college physics test bank chapter 17

Chapter 17. Electrostatics II: Electric Potential Energy and Electric Potential

Section 17 – 1. Electric energy is important in nature, technology, and biological systems

Section 17 – 2. Electric potential energy changes when a charge moves in an electric field

1. Two protons in a nucleus of 238U are 6.0 × 10–15 m apart. The electrostatic potential energy of the pair is approximately A. zero B. 4.7 × 10–34 J C. 4.3 × 10–24 J D. 3.8 × 10–14 J E. 2.4 × 104 J Ans: D Section: 17–2 Type: Numerical

2. The electrostatic potential energy of two protons separated by 2.6 × 10–15 m is approximately A. zero B. 4.7 × 10–34 JC. 4.3 × 10–24 J D. 3.8 × 10–14 J E. 8.9 × 10–14 J Ans: E Section: 17–2 Type: Numerical

3.

Which of the curves in the graph represents the electrostatic potential energy of a small negative charge plotted as a function of its distance from a positive point charge? A. 1 B. 2 C. 3 D. 4 E. 5 Ans: E Section: 17–2 Type: Conceptual

Test Bank for College Physics Tumer Sayman

4. A positive point charge of 10–4 C is located 3 m from another positive point charge of 10-5 C. Their mutual electric potential energy is A. 3 J B. 2 J C. 1 J D. zero E. –1 J Ans: A Section: 17–2 Type: Numerical

5.

The electrostatic potential energy of the system of point charges q1 = 1 μC, q2 = 2 μC, and q3 = 3 μC at the corners of the equilateral triangle whose side s = 30 cm is A. 1.10 J B. 0.990 J C. 0.631 J D. 0.330 J E. 0.123 J Ans: D Section: 17–2 Type: Numerical


6.

The electrostatic potential energy of the system of point charges q1 = 1 μC, q2 = –2 μC, and q3 = 3 μC at the corners of the equilateral triangle whose side s = 40 cm is A. 1.10 J B. 0.990 J C. –0.631 J D. 0.330 J E. –0.113 J Ans: E Section: 17–2 Type: Numerical

7.

The electrostatic potential energy of the system of point charges q1 = –1 μC, q2 = 2 μC, and q3 = 3 μC at the corners of the equilateral triangle whose side s = 50 cm is A. 18.0 mJ B. –18.0 mJ C. 21.6 mJ D. –24.4 mJ E. 1.23 mJ Ans: A Section: 17–2 Type: Numerical


8.

Four point charges q1 = –1 C, q2 = 2 C, q3 = 3 C, and q4 = 4 C are located at the corners of a square whose side s = 1 m. The electrostatic potential energy of this system of charges is A. 0.140 J B. 0.176 J C. 0.286 J D. 0.337 J E. 0.492 J Ans: A Section: 17–2 Type: Numerical

9.

Four point charges q1 = 1 C, q2 = 2 C, q3 = 3 C, and q4 = 4 C are located at the corners of a square whose side s = 1 m. The electrostatic potential energy of this system of charges is A. 0.167 J B. 0.176 J C. 0.286 J D. 0.337 J E. 0.492 J Ans: C Section: 17–2 Type: Numerical


10. Which of the following statements is false? A. The total work required to assemble a collection of discrete charges is the electrostatic potential energy of the system. B. The potential energy of a pair of positively charged bodies is positive. C. The potential energy of a pair of oppositely charged bodies is positive. D. The potential energy of a pair of oppositely charged bodies is negative. E. The potential energy of a pair of negatively charged bodies is negative. Ans: C Section: 17–2 Type: Factual

11.

The work required to bring a positively charged body from very far away is greatest for point _____. A. A B. B C. C D. D E. E Ans: E Section: 17–2 Type: Conceptual

12.

The electrostatic potential energy of a positively charged body is greatest at point _____. A. A B. B C. C D. D E. E


Ans: E Section: 17–2 Type: Conceptual

13.

The work required to bring a negatively charged body from very far is greatest for point _____. A. A B. B C. C D. D E. E Ans: A Section: 17–2 Type: Conceptual

14.

The electrostatic potential energy of a negatively charged body is greatest at point _____. A. A B. B C. C D. D E. E Ans: A Section: 17–2 Type: Conceptual


15. Three charges are brought from infinity and placed at the corner of an equilateral triangle. Which of the following statements is true?A. The work required to assemble the charges is always positive.B. The electrostatic potential energy of the system is always positive.C. The electrostatic potential energy does not depend on the order the charges are placed at the corners. D. The work required to assemble the charges depends on which charge is placed at which corner.E. The electrostatic potential energy depends on which charge is placed at which corner. Ans: C Section: 17–2 Type: Factual

16. Calculate the change in electrostatic potential energy of a charge, Q = 1 C, when it is moved from a distance x = 4 m to 2 m from an infinite plane of uniform surface charge density σ = 10 C/m2.A. 1.13 J B. 0.565 J C. 1.69 J D. 2.82 J E. zeroAns: A Section: 17–2 Type: Numerical

Section 17 – 3. Electric potential equals electric potential energy per charge

17. The voltage between the cathode and the screen of a television set is 22 kV. If we assume a speed of zero for an electron as it leaves the cathode, what is its speed just before it hits the screen? A. 8.8 × 107 m/sB. 2.8 × 106 m/sC. 6.2 × 107 m/s D. 7.7 × 1015 m/s E. 5.3 × 107 m/s Ans: A Section: 17–3 Type: Numerical

18. The voltage between the cathode and the screen of a computer monitor is 12 kV. If we assume a speed of zero for an electron as it leaves the cathode, what is its speed just before it hits the screen? A. 8.8 × 107 m/s B. 6.5 × 107 m/sC. 4.2 × 1015 m/s D. 7.7 × 1015 m/s E. 5.3 × 107 m/s Ans: B Section: 17–3 Type: Numerical


19. The magnitude of the electric field in a region is given by E=kQ / r2 where Q is the charge. What is the potential difference between r = a to r = b?

A.

B.

C.

D.

