


12. Ifa = 3.0 mm,b = 4.0 mm,Q1 = 60 nC,Q2 = 80 nC, andq = 24 nC in the figure, what is the magnitudeof the electric force onq?

a. 2.7 N b. 1.9 Nc. 2.3 Nd. 1.5 Ne. 0.52 N


13. Ifa = 3.0 mm,b = 4.0 mm,Q1 = 60 nC,Q2 = 80 nC, andq = 32 nC in the figure, what is the magnitudeof the electric force onq?


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a. 1.6 N b. 1.3 Nc. 1.9 Nd. 2.2 Ne. 0.040 N


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

on the negative charge?a. 80 N b. 40 Nc. 69 Nd. 57 Ne. 75 N


15. Three point charges, two positive and one negative, each having a magnitude of 20 C are placed atthe vertices of an equilateral triangle (30 cm on a side). What is the magnitude of the electrostatic foron one of the positive charges?a. 69 N b. 40 Nc. 80 Nd. 57 Ne. 20 N


16. A point chargeQ is placed at the origin. A second charge, 2Q, is placed on the x axis at x = 3.0 m. IfQ = 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 Nd. 4.4 Ne. 1.8 N

ANS: B PTS: 3 DIF: Challenging

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


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b. 19 Nc. 14 Nd. 22 Ne. 16 N


18. Identical point chargesQ are placed at each of the four corners of a 3.0 m 4.0 m rectangle. IfQ = 40 C, what is the magnitude of the electrostatic force on any one of the charges?a. 3.0 N b. 2.4 Nc. 1.8 Nd. 3.7 Ne. 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 placedon 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 Nc. 54 Nd. 72 Ne. 36 N


20. IfQ = 25 C, q = 10 C, and L = 40 cm in the figure, what is the magnitude of the electrostatic forceon q?

a. 28 N b. 22 Nc. 20 Nd. 14 Ne. 10 N


21. IfQ = 20 C and L = 60 cm, what is the magnitude of the electrostatic force on any one of the chargesshown?


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a. 25 N b. 19 Nc. 15 Nd. 9.1 Ne. 14 N

ANS: D PTS: 3 DIF: Challenging

22. Ifa = 60 cm,b = 80 cm,Q = 4.0 nC, andq = 1.5 nC, what is the magnitude of the electric field at point P?

a. 68 N/C b. 72 N/Cc. 77 N/Cd. 82 N/Ce. 120 N/CANS: A PTS: 2 DIF: Average

23. Ifa = 60 cm,b = 80 cm,Q = 6.0 nC, andq = 4.0 nC, what is the magnitude of the electric field at point P?

a. 35 N/C b. 42 N/Cc. 52 N/Cd. 64 N/C


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e. 104 N/C

ANS: A PTS: 2 DIF: Average

24. Ifa = 60 cm,b = 80 cm,Q = 6.0 nC, andq = 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/Cd. 52 N/Ce. 67 N/C


25. Ifa = 60 cm,b = 80 cm,Q = 6.0 nC, andq = 3.0 nC in the figure, what is the magnitude of theelectric field at point P?

a. 71 N/C b. 56 N/Cc. 60 N/Cd. 53 N/Ce. 67 N/C



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26. IfQ = 16 nC,a = 3.0 m, andb = 4.0 m, what is the magnitude of the electric field at point P?



27. IfQ = 80 nC,a = 3.0 m, andb = 4.0 m in the figure, what is the magnitude of the electric field at pointP?



28. A +2.0-nC point charge is placed at one corner of a square (1.5 m on a side), and a3.0-nC charge is placed on a corner diagonally away from the first charge. What is the magnitude of the electric field aeither of the two unoccupied corners?a. 20 N/C

b. 14 N/Cc. 4.0 N/Cd. 12 N/Ce. 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 axisat y = 2.0m. What is the magnitude of the electric field at the origin?


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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 chargeQ is placed on the x axis at x = +4.0 m. A second chargeq is located at the origin. IfQ = +75nC andq = 8.0 nC, what is the magnitude of the electric field on the y axis at y = +3.0 m?a. 19 N/C b. 23 N/Cc. 32 N/Cd. 35 N/Ce. 21 N/C


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 cmc. 4.9 cm

d. 6.0 cme. +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 themagnitude of the electric field at a point on the x axis with x = 8.0 m.a. 30 N/C b. 15 N/Cc. 48 N/Cd. 90 N/Ce. 60 N/C

ANS: B PTS: 3 DIF: Challenging 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.a. 81 N/C b. 74 N/Cc. 61 N/Cd. 88 N/Ce. 20 N/C


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35. A charge of 25 nC is uniformly distributed along a circular arc (radius = 2.0 m) that is subtended by a90-degree angle. What is the magnitude of the electric field at the center of the circle along which thearc lies?a. 81 N/C b. 61 N/Cc. 71 N/C

d. 51 N/Ce. 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/Cc. 19 N/Cd. 26 N/Ce. 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 onequadrant of a circle. What is the magnitude of the electric field at the center of the circle?a. 62 N/C b. 56 N/Cc. 50 N/Cd. 44 N/Ce. 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 asemicircle. What is the magnitude of the electric field at the center of the circle?a. 64 N/C b. 133 N/Cc. 48 N/Cd. 85 N/Ce. 34 N/C


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

b.

c.


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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 thefollowing 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 followingintegrals 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 ofthe following integrals is correct for the magnitude of the electric field at y = 4 m on the y axis?a.

b.

c.

d.

e. none of these


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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 thefollowing 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 othe electric field at a point which lies along the axis of the rod and is 3.0 m from the center of the roda. 40 N/C b. 45 N/Cc. 24 N/Cd. 90 N/Ce. 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 themagnitude of the electric field at the origin?a. 18 N/C b. 50 N/C

c. 30 N/Cd. 15 N/Ce. 90 N/C


46. A 24-nC charge is distributed uniformly along the x axis from x = 2 m to x = 6 m. Which of thefollowing 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



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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 onthe 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/Cc. 5.7 N/Cd. 6.2 N/Ce. 9.0 N/C


49. A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field isuniform and is given by E x = 2.5 N/C, E y = E z = 0. If the velocity of the particle att = 0 is given byv x = 80 m/s,v y = v z = 0, what is the speed of the particle att = 2.0 s?a. 40 m/s

b. 20 m/sc. 60 m/sd. 80 m/se. 180 m/s


50. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field isuniform and is given by E x = 2.5 N/C, E y = E z = 0. If the velocity of the particle att = 0 is given byv y =50 m/s,v x = v z = 0, what is the speed of the particle att = 2.0 s?a. 81 m/s b. 72 m/sc. 64 m/sd. 89 m/se. 25 m/s