E. none of the above

Ans: C Section: 17–3 Type: Numerical

20. A lithium nucleus with a charge of 3(1.6 × 10–19) C and a mass of 7(1.67 × 10–27) kg, and an alpha particle with a charge of 2(1.6 × 10–19) C and a mass of 4(1.67 × 10–27) kg, are at rest. They could be accelerated to the same kinetic energy by A. accelerating them through the same electrical potential difference. B. accelerating the alpha particle through V volts and the lithium nucleus through 2V/3 volts. C. accelerating the alpha particle through V volts and the lithium nucleus through 7V/4 volts. D. accelerating the alpha particle through V volts and the lithium nucleus through 7V/6 volts. E. none of these procedures Ans: B Section: 17–3 Type: Conceptual

21. Correct units for electric potential are A. N/C B. V/m C. N/kg D. J/C E. C/N Ans: D Section: 17–3 Type: Factual

22. The concept of difference in electric potential is most closely associated with A. the mechanical force on an electron. B. the number of atoms in one gram-atom. C. the charge on one electron. D. the resistance of a certain specified column of mercury. E. the work per unit quantity of electricity. Ans: E Section: 17–3 Type: Conceptual


23. A charge of 2.0 mC is located in a uniform electric field of intensity 4.0 × 105 N/C. How much work is required to move this charge 20 cm along a path making an angle of 60° with the electric field? A. 0.14 J B. 0.34 J C. 80 mJ D. 14 J E. 8.0 J Ans: C Section: 17–3 Type: Numerical

24. A charge of 5.0 mC is located in a uniform electric field of intensity 3.5 × 105 N/C. How much work is required to move this charge 50 cm along a path making an angle of 33° with the electric field? A. 0.27 J B. 0.16 J C. 0.54 J D. 0.73 J E. 7.3 mJ Ans: D Section: 17–3 Type: Numerical

25.

Charges Q and q (Q ≠ q), separated by a distance d, produce a potential VP = 0 at point P. This means that A. no force is acting on a test charge placed at point P. B. Q and q must have the same sign. C. the electric field must be zero at point P. D. the net work in bringing Q to distance d from q is zero. E. the net work needed to bring a charge from infinity to point P is zero. Ans: E Section: 17–3 Type: Conceptual

26. When 2.0 C of charge moves at constant speed along a path between two points differing in potential by 6.0 V, the amount of work done by the field is A. 2 J B. 3 J C. 6 J D. 12 J E. 24 J Ans: D Section: 17–3 Type: Numerical


27. When 5.0 C of charge moves at constant speed along a path between two points differing in potential by 12 V, the amount of work done by the field is A. 2.4 J B. 0.42 J C. 5.0 J D. 12 J E. 60 J Ans: E Section: 17–3 Type: Numerical

28. The electron volt is a unit of A. capacitance B. charge C. energy D. momentum E. potential Ans: C Section: 17–3 Type: Factual

29. Two parallel horizontal plates are spaced 0.40 cm apart in air. You introduce an oil droplet of mass 4.9 × 10–17 kg between the plates. If the droplet carries two electronic charges and if there were no air buoyancy, you could hold the droplet motionless between the plates if you kept the potential difference between them at A. 60 V B. 12 V C. 3.0 V D. 0.12 kV E. 6.0 V Ans: E Section: 17–3 Type: Numerical

30. Two parallel horizontal plates are spaced 0.60 cm apart in air. You introduce an oil droplet of mass 7.4 × 10–17 kg between the plates. If the droplet carries five electronic charges and if there were no air buoyancy, you could hold the droplet motionless between the plates if you kept the potential difference between them at A. 5.4 V B. 27 V C. 3.0 V D. 0.54 V E. 0.27 kV Ans: A Section: 17–3 Type: Numerical

31. Two parallel metal plates 5.0 cm apart have a potential difference between them of 75 V. The electric force on a positive charge of 3.2 × 10–19 C at a point midway between the plates is approximately A. 4.8 × 10–18 N B. 4.8 × 10–16 N C. 2.4 × 10–17 N D. 9.6 × 10–17 N E. 1.6 × 10–18 N


Ans: B Section: 17–3 Type: Numerical

32. Two parallel metal plates 0.35 cm apart have a potential difference between them of 175 V. The electric force on a positive charge of 6.4 × 10–19 C at a point midway between the plates is approximately A. 4.8 × 10–18 N B. 2.4 × 10–17 NC. 1.6 × 10–18 N D. 4.8 × 10–16 N E. 3.2 × 10–14 N Ans: E Section: 17–3 Type: Numerical

33. A uniform electric field exists between two parallel plates separated by 2.0 cm. The intensity of the field is 15 kN/C. What is the potential difference between the plates? A. 0.75 MV B. 30 kV C. 15 kV D. 0.30 kV E. 54 kV Ans: D Section: 17–3 Type: Numerical

34. A uniform electric field exists between two parallel plates separated by 1.2 cm. The intensity of the field is 23 kN/C. What is the potential difference between the plates? A. 7.5 MV B. 0.30 kV C. 3.0 MV D. 15 kVE. None of these is correct. Ans: E Section: 17–3 Type: Numerical


35.

The electrostatic potential as a function of distance along a certain line in space is shown in graph (1). Which of the curves in graph (2) is most likely to represent the electric field as a function of distance along the same line? A. 1 B. 2 C. 3 D. 4 E. 5 Ans: D Section: 17–3 Type: Conceptual

36.

Which of the points shown in the diagram are at the same potential? A. 2 and 5 B. 2, 3, and 5 C. 1 and 4 D. 1 and 5 E. 2 and 4 Ans: C Section: 17–3 Type: Conceptual


37.

Which point in the electric field in the diagram is at the highest potential? A. 1 B. 2 C. 3 D. 4 E. 5 Ans: E Section: 17–3 Type: Conceptual

38.

Which point in the electric field in the diagram is at the lowest potential? A. 1 B. 2 C. 3 D. 4 E. 5 Ans: C Section: 17–3 Type: Conceptual


39.

The figure shows two plates A and B. Plate A has a potential of 0 V and plate B a potential of 100 V. The dotted lines represent equipotential lines of 25, 50, and 75 V. A positive test charge of 1.6 × 10–19 C at point x is transferred to point z. The energy gained or expended by the test charge is A. 8 × 10–18 J, gained. B. 8 × 10–18 J, expended.C. 24 × 10–18 J, gained. D. 24 × 10–8 J, expended. E. 40 × 10–8 J, gained. Ans: B Section: 17–3 Type: Numerical

40.