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51. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field isuniform and is given by E x = 5.5 N/C, E y = E z = 0. If the position and velocity of the particle att = 0are given by x = y = z = 0 andv x = 50 m/s,v y = v z = 0, what is the distance from the origin to the particle att = 2.0 s?a. 60 m b. 28 mc. 44 md. 12 me. 88 m


52. A particle (mass = 5.0 g, charge = 40 mC) moves in a region of space where the electric field isuniform and is given by E x = 2.3 N/C, E y = E z = 0. If the position and velocity of the particle att = 0are given by x = y = z = 0 andv z = 20 m/s,v x = v y = 0, what is the distance from the origin to the particle att = 2.0 s?a. 60 m b. 54 mc. 69 md. 78 me. 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 fieldhas 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?a. 68 m/s b. 44 m/sc. 56 m/sd. 80 m/se. 36 m/s


54. A particle (q = 4.0 mC,m = 50 g) has a velocity of 25 m/s in the positive x direction when it firstenters a region where the electric field is uniform (60 N/C in the positive y direction). What is thespeed of the particle 5.0 s after it enters this region?a. 49 m/s b. 35 m/sc. 32 m/sd. 44 m/se. 24 m/s


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 electroreleased 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


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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'sspeed att = 5.0 s?a. 60 m/s b. 20 m/sc. 45 m/sd. 40 m/se. 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. Att = 0, the particle is moving 25 m/s in the positive x direction and is passing through theorigin. How far is the particle from the origin att = 2.0 s?a. 80 m b. 20 mc. 58 md. 10 me. 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. Att = 0, the particle is moving 30 m/s in the positive x direction and is passing through theorigin. Determine the maximum distance beyond x = 0 the particle travels in the positive x direction.a. 25 m b. 20 mc. 15 md. 30 me. 60 m


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

.

b..

c..

d..

e..


60. ChargeQ is distributed uniformly along a semicircle of radius a . Which formula below gives thecorrect magnitude of the force on a particle of chargeq located at the center of the circle?


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a..

b..

c..

d.

.e.

.


61. ChargeQ is uniformly distributed over a line segment of length 2 L, 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, electricfield lines in the space surrounding a charge distribution showa. 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 linesc. 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.

ANS: D PTS: 1 DIF: Easy


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63. When a positive chargeq is placed in the field created by two other chargesQ1 and Q2, each a distancer away fromq, the acceleration ofq isa. in the direction of the chargeQ1 or Q2 of smaller magnitude. b. in the direction of the chargeQ1 or Q2 of greater magnitude.c. in the direction of the negative charge ifQ1 and Q2 are of opposite sign.d. in the direction of the positive charge ifQ1 and Q2 are of opposite sign.e. in a direction determined by the vector sum of the electric fields ofQ1 and Q2.

ANS: E PTS: 1 DIF: Easy

64. Two charged particles,Q1 and Q2, are a distancer apart withQ2 = 5Q1. Compare the forces they exerton one another when is the forceQ2 exerts onQ1 and is the forceQ1 exerts onQ2.a. = 5 . b. = 5 .c. = .d. = .e. 5 = .


65. Rubber rods charged by rubbing with cat fur repel each other. Glass rods charged by rubbing with silrepel each other. A rubber rod and a glass rod charged respectively as above attract each other. A possible explanation is thata. 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 isnot a possible electric field configuration for a region of spacewhich doesnot 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 uniformelectric field pointing in the + x-direction. Which of the diagrams below shows its path while it is in theregion 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.



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68. A negatively charged particle is moving in the + x-direction when it enters a region with a uniformelectric field pointing in the + x-direction. Which graph gives its position as a function of timecorrectly? (Its initial position is x = 0 att = 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 anrepels Z. Since pith is an insulating material, we can conclude thata. 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 anrepels Z. Since pith is an insulating material, we can conclude thata. 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 show below.

One is positively charged; the other is neutral. We can conclude thata. all field lines leaving the positively charged pith ball end on the neutral pith ball.


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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 2 R respectively surround a positive point chargeQ located at the center of the concentric spheres. When compared to the number of field lines N 1 going

through the sphere of radius R, the number of electric field lines N 2 going through the sphere of radius2 R isa. .

b. .

c. N 2 = N 1.d. N 2 = 2 N 1.e. N 2 = 4 N 1.


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 chargis simply the absence of positive charge. Rosetta says that negative charge is created and that positivecharge 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 ofcharge.


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76. Three 2.50 C charges are placed on tiny conducting spheres at the ends of 1.00 m-long strings thatare connected at 120 angles as shown below. The magnitude, in N, of the force on any one of thecharges 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 thatare connected at 120 angles as shown below. The magnitude, in N, of the tension in any one of thestrings 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 thecenter is


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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 andfixed to the origin, the resulting electric field on the x axis at x = 2 m becomes zero. What is themagnitude of the electric field at x = 4 m on the x axis at this time?a. 0

b. 1 N/Cc. 2 N/Cd. 4 N/Ce. 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 iand charge has three field lines going into it. If one of the charges is 100 nC, what is the other onea. 25 nC b. 100 nCc. 25 nCd. 100 nCe. 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 unitlent of 1.5 nC/m, and the other has a charge per unit length of 1.5 nC/m. The semicircles are joined tomake a circle. What is the magnitude of the electric field at the center of the circle?a. 42 N/C b. 84 N/Cc. 34 N/Cd. 68 N/Ce. 0


PROBLEM

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

10 19 C) from rest to 3.00 107 m/s within a distance of 2.00 cm. What electric field is required?