Charges +Q and –Q are arranged at the corners of a square as shown. When the electric field E and the electric potential V are determined at P, the center of the square, we find that A. E ≠ 0 and V > 0 D. E ≠ 0 and V < 0 B. E = 0 and V = 0 E. None of these is correct. C. E = 0 and V > 0 Ans: B Section: 17–3 Type: Conceptual


41. An electric dipole that has a positive charge of 4.8 × 10–19 C is separated from a negative charge of the same magnitude by 6.4 × 10–10 m. The electric potential at a point 9.2 × 10–10 m from each of the two charges is A. 9.4 V B. zero C. 4.2 V D. 5.1 × 109 V E. 1.7 V Ans: B Section: 17–3 Type: Numerical

42. An electric dipole that has a positive charge of 4.80 × 10–19 C is separated from a negative charge of the same magnitude by 6.40 × 10–10 m. The magnitude of the electric field at the midpoint of the dipole is A. zero B. 27.0 N/C C. 4.22 × 1010 N/C D. 8.44 × 1010 N/C E. 12.3 × 1010 N/C Ans: D Section: 17–3 Type: Numerical

43.

ABC is a straight line with AB = BC = 0.60 nm. BP is perpendicular to ABC and BP = 0.80 nm. Charges of +3.2 × 10–19 C are placed at A and B. The magnitude of the electric field at P is A. 9.1 × 109 N/C D. 2.6 × 1010 N/C B. 6.8 × 109 N/C E. 3.3 × 1010 N/C C. 1.2 × 1010 N/C Ans: B Section: 17–3 Type: Numerical


44.

ABC is a straight line with AB = BC = 0.60 nm. BP is perpendicular to ABC and BP = 0.80 nm. Charges of +3.2 × 10–19 C are placed at A and B. The electric potential at P is approximately A. 2.9 V B. 3.6 V C. 6.5 V D. 9.3 V E. 1.5 V Ans: C Section: 17–3 Type: Numerical

45.

ABC is a straight line with AB = BC = 0.60 nm. BP is perpendicular to ABC and BP = 0.80 nm. Charges of +3.2 × 10–19 C are placed at A and C, and a charge of –3.2 × 10–19 C is placed at B. The electric potential at P is A. 2.2 V B. 9.4 V C. 29 V D. 0.43 nV E. 0.16 kV Ans: A Section: 17–3 Type: Numerical


46.

ABC is a straight line with AB = BC = 0.60 nm. BP is perpendicular to ABC and BP = 0.80 nm. Charges of +3.2 × 10–19 C are placed at A and C, and a charge of –3.2 × 10–19 C is placed at B. The magnitude of the electric field at P is approximately A.1.7 × 107 N/C B. 10 × 107 N/C C. 4.5 × 107 N/C D. 2.3 × 107 N/C E. zero Ans: B Section: 17–3 Type: Numerical

47.

Two equal positive charges are placed x m apart. The equipotential lines are at 100 V interval.The potential for line c is A. 100 VB. 100 VC. 200 VD. 200 VE. zeroAns: D Section: 17–3 Type: Numerical


48.

Two equal positive charges are placed x m apart. The equipotential lines are at 100 V interval.The work required to move a third charge, q = e, from the 100 V line to b is A. 100 eVB. 100 eVC. 200 eVD. 200 eVE. zeroAns: E Section: 17–3 Type: Numerical

49. The potential at a point due to a unit positive charge is found to be V. If the distance between the charge and the point is tripled, the potential becomes A. V/3 B. 3V C. V/9 D. 9V E. 1/V2 Ans: A Section: 17–3 Type: Conceptual

50. The electrical potential 2.5 cm from a point charge of Q1 = +4.5 × 10–9 C and 2.0 cm from a second charge Q2 is 3.2 kV. Find Q2. A. 2.7 × 10–9 C B. 4.4 × 10–9 C C. 1.1 × 10–8 C D. 3.5 × 10–9 C E. 5.5 × 10–9 C Ans: D Section: 17–3 Type: Numerical

51. The electrical potential 2.0 cm from a point charge of Q1 = +6.5 × 10–9 C and 3.5 cm from a second charge Q2 is 1.2 kV. Find Q2. A. –6.7 × 10–9 C B. –3.8 × 10–9 C C. –1.0 × 10–9 CD. 3.8 × 10–9 C E. 1.0 × 10–9 C Ans: A Section: 17–3 Type: Numerical


52. Two charges Q1 and Q2 are at rest a distance of 66 cm apart. How much work must be done to slowly move the charges to a separation of 33 cm? (Q1 = +6.6 × 10–9 C and Q2 = –3.3 × 10–9 C) A. –3.0 × 10–7 J B. 8.9 × 10–7 J C. –2.0 × 10–6 J D. –8.9 × 10–7 J E. 3.0 × 10–7 J Ans: A Section: 17–3 Type: Numerical

53. Two charges Q1 and Q2 are at rest a distance of 44 cm apart. How much work must be done to slowly move the charges to a separation of 33 cm? (Q1 = –4.2 × 10–9 C and Q2 = –2.2 × 10–9 C) A. –4.4 × 10–7 J B. –3.3 × 10–9 JC. 6.3 × 10–8 J D. –6.3 × 10–7 J E. 4.4 × 10–7 J Ans: C Section: 17–3 Type: Numerical

54. Two charges Q1 (= +6 C) and Q2 (= –2 C) are brought from infinity to positions on the x-axis of x = –4 cm and x = +4 cm, respectively. How much work was done in bringing the charges together? A. –1.80 × 106 J B. –9.00 × 105 J C. –16.9 J D. –1.35 J E. none of the above Ans: D Section: 17–3 Type: Numerical

55. Two charges Q1 (= +6 C) and Q2 (= –2 C) are brought from infinity to positions on the x-axis of x = –4 cm and x = +4 cm, respectively. Is it possible to bring a third charge Q3 (= +3 C) from infinity to a point on the x-axis between the charges where the potential is zero, and if so, where would this position be? A. it is not possibleB. x = 0 cm C. x = +2 cm D. x = +6 cm E. x = +1.5 cm Ans: C Section: 17–3 Type: Numerical


56. A proton (charge = e, mass = 1.67 × 10–27 kg) with initial kinetic energy 3 MeV is fired head-on towards a fixed stationary uranium nucleus (charge 92e, mass = 3.95 × 10–25 kg). Calculate how close to the uranium the proton gets before it comes to rest. (Assume the uranium nucleus does not move.) A. 2.75 × 105 m B. 4.40 × 10–8 mC. 4.40 × 10–14 m D. 2.10 × 10–7 m E. none of the above Ans: C Section: 17–3 Type: Numerical

57.