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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 theelectrical force acting on the alpha particle when it is at a distance of 2 10 14 m away from the goldnucleus? (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 electricfield 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 chargesQ on the Earth and +Q on the Moon are necessary to hold theMoon in a circular orbit with a period of 27.3 days? The Earth-Moon distance is 384 000 km and themass 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. Determinethe net electric flux through the surface of the cube.a. +2.8 N m2/C b. 1.1 N m2/Cc. +1.1 N m2/Cd. 2.8 N m2/Ce. 0.47 N m2/C


2. The total electric flux through a closed cylindrical (length = 1.2 m, diameter = 0.20 m) surface is equto 5.0 N m2/C. Determine the net charge within the cylinder.a. 62 pC b. 53 pCc. 44 pC


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d. 71 pCe. 16 pC


3. Chargesq and Q are placed on the x axis at x = 0 and x = 2.0 m, respectively. Ifq = 40 pC andQ =+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/Cc. 8.5 N m2/Cd. 4.5 N m2/Ce. 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/Cc. 45 N m2/Cd. 79 N m2/Ce. 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 theelectric flux through this surface.a. 7.1 N m2/C b. 3.6 N m2/Cc. 12 N m2/Cd. 19 N m2/Ce. 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 radiusr = 2a is centered at the origin. The flux through thisGaussian surface isa. 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.ANS: A PTS: 1 DIF: Easy

7. The xy plane is "painted" with a uniform surface charge density which is equal to 40 nC/m2. Consider aspherical surface with a 4.0-cm radius that has a point in the xy plane as its center. What is the electricflux through that part of the spherical surface for which z > 0?a. 14 N m2/C b. 11 N m2/C


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c. 17 N m2/Cd. 20 N m2/Ce. 23 N m2/C


8. A long cylinder (radius = 3.0 cm) is filled with a nonconducting material which carries a uniformcharge 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/Cc. 6.4 N m2/Cd. 7.2 N m2/Ce. 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/Cc. 2.3 N m2/Cd. 4.0 N m2/Ce. 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 totalelectric flux through the surface of this cube?a. 2.9 N m2/C b. 2.0 N m2/Cc. 2.6 N m2/Cd. 2.3 N m2/Ce. 1.8 N m2/CANS: D PTS: 2 DIF: Average

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 thelectric flux through one face of the cube?a. 90 N m2/C b. 15 N m2/Cc. 45 N m2/Cd. 23 N m2/Ce. 64 N m2/C


12. A hemispherical surface (half of a spherical surface) of radius R is located in a uniform electric field ofmagnitude E that is parallel to the axis of the hemisphere. What is the magnitude of the electric fluxthrough the hemisphere surface?a. R2 E b. 4 R2 E /3c. 2 R2 E /3d. R2 E /2


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e. R2 E /3


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

a. 90 N m2/C b. 6.0 N m2/Cc. 54 N m2/Cd. 12 N m2/Ce. 126 N m2/C


14. Charge of uniform surface density (0.20 nC/m2) is distributed over the entire xy plane. Determine themagnitude of the electric field at any point having z = 2.0 m.a. 17 N/C b. 11 N/Cc. 23 N/Cd. 28 N/Ce. 40 N/C


15. Two infinite parallel surfaces carry uniform charge densities of 0.20 nC/m2 and 0.60 nC/m2. What isthe magnitude of the electric field at a point between the two surfaces?a. 34 N/C b. 23 N/Cc. 45 N/Cd. 17 N/Ce. 90 N/C


16. Two infinite, uniformly charged, flat surfaces are mutually perpendicular. One of the sheets has acharge density of +60 pC/m2, and the other carries a charge density of80 pC/m2. What is themagnitude of the electric field at any point not on either surface?a. 1.1 N/C b. 5.6 N/Cc. 7.9 N/C


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d. 3.8 N/Ce. 4.0 N/C


17. Charge of a uniform density (8.0 nC/m2) is distributed over the entire xy plane. A charge of uniformdensity (3.0 nC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine themagnitude of the electric field for any point with z = 3.0 m.a. 0.79 kN/C

b. 0.17 kN/Cc. 0.62 kN/Cd. 0.34 kN/Ce. 0.28 kN/C


18. Charge of a uniform density (8.0 nC/m2) is distributed over the entire xy plane. A charge of uniformdensity (5.0 nC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine themagnitude of the electric field for any point with z = 1.0 m.a. 0.45 kN/C b. 0.17 kN/Cc. 0.28 kN/Cd. 0.73 kN/Ce. 0.62 kN/C


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 atany point not in either of the two charged planes?a. 40 N/C b. 34 N/Cc. 28 N/Cd. 46 N/Ce. 6.0 N/CANS: C PTS: 2 DIF: Average

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 axisof the cylinder.a. 25 N/C b. 20 N/Cc. 14 N/Cd. 31 N/Ce. 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 othe cylinder.a. 20 N/C b. 27 N/Cc. 16 N/C


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d. 12 N/Ce. 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 uniformlythroughout its volume. What is the magnitude of the electric field at a point 5.0 mm from the axis ofthe cylinder?a. 9.9 kN/C

b. 8.1 kN/Cc. 9.0 kN/Cd. 7.2 kN/Ce. 18 kN/C


23. A long nonconducting cylinder (radius = 6.0 mm) has a nonuniform volume charge density given by r 2, where = 6.2 mC/m5 and r is the distance from the axis of the cylinder. What is the magnitude ofthe 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/Cd. 2.0 N/Ce. 5.4 N/C


24. A long cylindrical shell (radius = 2.0 cm) has a charge uniformly distributed on its surface. If themagnitude 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 nCc. 0.19 nCd. 0.57 nCe. 0.98 nCANS: B PTS: 2 DIF: Average

25. Charge of uniform linear density (4.0 nC/m) is distributed along the entire x axis. Determine themagnitude of the electric field on the y axis at y = 2.5 m.a. 36 N/C b. 29 N/Cc. 43 N/Cd. 50 N/Ce. 58 N/C


26. Charge of uniform density (80 nC/m3) is distributed throughout a hollow cylindrical region formed bytwo coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electricfield at a point which is 2.0 mm from the symmetry axis.a. 7.9 N/C b. 9.0 N/Cc. 5.9 N/Cd. 6.8 N/C


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e. 18 N/C


27. Charge of uniform density (80 nC/m3) is distributed throughout a hollow cylindrical region formed bytwo coaxial cylindrical surfaces of radii 1.0 mm and 3.0 mm. Determine the magnitude of the electricfield 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/Cd. 8.9 N/Ce. 17 N/C