The figure depicts a uniform electric field. The direction in which there is no change in the electric potential is A. 1 B. 2 C. 3 D. 4 E. 5 Ans: C Section: 17–3 Type: Conceptual


58.

The figure depicts a uniform electric field. The direction in which the increase in the electric potential is a maximum is A. 1 B. 2 C. 3 D. 4 E. 5 Ans: E Section: 17–3 Type: Conceptual

Section 17 – 4. The electric potential has the same value everywhere on an equipotential surface

59. Which of the following statements regarding potential is true? A. The units of potential are N/C. B. Potential is a vector quantity. C. Equipotential surfaces are at right angles to lines of force. D. Potential differences can be measured directly with a ballistic galvanometer. E. Equipotential surfaces for an isolated point charge are cubes concentric with the charge. Ans: C Section: 17–4 Type: Conceptual

60. The potential on the surface of a solid conducting sphere of radius r = 20 cm is 100 V. The potential at r = 10 cm is A. 100 V B. 50 V C. 25 V D. zero E. cannot be determined Ans: A Section: 17–4 Type: Conceptual


61.

The figure shows portions of four equipotential surfaces whose potentials are related as follows: V1 > V2 > V3 > V4. The lines represent four paths (A → A', B → B', C → C', D → D') along which equal test charges are moved. The work involved can be said to be A. the greatest for path A → A'. B. the greatest for path B → B'. C. the greatest for path C → C'. D. the greatest for path D → D'. E. the same for all paths. Ans: E Section: 17–4 Type: Conceptual

62.

The vector that best represents the direction of the electric field intensity at point x on the 20-V equipotential line is A. 1 B. 2 C. 3 D. 4 E. None of these is correct. Ans: C Section: 17–4 Type: Conceptual


63.

The vector that best represents the direction of the electric field intensity at point x on the 200-V equipotential line is A. 1 B. 2 C. 3 D. 4 E. None of these is correct. Ans: D Section: 17–4 Type: Conceptual

64. The metal sphere at the top of a small Van de Graff generator has a radius of 10 cm. How much charge can be accumulated on this sphere before dielectric breakdown of the air around it occurs? (The dielectric strength of air is 3.0 MV/m.) A. 67 μC B. 33 μC C. 13 μC D. 6.7 μC E. 3.3 μC Ans: E Section: 17–4 Type: Numerical

65. The metal sphere at the top of a small Van de Graff generator has a radius of 8.0 cm. How much charge can be accumulated on this sphere before dielectric breakdown of the air around it occurs? (The dielectric strength of air is 3.0 MV/m.) A. 2.1 μC B. 3.3 μC C. 1.3 nC D. 6.7 μC E. 4.2 μC Ans: A Section: 17–4 Type: Numerical


66. The dielectric strength of the atmosphere is of the order of A. 1 V/m B. 102 V/m C. 104 V/m D. 106 V/m E. 108 V/m Ans: D Section: 17–4 Type: Factual

67.

Two charged metal spheres are connected by a wire. Sphere A is larger than sphere B, as shown. The magnitude of the electric potential of sphere A A. is greater than that at the surface of sphere B. B. is less than that at the surface of sphere B. C. is the same as that at the surface of sphere B. D. could be greater than or less than that at the surface of sphere B, depending on the radii of the spheres. E. could be greater than or less than that at the surface of sphere B, depending on the charges on the spheres. Ans: C Section: 17–4 Type: Conceptual

68. A solid spherical conductor of radius 15 cm has a charge Q = 6.5 nC on it. A second, initially uncharged, spherical conductor of radius 10 cm is moved toward the first until they touch and is then moved far away from it. How much charge is there on the second sphere after the two spheres have been separated? A. 2.6 nC B. 2.2 nC C. 3.2 nC D. 3.9 nC E. 4.3 nC Ans: A Section: 17–4 Type: Numerical

69. A solid spherical conductor of radius 20 cm has a charge Q = 25 nC on it. A second, initially uncharged, spherical conductor of radius 12 cm is moved toward the first until they touch and is then moved far away from it. How much charge is there on the second sphere after the two spheres have been separated? A. 15 nC B. 9.4 nC C. 25 nC D. 3.9 nC E. 2.1 nC Ans: B Section: 17–4 Type: Numerical


70. What is the approximate radius of an equipotential spherical surface of 30 V about a point charge of +15 nC if the potential at an infinite distance from the surface is zero? A. 1.0 m B. 2.1 m C. 3.0 m D. 4.5 m E. 6.8 m Ans: D Section: 17–4 Type: Numerical

71. What is the approximate radius of an equipotential spherical surface of 100 V about a point charge of +45 nC if the potential at an infinite distance from the surface is zero? A. 1.0 m B. 2.1 m C. 3.0 m D. 4.5 m E. 4.0 m Ans: E Section: 17–4 Type: Numerical

72. When a small, positively charged metal ball comes in contact with the interior of a positively charged metal shell, A. the charge on the ball becomes negative. B. the amount of positive charge on the ball increases. C. the positive charge on the shell decreases. D. the charge on the shell and the ball reach the same value. E. the ball loses all of its excess charge. Ans: E Section: 17–4 Type: Conceptual

73. A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius rb1 and outer radius rb2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The potential for rb1 < r < rb2 is

A.

€

kQra

B.

€

kQrb1

C.

€

kQrb2

D.

€

kQr

E. zeroAns: C Section: 17–4 Type: Conceptual


74. A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius rb1 and outer radius rb2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The potential for r < ra is

A.

B.