28. Charge of uniform density (20 nC/m2) is distributed over a cylindrical surface (radius = 1.0 cm), and asecond coaxial surface (radius = 3.0 cm) carries a uniform charge density of12 nC/m2. Determine themagnitude of the electric field at a point 2.0 cm from the symmetry axis of the two surfaces.a. 2.3 kN/C b. 1.1 kN/Cc. 1.7 kN/C

d. 3.4 kN/Ce. 4.5 kN/C


29. Charge of uniform density (20 nC/m2) is distributed over a cylindrical surface (radius = 1.0 cm), and asecond coaxial surface (radius = 3.0 cm) carries a uniform charge density of12 nC/m2. Determine themagnitude of the electric field at a point 4.0 cm from the symmetry axis of the two surfaces.a. 0.45 kN/C b. 1.0 kN/Cc. 0.73 kN/Cd. 0.56 kN/Ce. 2.3 kN/C


30. Charge of uniform density (40 pC/m2) is distributed on a spherical surface (radius = 1.0 cm), and asecond 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/Cc. 3.5 N/Cd. 3.2 N/Ce. 0.28 N/C


31. A solid nonconducting sphere (radius = 12 cm) has a charge of uniform density (30 nC/m3) distributedthroughout its volume. Determine the magnitude of the electric field 15 cm from the center of thesphere.a. 22 N/C b. 49 N/Cc. 31 N/Cd. 87 N/C


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e. 26 N/C


32. A 5.0-nC point charge is embedded at the center of a nonconducting sphere (radius = 2.0 cm) whichhas a charge of 8.0 nC distributed uniformly throughout its volume. What is the magnitude of theelectric 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/Cc. 3.6 105 N/Cd. 2.7 105 N/Ce. 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 secondcharge 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/Cc. 40 N/C

d. 20 N/Ce. 70 N/C


34. A charge of 8.0 pC is distributed uniformly on a spherical surface (radius = 2.0 cm), and a secondcharge 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/Cc. 22 N/Cd. 18 N/C

e. 40 N/CANS: D PTS: 2 DIF: Average

35. A point charge (5.0 pC) is located at the center of a spherical surface (radius = 2.0 cm), and a charge 3.0 pC is spread uniformly upon this surface. Determine the magnitude of the electric field 1.0 cmfrom the point charge.a. 0.72 kN/C b. 0.45 kN/Cc. 0.63 kN/Cd. 0.90 kN/Ce. 0.18 kN/C


36. Charge of uniform density (40 pC/m2) is distributed on a spherical surface (radius = 1.0 cm), and asecond 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/Cc. 1.4 N/Cd. 5.6 N/C


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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 cmconducting sphere which has a net charge of 4.0 pC. Determine the magnitude of the electric field at point which is 6.0 cm from the point charge.a. 35 N/C b. 25 N/C

c. 30 N/Cd. 20 N/Ce. 10 N/C


38. The axis of a long hollow metallic cylinder (inner radius = 1.0 cm, outer radius = 2.0 cm) coincideswith a long wire. The wire has a linear charge density of8.0 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/Cc. 4.3 N/C

d. 3.6 N/Ce. 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.a. 18 N/C b. 23 N/Cc. 30 N/Cd. 15 N/Ce. 60 N/C


40. If the electric field just outside a thin conducting sheet is equal to 1.5 N/C, determine the surfacecharge 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 pointsradially outward and has a magnitude of 200 N/C. What is the charge density on the surface of thecylinder?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



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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 of3.0 pC.What is the magnitude of the electric field 2.0 cm from the center of these conductors?a. 23 N/C b. zeroc. 45 N/Cd. 90 N/Ce. 110 N/C


43. A long cylindrical conductor (radius = 1.0 mm) carries a charge density of 4.0 pC/m and is inside acoaxial, hollow, cylindrical conductor (inner radius = 3.0 mm, outer radius = 4.0 mm) that has a totalcharge of 8.0 pC/m. What is the magnitude of the electric field 2.0 mm from the axis of theseconductors?a. 24 N/C b. 18 N/Cc. zerod. 36 N/Ce. 226 N/C


44. The electric field just outside the surface of a hollow conducting sphere of radius 20 cm has amagnitude of 500 N/C and is directed outward. An unknown chargeQ is introduced into the center ofthe 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 chargeQ?a. 1.5 nC b. 1.8 nCc. 1.3 nCd. 1.1 nCe. 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 cmouter radius = 2.0 cm) which has a net charge of4.0 nC. Determine the resulting charge density onthe 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 thedeposit 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


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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 anon-conducting thread. The sphere is given a negative charge before the cover is placed on the buckeThe 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 chargeq is placed off center inside an uncharged metal sphere insulated from theground 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.ANS: A PTS: 1 DIF: Easy

49. A positive point chargeq is placed at the center of an uncharged metal sphere insulated from theground. The outside of the sphere is then grounded as shown. Then the ground wire is removed. A isthe 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.e. The charge on A is q; there is no charge on B.


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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 chargeq is brought close to the sphere, but does not touch it. As therod is brought in, the spherea. 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 hassurface charge density placed on it while the lower plate receives surface charge density . The netcharge induced on the center plate is

a. 0. b. /2.c. + /2.d. .e. + .


52. Two concentric imaginary spherical surfaces of radius R and 2 R respectively surround a positive point

chargeQ located at the center of the surfaces. When compared to the electric flux1 through thesurface of radius R, the electric flux 2 through the surface of radius 2 R isa. .

b. .

c. 2 = 1.d. 2 = 2 1.e. 2 = 4 1.


53. Two concentric imaginary spherical surfaces of radius R and 2 R respectively surround a positive pointcharge Q located at the center of the surfaces. When compared to the electric flux1 through thesurface of radius R, the electric flux 2 through the surface of radius 2 R isa. .

b. .

c. 2 = 1.


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d. 2 = 2 1.e. 2 = 4 1.


54. When a cube is inscribed in a sphere of radiusr , the length L of a side of the cube is . If a

positive point chargeQ 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 isa. .

b..

c. 1.d.

.

e. .

ANS: C PTS: 1 DIF: Easy 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 thata. 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 r 2 0 E = Q. b. 2 rL 0 E = Q.c. .d. .e. .


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


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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 chargeqin = Q. b. Sphere B contains chargeqin = Q.c. Sphere B contains chargeqin = +Q.d.

Each sphere contains charge .

e. The sum of the charges contained in both spheres isQ.


64. If we define the gravitational field , where is a unit radial vector, then Gauss's Law

for gravity isa. . b. .c. .d. .e. .


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65. Gino says that the analog of Gauss's law for the flow of an incompressible fluid of density atconstant velocity is for an imaginary surface within the fluid. Lorenzo says that it istrue 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 otherthan 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 ofarea A is . If we imagine a cylindrical Gaussian surface of radiusr and length centered on the beam, the electron flux through the surface isa. 0. b. v f A.c. v f A.d. v f ( A+2 r ).e. v f ( A+ r ).