C.

D.

€

kQr

E. zeroAns: A Section: 17–4 Type: Conceptual

75.

A metal ball of charge +Q is lowered into an insulated, uncharged metal shell and allowed to rest on the bottom of the shell. When the charges reach equilibrium, A. the outside of the shell has a charge of –Q and the ball has a charge of +Q. B. the outside of the shell has a charge of +Q and the ball has a charge of +Q. C. the outside of the shell has a charge of zero and the ball has a charge of +Q. D. the outside of the shell has a charge of +Q and the ball has zero charge. E. the outside of the shell has a charge of +Q and the ball has a charge of –Q. Ans: D Section: 17–4 Type: Conceptual

76.


A charged metal ball is lowered into an insulated metal can and permitted to touch the inside of the can. If the ball is withdrawn and hung on a stand, an uncharged ball will be attracted to A. the outside of the can. B. the inside of the can. C. the outside and the inside of the can. D. the metal ball and the inside of the can. E. the metal ball, the inside of the can, and the outside of the can. Ans: A Section: 17–4 Type: Conceptual

77.

We give the same charge to a metal sphere of radius R and a metal cone of radius R and height 2R. The shaded regions in the figure are of equal area. Which region has the greatest surface charge density? A. 1 B. 2 C. 3 D. 4 E. all have equal charge densities Ans: D Section: 17–4 Type: Conceptual


78. An electric charge q is placed on an isolated metal sphere of radius r1. If an uncharged sphere of radius r2 (with r2 > r1) is then connected to the first sphere, the spheres will have equal A. and like charges on their surfaces. B. electric fields. C. potentials. D. capacitances. E. but opposite charges on their surfaces. Ans: C Section: 17–4 Type: Conceptual

79. Dielectric breakdown occurs in the air at an electric field strength of Emax = 3.0 × 106 V/m. If the maximum charge that can be placed on a spherical conductor is 2.0 × 10–3 C before breakdown, calculate the diameter of the sphere. A. 6.0 m B. 4.9 m C. 1.2 m D. 2.5 m E. 3.0 m Ans: B Section: 17–4 Type: Numerical

80. Dielectric breakdown occurs in the air at an electric field strength of Emax = 3.0 × 106 V/m. What is the maximum surface charge density that can be placed on a spherical conductor of radius 1.5 m before breakdown? A. 2.7 × 10–5 C/m2 B. 1.2 × 10–5 C/m2 C. 8.1 × 10–5 C/m2

D. 8.6 × 10–6 C/m2 E. 1.8 × 10–5 C/m2 Ans: A Section: 17–4 Type: Numerical

81. Dielectric breakdown occurs in the air at an electric field strength of Emax = 3.0 × 106 V/m. If the maximum potential at the surface of a spherical conductor is 5.0 × 106 V, then calculate the radius of the sphere. A. 0.60 m B. 1.3 m C. 1.7 m D. 0.77 m E. 15 m Ans: C Section: 17–4 Type: Numerical

Section 17 – 5. A capacitor stores equal amounts of positive and negative charge

82.


Two flat parallel plates are d = 0.40 cm apart. The potential difference between the plates is 360 V. The electric field at the point P at the center is approximately A. 90 kN/C B. 3.6 kN/C C. 0.9 kN/C D. zero E. 3.6 × 105 N/C Ans: A Section: 17–5 Type: Numerical

83. Two large metallic plates are parallel to each other and charged. The distance between the plates is d. The potential difference between the plates is V. The magnitude of the electric field in the region between the plates and away from the edges is given by A. d/V B. V2/d C. dV D. V/d2 E. None of these is correct. Ans: E Section: 17–5 Type: Conceptual

84. A capacitor of capacitance C holds a charge Q when the potential difference across the plates is V. If the charge Q on the plates is doubled to 2Q, A. the capacitance becomes (1/2)V. B. the capacitance becomes 2C. C. the potential changes to (1/2)V. D. the potential changes to 2V. E. the potential does not change. Ans: D Section: 17–5 Type: Numerical

85. If a capacitor of capacitance 2.0 μF is given a charge of 1.0 mC, the potential difference across the capacitor is A. 0.50 kV B. 2.0 V C. 2.0 μV D. 0.50 V E. None of these is correct. Ans: A Section: 17–5 Type: Numerical

86. If the area of the plates of a parallel-plate capacitor is doubled, the capacitance is


A. not changed. B. doubled. C. halved. D. increased by a factor of 4. E. decreased by a factor of 1/4. Ans: B Section: 17–5 Type: Conceptual

87. An 80-nF capacitor is charged to a potential of 500 V. How much charge accumulates on each plate of the capacitor? A. 4.0 × 10–4 C B. 4.0 × 10–5 C C. 4.0 × 10–10 C D. 1.6 × 10–10 C E. 1.6 × 10–7 C Ans: B Section: 17–5 Type: Numerical

88. You want to store 1010 excess electrons on the negative plate of a capacitor at 9.0 V. How large a capacitance must you use? A. 0.014 μF B. 0.18 μF C. 0.18 nF D. 14 pF E. 5.6 pF Ans: C Section: 17–5 Type: Numerical

89. A parallel-plate capacitor has square plates of side 8.0 cm separated by 0.80 mm. If you charge this capacitor to 15-V, the amount of charge transferred from one plate to the other is A. 71 nC B. 7.1 nC C. 1.1 pC D. 1.1 nC E. 7.1 pC Ans: D Section: 17–5 Type: Numerical

90. A coaxial cable consists of a wire of radius 0.30 mm and an outer conducting shell of radius 1.0 mm. Its capacitance per unit length is approximately A. 17 nF/m B. 0.11 nF/m C. 92 pF/m D. 23 pF/m E. 46 pF/m Ans: E Section: 17–5 Type: Numerical

91. A coaxial cable consists of a wire of radius 0.30 mm and an outer conducting shell of radius


1.0 mm. Its capacitance for a 2 m length of the cable is approximately A. 0.22 nF B. 34 nF C. 46 pF D. 92 pF E. 184 pF Ans: D Section: 17–5 Type: Numerical

92.

In which of these configurations is (are) the electric field(s) uniform? A. 1 B. 2 C. 3 D. 1 and 3 E. 1, 2, and 3 Ans: A Section: 17–5 Type: Conceptual

93.