67. A student has made the statement that the electric flux through one half of a Gaussian surface isalways equal and opposite to the flux through the other half of the Gaussian surface. This isa. 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 isalways equal to the flux through the other half of the Gaussian surface. This isa. 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.



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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 magnitudesa. 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 regio

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 isa. , .

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 symmetricaldistribution of charge as long as over the whole Gaussian surface. Algie says that theelectric field must be a constant vector over the entire Gaussian surface. Which one, if either, iscorrect?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.



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72. A uniform electric field is present in the region between the infinite parallel planes of charge A anB, and a uniform electric field is present in the region between the infinite parallel planes of chargB 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 anduniform electric field is present in the region between infinite parallel plane plates B and C. Whenthe plates are vertical, is directed to the right and to the left. The signs of the charges on platesA, B and C may bea. , , . 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 uniforelectric field to the left of plane A and a uniform electric field to the right of plane C. The fiel

points to the left and the field points to the right. The signs of the charges on plates A, B and Cmay bea. , , . 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

/Cd. 0.48 N m2/Ce. 0



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76. A point charge is located at the origin. Centered along the x axis is a cylindrical closed surface ofradius 10 cm with one end surface located at x = 2 m and the other end surface located at x = 4 m. Ifthe magnitude of the electric flux through the surface at x = 2 m is 4 N m2/C, what is the magnitudeof the electric flux through the surface at x = 4 m?a. 1 N m2/C b. 2 N m2/Cc. 4 N m2/Cd. 16 N m2/C

e. The correct value is not given.ANS: A PTS: 2 DIF: Average

PROBLEM

77. The nucleus of lead-208, , has 82 protons within a sphere of radius 6.34 10 15. Each electriccharge has a value of 1.60 10 19 C. Assuming that the protons create a spherically symmetricdistribution 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 eachwith 46 protons and a radius of 5.9 10 15 m. What is the repulsive force pushing the two spheresapart 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 protonand 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 thecylinder carry equal and opposites charges of 8.0 10 10 C all along their length of 10.0 cm. What isthe magnitude of the electric field at the surface of the wire? ANS:7.2 106 N/C PTS: 2 DIF: Average


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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 particleis an electric force, is released from rest at point A. At point B the kinetic energy of the particle isequal to 4.8 J. What is the electric potential differenceV B V A?

a. 0.60 kV b. +0.60 kVc. +0.80 kVd. 0.80 kVe. +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 theelectric potential difference,V B V A.a. 50 V

b. 40 Vc. 30 Vd. 60 Ve. +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 differenceV A V B?a. 33 V b. 27 Vc. 30 Vd. 24 Ve. 11 V


4. A particle (charge = +2.0 mC) moving in a region where only electric forces act on it has a kineticenergy 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 movesthrough point B.a. 3.0 J b. 2.0 Jc. 5.0 Jd. 8.0 Je. 10.0 JANS: B PTS: 2 DIF: Average

5. A particle (mass = 6.7 10 27 kg, charge = 3.2 10 19 C) moves along the positive x axis with a speedof 4.8 105 m/s. It enters a region of uniform electric field parallel to its motion and comes to restafter 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


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c. 1.2 kN/Cd. 3.5 kN/Ce. 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 theinfluence of an electrostatic force only. At point A the proton moves with a speed of 50 km/s. At poinB the speed of the proton is 80 km/s. Determine the potential differenceV B V A.a. +20 V b. 20 Vc. 27 Vd. +27 Ve. 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 theinfluence of an electrostatic force only. At point A the proton moves with a speed of 60 km/s. At poinB the speed of the proton is 80 km/s. Determine the potential differenceV B V A.a. +15 V

b. 15 Vc. 33 Vd. +33 Ve. 20 V


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

d. 1.2 106 m/se. 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 potentialdifferenceV A V B.a. 71 V b. +71 Vc. 26 Vd. +26 V

e. 140 VANS: A PTS: 2 DIF: Average

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/sat point B. Only electric forces act on it during this motion. Determine the electric potential differencV B V A.a. +8.5 V b. 8.5 V


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c. 4.8 Vd. +4.8 Ve. 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 electricforces acting on it) to point B where its speed is 80 m/s. Determine the electric potential differenceV A

V B.a. 2.2 kV b. +1.1 kVc. 1.1 kVd. +2.2 kVe. +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 movesto point B where it momentarily stops. Only electric forces act on the particle during this motion.Determine the electric potential differenceV A V B.a. +4.2 V b. 4.2 Vc. 9.4 Vd. +9.4 Ve. 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 differenceV A V B?a. +60 V b. 60 Vc. +80 Vd. 80 Ve. +50 V


14. Ifa = 30 cm,b = 20 cm,q = +2.0 nC, andQ = 3.0 nC in the figure, what is the potential differenceV A V B?

a. +60 V b. +72 Vc. +84 Vd. +96 Ve. +48 V



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15. Several charges in the neighborhood of point P produce an electric potential of 6.0 kV (relative to zerat infinity) and an electric field of N/C at point P. Determine the work required of an externalagent to move a 3.0- C charge along the x axis from infinity to point P without any net change in thekinetic energy of the particle.a. 21 mJ b. 18 mJc. 24 mJd. 27 mJ

e. 12 mJANS: B PTS: 2 DIF: Average

16. Point chargesq and Q are positioned as shown. Ifq = +2.0 nC,Q = 2.0 nC,a = 3.0 m, andb = 4.0 m,what is the electric potential difference,V A V B?

a. 8.4 V b. 6.0 Vc. 7.2 Vd. 4.8 Ve. 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 Vc. +5.8 Vd. 72 Ve. 18 V


18. Point charges of equal magnitudes (25 nC) and opposite signs are placed on (diagonally) oppositecorners of a 60-cm 80-cm rectangle. If point A is the corner of this rectangle nearest the positivecharge and point B is located at the intersection of the diagonals of the rectangle, determine the potential difference,V B V A.a. 47 V b. +94 Vc. zerod. 94 Ve. +47 V



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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 kVc. 76 kVd. 64 kVe. 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 axisat 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 kVc. 9.6 kVd. 4.8 kVe. 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 kVc. 1.8 kVd. 3.6 kVe. 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 Vc. 43 Vd. 84 Ve. 11 V


23. Three identical point charges (+2.0 nC) are placed at the corners of an equilateral triangle with sides 2.0-m length. If the electric potential is taken to be zero at infinity, what is the potential at the midpoiof any one of the sides of the triangle?a. 16 V b. 10 Vc. 70 Vd. 46 Ve. 44 V



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24. A particle (charge =Q) is kept in a fixed position at point P, and a second particle (charge =q) isreleased from rest when it is a distance R from P. IfQ = +2.0 mC,q = 1.5 mC, and R = 30 cm, whatis the kinetic energy of the moving particle after it has moved a distance of 10 cm?a. 60 kJ b. 45 kJc. 75 kJd. 90 kJe. 230 kJ


25. Particle A (mass =m, charge =Q) and B (mass =m, charge = 5Q) are released from rest with thedistance between them equal to 1.0 m. IfQ = 12 C, what is the kinetic energy of particle B at theinstant when the particles are 3.0 m apart?a. 8.6 J b. 3.8 Jc. 6.0 Jd. 2.2 Je. 4.3 J


26. A particle (charge = 40 C) moves directly toward a second particle (charge = 80 C) which is held ina fixed position. At an instant when the distance between the two particles is 2.0 m, the kinetic energyof the moving particle is 16 J. Determine the distance separating the two particles when the moving particle is momentarily stopped.a. 0.75 m b. 0.84 mc. 0.95 md. 0.68 me. 0.56 m


27. A particle (charge 7.5 C) is released from rest at a point on the x axis, x = 10 cm. It begins to movedue to the presence of a 2.0- C charge which remains fixed at the origin. What is the kinetic energy ofthe particle at the instant it passes the point x = 1.0 m?a. 3.0 J b. 1.8 Jc. 2.4 Jd. 1.2 Je. 1.4 J


28. A particle (charge = 5.0 C) is released from rest at a point x = 10 cm. If a 5.0- C charge is held fixedat the origin, what is the kinetic energy of the particle after it has moved 90 cm?a. 1.6 J b. 2.0 Jc. 2.4 Jd. 1.2 Je. 1.8 J



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29. A 60- C charge is held fixed at the origin and a20- C charge is held fixed on the x axis at a point x = 1.0 m. If a 10- C charge is released from rest at a point x = 40 cm, what is its kinetic energy theinstant it passes the point x = 70 cm?a. 9.8 J b. 7.8 Jc. 8.8 Jd. 6.9 Je. 2.8 J


30. Two identical particles, each with a mass of 2.0 g and a charge of 25 nC, are released simultaneouslyfrom rest when the two are 4.0 cm apart. What is the speed of either particle at the instant when thetwo are separated by 10 cm?a. 7.3 m/s b. 9.8 m/sc. 9.2 m/sd. 6.5 m/se. 4.6 m/s


31. Two particles, each having a mass of 3.0 g and having equal but opposite charges of magnitude 5.0nC, are released simultaneously from rest when the two are 5.0 cm apart. What is the speed of either particle at the instant when the two are separated by 2.0 cm?a. 2.1 m/s b. 1.5 m/sc. 1.8 m/sd. 2.4 m/se. 3.2 m/s


32. Two identical particles, each with a mass of 4.5 g and a charge of 30 nC, are moving directly towardeach other with equal speeds of 4.0 m/s at an instant when the distance separating the two is equal to25 cm. How far apart will they be when closest to one another?a. 9.8 cm b. 12 cmc. 7.8 cmd. 15 cme. 20 cm


33. Two particles, each having a mass of 3.0 g and having equal but opposite charges of magnitude of 6.0nC, are released simultaneously from rest when they are a very large distance apart. What distanceseparates the two at the instant when each has a speed of 5.0 m/s?a. 4.3 mm b. 8.6 mmc. 7.3 mmd. 5.6 mme. 2.2 mm



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34. A particle (q = +5.0 C) is released from rest when it is 2.0 m from a charged particle which is held atrest. After the positively charged particle has moved 1.0 m toward the fixed particle, it has a kineticenergy of 50 mJ. What is the charge on the fixed particle?a. 2.2 C b. +6.7 Cc. 2.7 Cd. +8.0 Ce. 1.1 C


35. Four identical point charges (+4.0 C) are placed at the corners of a square which has 20-cm sides.How much work is required to assemble this charge arrangement starting with each of the charges avery large distance from any of the other charges?a. +2.9 J b. +3.9 Jc. +2.2 Jd. +4.3 Je. +1.9 J


36. Identical 8.0- C point charges are positioned on the x axis at x = 1.0 m and released from restsimultaneously. What is the kinetic energy of either of the charges after it has moved 2.0 m?a. 84 mJ b. 54 mJc. 96 mJd. 63 mJe. 48 mJ


37. Through what potential difference must an electron (starting from rest) be accelerated if it is to reach

speed of 3.0 107

m/s?a. 5.8 kV b. 2.6 kVc. 7.1 kVd. 8.6 kVe. 5.1 kV


38. Identical point charges (+50 C) are placed at the corners of a square with sides of 2.0-m length. Howmuch external energy is required to bring a fifth identical charge from infinity to the geometric centerof the square?a. 41 J b. 16 Jc. 64 Jd. 10 Je. 80 J



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39. A charge of +3.0 C is distributed uniformly along the circumference of a circle with a radius of 20cm. How much external energy is required to bring a charge of 25 C from infinity to the center of thecircle?a. 5.4 J b. 3.4 Jc. 4.3 Jd. 2.7 Je. 6.8 J


40. Identical point charges (+20 C) are placed at the corners of an equilateral triangle with sides of 2.0-mlength. How much external energy is required to bring a charge of 45 C from infinity to the midpointof one side of the triangle?a. 26 J b. 16 Jc. 23 Jd. 21 Je. 12 J


41. Identical point charges (+30 C) are placed at the corners of a rectangle (4.0 m 6.0 m). How muchexternal energy is required to bring a charge of 55 C from infinity to the midpoint of one of the 6.0-mlong sides of the rectangle?a. 22 J b. 16 Jc. 13 Jd. 19 Je. 8.0 J


42. A charge per unit length given by ( x) = bx, whereb = 12 nC/m2, is distributed along the x axis from x = +9.0 cm to x = +16 cm. If the electric potential at infinity is taken to be zero, what is the electric potential at the point P on the y axis at y = 12 cm?a. 5.4 V b. 7.2 Vc. 9.0 Vd. 9.9 Ve. 16 V