As the voltage in the circuit is increased (but not to the breakdown voltage), the capacitance A. increases. B. decreases. C. does not change. D. increases, decreases, or does not change, depending on the charge on the plates of the capacitor. E. does none of these. Ans: C Section: 17–5 Type: Conceptual

94. Doubling the potential difference across a capacitor


A. doubles its capacitance. B. halves its capacitance. C. quadruples the charge stored on the capacitor. D. doubles the charge stored on the capacitor. E. produces none of the above results. Ans: D Section: 17–5 Type: Conceptual

95. Doubling the potential difference across a capacitor A. doubles its capacitance. B. halves its capacitance. C. quadruples the charge stored on the capacitor. D. halves the charge stored on the capacitor. E. does not change the capacitance of the capacitor. Ans: E Section: 17–5 Type: Conceptual

96. If the area of the plates of a parallel plate capacitor is halved and the separation between the plates tripled, then by what factor does the capacitance change? A. increase by a factor of 6 B. decrease by a factor of 2/3C. decrease by a factor of 1/6 D. increase by a factor of 3/2 E. decrease by a factor of 1/2 Ans: C Section: 17–5 Type: Conceptual

97. You make a homemade capacitor out of two flat circular metal plates, each of radius 5 cm, and hold them a distance of 1 cm apart. You then connect each plate to the terminals of a 6-V battery. What would be the capacitance of your capacitor? A. 7.0 × 10–12 F B. 2.2 × 10–11 F C. 2.2 × 10–12 F D. 2.2 × 10–10 F E. 7.0 × 10–10 F Ans: A Section: 17–5 Type: Numerical

Section 17 – 6. A capacitor is a storehouse of electric potential energy

98. Which of the following statements is false? A. In the process of charging a capacitor, an electric field is produced between its plates. B. The work required to charge a capacitor can be thought of as the work required to create the electric field between its plates. C. The energy density in the space between the plates of a capacitor is directly proportional to the first power of the electric field. D. The potential difference between the plates of a capacitor is directly proportional to the electric field. E. All of these are false. Ans: C Section: 17–6 Type: Factual


99. Which of the following statements about parallel plate capacitor is false?A. The two plates have equal charges.B. The capacitor store charges on the plates.C. The capacitance is proportional to the area.D. The capacitance is inversely proportional to the separation between the plates.E. A charged capacitor stores energy.Ans: A Section: 17–6 Type: Factual

100. If you increase the charge on a parallel-plate capacitor from 3 μC to 9 μC and increase the plate separation from 1 mm to 3 mm, the energy stored in the capacitor changes by a factor of A. 27 B. 9 C. 3 D. 8 E. 1/3 Ans: A Section: 17–6 Type: Numerical

101. If you decrease the charge on a parallel-plate capacitor from 12 μC to 4 μC and increase the plate separation from 1 mm to 3 mm, the energy stored in the capacitor changes by a factor of A. 27 B. 1/3 C. 3 D. 8 E. 1/4 Ans: B Section: 17–6 Type: Numerical

102. A 2.0-μF capacitor has a potential difference of 5000 V. The work done in charging it was A. 2.5 J B. 5.0 J C. 25 J D. 5.0 mJ E. 0.50 kJ Ans: C Section: 17–6 Type: Numerical

103. You attach a 30-pF capacitor across a 1.5-V battery. How much energy is stored in the capacitor? A. 3.4 × 10–11 JB. 4.5 × 10–11 JC. 6.7 × 10–11 J D. 3.4 × 10–8 J E. 4.5 × 10–8 J Ans: A Section: 17–6 Type: Numerical

104. You charge a 4.0-μF capacitor to 150 V. How much additional energy must you add to


charge it to 300 V? A. 0.60 mJ B. 0.14 J C. 18 μJ D. 0.30 mJ E. 0.28 J Ans: B Section: 17–6 Type: Numerical

105. If the potential difference of a capacitor is reduced by one-half, the energy stored in that capacitor is A. reduced to one-half. B. reduced to one-quarter.C. increased by a factor of 2.D. increased by a factor of 4. E. not changed. Ans: B Section: 17–6 Type: Conceptual

106. The energy stored in a capacitor is directly proportional to A. the voltage across the capacitor. B. the charge on the capacitor. C. the reciprocal of the charge on the capacitor. D. the square of the voltage across the capacitor. E. None of these is correct. Ans: D Section: 17–6 Type: Conceptual

107. If the area of the plates of a parallel plate capacitor is halved and the separation between the plates tripled, while the charge on the capacitor remains constant, then by what factor does the energy stored in the capacitor change? A. increase by a factor of 2 B. decrease by a factor of 2/3 C. increase by a factor of 6 D. increase by a factor of 3/2 E. decrease by a factor of 1/6 Ans: C Section: 17–6 Type: Numerical

108. A cardiac defibrillator can be used to help an erratic heartbeat in a regular fashion. A defibrillator contains a capacitor charged to a voltage of 6000 V with an energy storage of 200 J. Calculate the capacitance of the capacitor. A. 6.67 × 10–2 F B. 1.11 × 10–5 F C. 5.56 × 10–6 F D. 2.22 × 10–5 F E. 13.3 F Ans: B Section: 17–6 Type: Numerical

109. If 20 capacitors, each of 100 μF, were connected in parallel across a 12-V battery, what


would be the total energy stored in the capacitors? A. 2.9 × 10–1 J B. 7.2 × 10–3 J C. 1.2 × 10–2 J D. 1.4 × 10–1 J E. 3.6 × 10–4 J Ans: D Section: 17–6 Type: Numerical

110. A parallel plate capacitor is constructed using two square metal sheets, each of side L = 10 cm. The plates are separated by a distance d = 2 mm and a voltage applied between the plates. The electric field strength within the plates is E = 4000 V/m. The energy stored in the capacitor isA. 0.71 nJ B. 1.42 nJ C. 2.83 nJ D. 3.67 nJ E. zeroAns: B Section: 17–6 Type: Numerical

Section 17 – 7. Capacitors can be combined in series or in parallel

111. You connect three capacitors as shown in the diagram below.

If the potential difference between A and B is 24.5-V, what is the total energy stored in this system of capacitors if C1 = 5.0 μF, C2 = 4.0 μF, and C3 = 3.0 μF? A. 1.7 × 10–4 JB. 1.5 × 10–4 JC. 2.2 × 10–5 J D. 6.8 × 10–4 J E. 4.0 × 10–4 J Ans: D Section: 17–7 Type: Numerical

112. You connect three capacitors as shown in the diagram below.


The effective capacitance of this combination when C1 = 5.0 μF, C2 = 4.0 μF, and C3 = 3.0 μF is approximately A. 0.44 μF B. 2.3 μF C. 3.5 μF D. 5.2 μF E. 12 μF Ans: B Section: 17–7 Type: Numerical

113. You connect three capacitors as shown in the diagram.

C1 = 5.0 μF, C2 = 4.0 μF, and C3 = 3.0 μF. If you apply 12-V between points A and B, the energy stored in C3 will be approximately A. 0.16 mJ B. 41 μJ C. 0.12 mJ D. 0.41 mJ E. 16 mF Ans: C Section: 17–7 Type: Numerical



C1 = C3 = 2.5 μF, and C2 = 5.0 μF. A potential difference of 9.0 V is maintained between the terminals A and B. The magnitude of the charge on capacitor C3 is approximately A. 4.2 μC B. 4.8 μC C. 17 μC D. 37 μC E. 90 μC Ans: C Section: 17–7 Type: Numerical


C1 = C3 = 2.5 μF, and C2 = 5.0 μF. A potential difference of 9.0 V is maintained between the terminals A and B. The voltage across on capacitor C3 is approximately A. 1.2 V B. 7.9 V C. 3.2 V D. 5.4 V E. 6.8 V Ans: E Section: 17–7 Type: Numerical

116. The charge on each capacitor in a set of capacitors in parallel is A. directly proportional to its capacitance. B. inversely proportional to its capacitance. C. independent of its capacitance. D. the same. E. None of these is correct. Ans: A Section: 17–7 Type: Conceptual


117. The voltage across each capacitor in a set of capacitors in parallel is A. directly proportional to its capacitance. B. inversely proportional to its capacitance. C. independent of its capacitance. D. the same. E. None of these is correct. Ans: D Section: 17–7 Type: Conceptual

118. The charge on each capacitor in a set of capacitors in series is A. directly proportional to its capacitance. B. inversely proportional to its capacitance. C. independent of its capacitance. D. the same. E. None of these is correct. Ans: D Section: 17–7 Type: Conceptual

119. The voltage across each capacitor in a set of capacitors in series is A. directly proportional to its capacitance. B. inversely proportional to its capacitance. C. independent of its capacitance. D. the same. E. None of these is correct. Ans: B Section: 17–7 Type: Conceptual

120. You connect two capacitors C1 = 15 pF and C2 = 30 pF in series across a 1.5-V battery. The potential difference across capacitor C1 is approximately A. 0.50 V B. 1.0 V C. 1.5 V D. 0.33 V E. 0.67 V Ans: B Section: 17–7 Type: Numerical

121.

If C1 < C2 < C3 < C4 for the combination of capacitors shown, the equivalent capacitance A. is less than C1. B. is more than C4. C. is between C2 and C3. D. is less than C2. E. could be any value depending on the applied voltage. Ans: B Section: 17–7 Type: Conceptual


122.

If C1 < C2 < C3 < C4 for the combination of capacitors shown, the equivalent capacitance A. is less than C1. B. is more than C4. C. is between C2 and C3. D. is more than C2. E. could be any value depending on the applied voltage. Ans: A Section: 17–7 Type: Conceptual

123. A 1.0-μF capacitor and a 2.0-μF capacitor are connected in series across a 1200-V source. The charge on each capacitor is A. 0.40 mC B. 0.80 mC C. 1.2 mC D. 1.8 mC E. 3.6 mC Ans: B Section: 17–7 Type: Numerical

124. You connect two 12-μF capacitors and a 6-μF capacitor in parallel. The equivalent capacitance of the combination is A. 18 μF B. 4 μF C. 3 μF D. 30 μF E. None of these is correct. Ans: D Section: 17–7 Type: Numerical

125. The equivalent capacitance of three capacitors in series is A. the sum of their capacitances. B. the sum of the reciprocals of their capacitances. C. always greater than the larger of their capacitances. D. always less than the smaller of the capacitances. E. described by none of the above. Ans: D Section: 17–7 Type: Conceptual

126.


You want to use three capacitors in a circuit. If each capacitor has a capacitance of 3 pF, the configuration that gives you an equivalent capacitance of 2 pF between points x and y is A. 1 B. 2 C. 3 D. 4 E. None of these is correct. Ans: D Section: 17–7 Type: Numerical

127. The equivalent capacitance of two capacitors in series is A. the sum of their capacitances. B. the sum of the reciprocals of their capacitances. C. always greater than the larger of their capacitances. D. always less than the smaller of the capacitances. E. described by none of the above. Ans: D Section: 17–7 Type: Conceptual

128. The equivalent capacitance of two capacitors in parallel is A. the sum of the reciprocals of their capacitances. B. the reciprocal of the sum of the reciprocals of their capacitances. C. always greater than the larger of their capacitances. D. always less than the smaller of the two capacitances. E. described by none of the above. Ans: C Section: 17–7 Type: Conceptual

129. The equivalent capacitance of three capacitors in parallel is


A. the sum of the reciprocals of their capacitances. B. the reciprocal of the sum of the reciprocals of their capacitances. C. always greater than the larger of their capacitances. D. always less than the smaller of the two capacitances. E. described by none of the above. Ans: C Section: 17–7 Type: Conceptual

130. Three capacitors 2 μF, 4 μF and 8 μF are connected in parallel across a 120-V source. The charge on the 4 μF capacitor is A. 2.4 × 10–4 C B. 9.6 × 10–4 C C. 2.1 × 103 C D. 1.7 × 10–3 C E. 4.8 × 10–4 CAns: E Section: 17–7 Type: Numerical

131.