43. A chargeQ is uniformly distributed along the x axis from x = a to x = b. If Q = 45 nC,a = 3.0 m, andb = 2.0 m, what is the electric potential (relative to zero at infinity) at the point, x = 8.0 m, on the x axis?a. 71 V b. 60 Vc. 49 Vd. 82 Ve. 150 V



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44. Charge of uniform density (3.5 nC/m) is distributed along the circular arc shown. Determine theelectric potential (relative to zero at infinity) at point P.

a. 61 V b. 42 Vc. 52 Vd. 33 Ve. 22 V


45. A charge of uniform density (0.80 nC/m) is distributed along the x axis from the origin to the point x =10 cm. What is the electric potential (relative to zero at infinity) at a point, x = 18 cm, on the x axis?a. 7.1 V b. 5.8 Vc. 9.0 Vd. 13 Ve. 16 V


46. A charge of 20 nC is distributed uniformly along the x axis from x = 2.0 m to x = +2.0 m. What is theelectric potential (relative to zero at infinity) at the point x = 5.0 m on the x axis?a. 57 V b. 48 Vc. 38 Vd. 67 Ve. 100 V


47. Charge of uniform density 12 nC/m is distributed along the x axis from x = 2.0 m to x = 5.0 m. What isthe electric potential (relative to zero at infinity) at the origin ( x = 0)?a. 91 V b. 99 Vc. 82 V

d. 74 Ve. 140 V


48. A linear charge of nonuniform density = bx, whereb = 2.1 nC/m2, is distributed along the x axisfrom x = 2.0 m to x = 3.0 m. Determine the electric potential (relative to zero at infinity) of the point y = 4.0 m on the y axis.a. 36 V


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b. 95 Vc. 10 Vd. 17 Ve. 15 V


49. A nonuniform linear charge distribution given by ( x) = bx, whereb is a constant, is distributed alongthe x axis from x = 0 to x = + L. If b = 40 nC/m2 and L = 0.20 m, what is the electric potential (relativeto a potential of zero at infinity) at the point y = 2 L on the y axis?a. 19 V b. 17 Vc. 21 Vd. 23 Ve. 14 V


50. A charge of 10 nC is distributed uniformly along the x axis from x = 2 m to x = +3 m. Which of thefollowing integrals is correct for the electric potential (relative to zero at infinity) at the point x = +5 mon the x axis?

a. b.

c.

d.

e.


51. Charge of uniform linear density 3.0 nC/m is distributed along the x axis from x = 0 to x = 3 m. Whichof the following integrals is correct for the electric potential (relative to zero at infinity) at the point x =+4 m on the x axis?a.

b.

c.

d.

e.


52. A charge of 4.0 nC is distributed uniformly along the x axis from x = +4 m to x = +6 m. Which of thefollowing integrals is correct for the electric potential (relative to zero at infinity) at the origin?


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a.

b.

c.

d.

e.


53. A charge of 20 nC is distributed uniformly along the y axis from y = 0 to y = 4 m. Which of thefollowing integrals is correct for the electric potential (relative to zero at infinity) at the point x = +3 mon the x axis?a.

b.

c.

d.

e.


54. Charge of uniform linear density 6.0 nC/m is distributed along the x axis from x = 0 to x = +3 m.Which of the following integrals is correct for the electric potential (relative to zero at infinity) at the point y = +4 m on the y axis?a.

b.

c.

d.

e.



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55. A rod (length = 2.0 m) is uniformly charged and has a total charge of 5.0 nC. What is the electric potential (relative to zero at infinity) at a point which lies along the axis of the rod and is 3.0 m fromthe center of the rod?a. 22 V b. 19 Vc. 16 Vd. 25 Ve. 12 V


56. A charge of 18 nC is uniformly distributed along the y axis from y = 3 m to y = 5 m. Which of thefollowing integrals is correct for the electric potential (relative to zero at infinity) at the point x = +2 mon the x axis?a.

b.

c.

d.

e.


57. Two large parallel conducting plates are 8.0 cm apart and carry equal but opposite charges on theirfacing surfaces. The magnitude of the surface charge density on either of the facing surfaces is 2.0

nC/m2

. Determine the magnitude of the electric potential difference between the plates.a. 36 V b. 27 Vc. 18 Vd. 45 Ve. 16 V


58. A solid conducting sphere (radius = 5.0 cm) has a charge of 0.25 nC distributed uniformly on itssurface. If point A is located at the center of the sphere and point B is 15 cm from the center, what isthe magnitude of the electric potential difference between these two points?a. 23 V b. 30 Vc. 15 Vd. 45 Ve. 60 V



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59. Charge of uniform density 50 nC/m3 is distributed throughout the inside of a long nonconductingcylindrical rod (radius = 5.0 cm). Determine the magnitude of the potential difference of point A (2.0cm from the axis of the rod) and point B (4.0 cm from the axis).a. 2.7 V b. 2.0 Vc. 2.4 Vd. 1.7 Ve. 3.4 V

ANS: D PTS: 3 DIF: Challenging 60. Charge of uniform density 90 nC/m3 is distributed throughout the inside of a long nonconducting

cylindrical rod (radius = 2.0 cm). Determine the magnitude of the potential difference of point A (2.0cm from the axis of the rod) and point B (4.0 cm from the axis).a. 1.9 V b. 1.4 Vc. 2.2 Vd. 2.8 Ve. 4.0 V


61. A nonconducting sphere of radius 10 cm is charged uniformly with a density of 100 nC/m3. What isthe magnitude of the potential difference between the center and a point 4.0 cm away?a. 12 V b. 6.8 Vc. 3.0 Vd. 4.7 Ve. 2.2 V


62. A charge of 40 pC is distributed on an isolated spherical conductor that has a 4.0-cm radius. Point A 1.0 cm from the center of the conductor and point B is 5.0 cm from the center of the conductor.Determine the electric potential differenceV A V B.a. +1.8 V b. +29 Vc. +27 Vd. +7.2 Ve. +9.0 V


63. Two flat conductors are placed with their inner faces separated by 6.0 mm. If the surface chargedensity on one of the inner faces is 40 pC/m2, what is the magnitude of the electric potentialdifferences between the two conductors?

a. 36 mV b. 18 mVc. 32 mVd. 27 mVe. 14 mV



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64. The electric field in a region of space is given by E x = (3.0 x) N/C, E y = E z = 0, where x is in m. PointsA and B are on the x axis at xA = 3.0 m and xB = 5.0 m. Determine the potential differenceV B V A.a. 24 V b. +24 Vc. 18 Vd. +30 Ve. 6.0 V


65. Equipotentials are lines along whicha. the electric field is constant in magnitude and direction. b. the electric charge is constant in magnitude and direction.c. maximum work against electrical forces is required to move a charge at constant speed.d. a charge may be moved at constant speed without work against electrical forces.e. charges move by themselves.