If all the four capacitors have equal values of 50 μF then calculate the equivalent capacitance of the circuit shown above. A. 50 μF B. 30 μF C. 75 μF D. 100 μF E. 83 μF Ans: B Section: 17–7 Type: Numerical

132. A capacitor, C1 = 5.0 μF, is charged up to 8 V. It is then connected to a second uncharged capacitor C2 = 2.5 μF. The voltage across the capacitor C1 after the system has come to equilibrium is A. 2.67 V B. 4.0 V C. 5.33 V D. 8.0 V E. 12.0 V Ans: C Section: 17–7 Type: Numerical

133. A capacitor, C1 = 5.0 μF, is charged up to 8 V. It is then connected to a second uncharged


capacitor C2 = 2.5 μF. The charge on C1 after the system has come to equilibrium is A. 26.7 C B. 13.3 C C. 20.0 C D. 40.0 C E. 6.67 C Ans: A Section: 17–7 Type: Numerical

134. A capacitor, C1 = 5.0 μF, is charged up to 8 V. It is then connected to a second uncharged capacitor C2 = 2.5 μF. The charge on C2 after the system has come to equilibrium is A. 26.7 μC B. 13.3 μC C. 20.0 μC D. 40.0 μC E. 6.67 μC Ans: B Section: 17–7 Type: Numerical

Section 17 – 8. Placing a dielectric between the plates of a capacitor increases the capacitance

135. A capacitor is made with two strips of metal foil, each 2.5 cm wide by 50 cm long, with a 0.70-μm thick strip of paper (κ = 3.7) sandwiched between them. The capacitor is rolled up to save space. What is the capacitance of this device? (The permittivity of free space 0 = 8.85 × 10–12 F/m.) A. 43 nF B. 0.16 F C. 0.58 F D. 2.0 F E. 7.3 F Ans: C Section: 17–8 Type: Numerical

136. The capacitance of a parallel-plate capacitor A. is defined as the amount of work required to move a charge from one plate to the other. B. decreases if a dielectric is placed between its plates. C. is independent of the distance between the plates. D. has units of J/C. E. is independent of the charge on the capacitor. Ans: E Section: 17–8 Type: Conceptual

137. When you insert a piece of paper (κ = 3.7) into the air between the plates of a capacitor, the capacitance A. increases. B. decreases. C. does not change. D. could increase, decrease, or not change depending on the dielectric constant of the paper. E. does none of these. Ans: A Section: 17–8 Type: Factual138.


A capacitor is connected to a battery as shown. When a dielectric is inserted between the plates of the capacitor, A. only the capacitance changes. B. only the voltage across the capacitor changes. C. only the charge on the capacitor changes. D. both the capacitance and the voltage change. E. both the capacitance and the charge change. Ans: E Section: 17–8 Type: Conceptual

139. The capacitance of a parallel-plate capacitor is 24 μF when the plates are separated by a material of dielectric constant 2.0. If this material is removed, leaving air between the plates, and the separation between the plates is tripled, the capacitance is A. unchanged B. 16 μF C. 36 μF D. 0.14 mF E. 4.0 μF Ans: E Section: 17–8 Type: Numerical

140.

Two identical capacitors A and B are connected across a battery, as shown. If mica (κ = 5.4) is inserted in B, A. both capacitors will retain the same charge. B. B will have the larger charge. C. A will have the larger charge. D. the potential difference across B will increase. E. the potential difference across A will increase. Ans: B Section: 17–8 Type: Conceptual

141. If a dielectric is inserted between the plates of a parallel-plate capacitor that is connected to


a 100-V battery, the A. voltage across the capacitor decreases. B. electric field between the plates decreases. C. electric field between the plates increases. D. charge on the capacitor plates decreases. E. charge on the capacitor plates increases. Ans: E Section: 17–8 Type: Conceptual

142. A parallel-plate capacitor has square plates of side 12 cm and a separation of 6.0 mm. A dielectric slab of constant κ = 2.0 has the same area as the plates but has a thickness of 3.0 mm. What is the capacitance of this capacitor with the dielectric slab between its plates? A. 28 рF B. 21 pF C. 16 pF D. 37 pF E. 53 pF Ans: A Section: 17–8 Type: Numerical

143.

A charged capacitor has an initial electric field E0 and potential difference V0 across its plates. Without connecting any source of emf, you insert a dielectric (κ > 1) slab between the plates to produce an electric field Ed and a potential difference Vd across the capacitor. The pair of statements that best represents the relationships between the electric fields and potential differences is A. Ed > E0; Vd > V0 B. Ed = E0; Vd > V0 C. Ed > E0; Vd = V0 D. Ed < E0; Vd > V0

E. Ed < E0; Vd < V0

Ans: E Section: 17–8 Type: Conceptual

144. A parallel plate capacitor of area A = 30 cm2 and separation d = 5 mm is charged by a


battery of 60-V. If the air between the plates is replaced by a dielectric of κ = 4 with the battery still connected, then what is the ratio of the initial charge on the plates divided by the final charge on the plates? A. 4.3 B. 1 C. 16 D. 0.25 E. 4.0 Ans: D Section: 17–8 Type: Numerical

145. A parallel plate capacitor has a plate spacing of 1.5 mm, which is filled with a dielectric of κ = 4.3, and its capacitance is 80 μF. If the dielectric is taken out and the plate spacing doubled, then what is the new capacitance? A. 690 μF B. 37 μF C. 9.3 μF D. 170 μF E. 19 μF Ans: C Section: 17–8 Type: Numerical

146. Two parallel plate air capacitors, each of capacitance X F are in series with a battery of 12-V. If a dielectric with κ = 3 is inserted between the plates of one of the capacitors, then calculate the change in electrical charge (in Coulombs) that occurs on one of its plates. A. 9X B. 3X/4 C. 3X D. 16X E. none of the above Ans: C Section: 17–8 Type: Numerical

147. An electric field, E, is applied to a dielectric. Which of the following statements is true?A. The electric field within the dielectric is less than E.B. The dielectric produces an electric field in the opposite direction to E.C. The molecules in the dielectric become polarized.D. The electric field will produce a torque on molecules in dielectrics, which have permanent dipoles.E. All the above statements are true.Ans: E Section: 17–8 Type: Factual


college physics test bank chapter 17

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