66. When a charged particle is moved along an electric field line,a. the electric field does no work on the charge.

b. the electrical potential energy of the charge does not change.c. the electrical potential energy of the charge undergoes the maximum change in magnitude.d. the voltage changes, but there is no change in electrical potential energy.e. the electrical potential energy undergoes the maximum change, but there is no change in

voltage.


67. When a positive charge is released and moves along an electric field line, it moves to a position ofa. lower potential and lower potential energy. b. lower potential and higher potential energy.c. higher potential and lower potential energy.d. higher potential and higher potential energy.e. greater magnitude of the electric field.


68. When a negative charge is released and moves along an electric field line, it moves to a position ofa. lower potential and lower potential energy. b. lower potential and higher potential energy.c. higher potential and lower potential energy.d. higher potential and higher potential energy.e. decreasing magnitude of the electric field.


69. A charge is placed on a spherical conductor of radiusr 1. This sphere is then connected to a distantsphere of radiusr 2 (not equal tor 1) by a conducting wire. After the charges on the spheres are inequilibrium,a. the electric fields at the surfaces of the two spheres are equal. b. the amount of charge on each sphere isq/2.c. both spheres are at the same potential.


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d.the potentials are in the ratio .

e.the potentials are in the ratio .


70. The electric potential inside a charged solid spherical conductor in equilibriuma. is always zero. b. is constant and equal to its value at the surface.c. decreases from its value at the surface to a value of zero at the center.d. increases from its value at the surface to a value at the center that is a multiple of the

potential at the surface.e. is equal to the charge passing through the surface per unit time divided by the resistance.


71. Which statement is always correct when applied to a charge distribution located in a finite region ofspace?a. Electric potential is always zero at infinity. b. Electric potential is always zero at the origin.c. Electric potential is always zero at a boundary surface to a charge distribution.d. Electric potential is always infinite at a boundary surface to a charge distribution.e. The location where electric potential is zero may be chosen arbitrarily.


72. Which of the following represents the equipotential lines of a dipole?a.

b.

c.

d.


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e.


73. Can the lines in the figure below be equipotential lines?

a. No, because there are sharp corners. b. No, because they are isolated lines.c. Yes, because any lines within a charge distribution are equipotential lines.d. Yes, they might be boundary lines of the two surfaces of a conductor.e. It is not possible to say without further information.


74. A series ofn uncharged concentric shells surround a small central chargeq. The charge distributed onthe outside of thenth shell isa. nq. b. (ln n)q.c. +q.d. +(lnn)q.e. +nq .


75. A series of 3 uncharged concentric shells surround a small central chargeq. The charge distributed onthe outside of the third shell isa. 3q. b. (ln 3)q.c. +q.d. +(ln 3)q.e. +3q.


76. A series ofn uncharged concentric spherical conducting shells surround a small central chargeq. The potential at a point outside the nth shell, at distancer from the center, and relative toV = 0 at , isa. .

b..

c..


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d..

e..


77. A series of 3 uncharged concentric spherical conducting shells surround a small central chargeq. The

potential at a point outside the third shell, at distancer from the center, and relative toV = 0 at , isa..

b..

c..

d..

e..


78. The electric field in the region defined by the y-z plane and the negative x axis is given by E = ax ,wherea is a constant. (There is no field for positive values of x.) As x increases in magnitude, relativeto V = 0 at the origin, the electric potential in the region defined above isa. a decreasing function proportional to| x2|. b. a decreasing function proportional to| x|.c. constant.d. an increasing function proportional to +| x|.e. an increasing function proportional to +| x2|.


79. The electric field in the region defined by the y-z plane and the positive x axis is given by E = ax ,wherea is a constant. (There is no field for negative values of x.) As x increases in magnitude, relativeto V = 0 at the origin, the electric potential in the region defined above isa. a decreasing function proportional to| x2|. b. a decreasing function proportional to| x|.c. constant.d. an increasing function proportional to +| x|.e. an increasing function proportional to +| x2|.


80. Two charges lie on the x axis, +3q at the origin, and 2q at x = 5.0 m. The point on the x axis wherethe electric potential has a zero value (when the value at infinity is also zero) isa. 1.0 m. b. 2.0 m.c. 2.5 m.d. 3.0 m.e. 4.0 m.



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81. Two charges lie on the x axis, +2q at the origin, and 3q at x = 5.0 m. The point on the x axis where

the electric potential has a zero value (when the value at infinity is also zero) isa. 1.0 m. b. 2.0 m.c. 2.5 m.d. 3.0 m.e. 4.0 m.


82. When introduced into a region where an electric field is present, an electron with initial velocity weventually movea. along an electric field line, in the positive direction of the line. b. along an electric field line, in the negative direction of the line.c. to a point of decreased potential.d. to a point of increased potential.e. as described in both (b) and (d).


83. When introduced into a region where an electric field is present, a proton with initial velocity willeventually movea. along an electric field line, in the positive direction of the line. b. along an electric field line, in the negative direction of the line.c. to a point of decreased potential.d. to a point of decreased potential.e. as described in both (a) and (c).


84. A system consisting of a positively-charged particle and an electric fielda. loses potential difference and kinetic energy when the charged particle moves in the

direction of the field. b. loses electric potential energy when the charged particle moves in the direction of thefield.

c. loses kinetic energy when the charged particle moves in the direction of the field.d. gains electric potential energy when the charged particle moves in the direction of the

field.e. gains potential difference and electric potential energy when the charged particle moves in

the direction of the field.


85. A system consisting of a negatively-charged particle and an electric fielda. gains potential difference and kinetic energy when the charged particle moves in the

direction of the field. b. loses electric potential energy when the charged particle moves in the direction of the

field.c. gains kinetic energy when the charged particle moves in the direction of the field.d. gains electric potential energy when the charged particle moves in the direction of the

field.e. gains potential difference and electric potential energy when the charged particle moves in

the direction of the field.


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86. The Bohr model pictures a hydrogen atom in its ground state as a proton and an electron separated by

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