(Test Bank) College Physics Reasoning and Relationships (Volume 2)

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Chapter 17: Electric Forces and Fields MULTIPLE CHOICE 17.1 Evidence for Electric Forces: The Observational Facts 1. Doug rubs a piece of fur on a hard rubber rod, giving the rod a negative charge. What happens? a. Protons are removed from the rod. c. Electrons are added to the rod. b. The fur is left neutral. d. The fur is also charged negatively. ANS: C PTS: 1 DIF: 1 2. A repelling force must occur between two charged objects under which conditions? a. Charges are of equal magnitude. c. Charges are of unequal magnitude. b. Charges are of unlike signs. d. Charges are of like signs. ANS: D PTS: 1 DIF: 1 3. A metallic object holds a charge of −2.9  10−5 C. What total number of electrons does this represent? (e = 1.6  10−19 C is the magnitude of the electronic charge.) a. 1.8  1014 c. 6.1  1013 b. 2.4  1013 d. 4.2  1014 ANS: A PTS: 1 DIF: 2 4. About how many electrons are in 0.3 gram of water (H 2O)? a. 1023 c. 1025 b. 1021 d. 1019 ANS: A PTS: 1 DIF: 3 5. The charge per unit len gth on an insulator is . On a 2.0 -m length of this material, what is the difference in the number of electrons and the number of protons? a. There are more electrons than protons. b. There are more protons than electrons. c. There are more protons than electrons. d. There are more electrons than protons. ANS: B PTS: 1 DIF: 2 17.2 Electric Forces and Coulomb’s Law 6. Object A has a charge q on it, object B has a charge q on it, and object C has a charge 2 q on it. These charges are arranged, one each, at the vertices of an equilateral triangle. Which charge has the greatest magnitude electric force on it? a. A b. C c. B d. All have equal magnitude forces on them. ANS: B PTS: 1 DIF: 2 7. Two point charges are 4 cm apart. They are moved to a new separation of 8 cm. By what factor does the resulting mutual force between them change? a. 1/4 c. 1/2 b. 2 d. 4 ANS: A PTS: 1 DIF: 1 8. If the distance between two point charges is quadrupled, the mutual force between them will be changed b y what factor? a. 8 c. 1/16 b. 4 d. 1/4 ANS: C PTS: 1 DIF: 1 9. If the size of the charge value is tripled for one of two point charges maintained at a constant separation, the mutual force between them will be changed by what factor? a. 3.0 c. 9.0 b. 1/9 d. 0.33 ANS: A PTS: 1 DIF: 1 10. The constant ke, which appears in Coulomb’s law formula, is equivalent dimensionally to which of the following? a. N/C c. N/C2 b. Nm2/C2 d. Nm/C ANS: B PTS: 1 DIF: 1 11. Two point charges, separated by 15 cm, have charge values of +2.0 µC and −4.0 µC, respectively. What is the value of the mutual force between them? ( ke = 8.99  109 Nm2/C2) a. 8.0  10−12 N c. 320 N b. 3.6  10−8 N d. 3.2 N ANS: D PTS: 1 DIF: 2 12. Four charges are at the corners of a square, with B and C on opposite corners. Charges A and D, on the other two corners, have equal charge, while both B and C have a charge of +1.0 C. What is the charge on A s o that the force on B is zero? a. −0.50 C c. −1.0 C b. −0.71 C d. −0.35 C ANS: D PTS: 1 DIF: 3 13. Charge A and charge B are 3.00 m apart, and charge A is +2.00 C and charge B is +3.00 C. Charge C is located between them at a certain point and the force on charge C is zero. How far from charge B is charge C? a. 1.35 m c. 1.65 m b. 0.667 m d. 0.555 m ANS: C PTS: 1 DIF: 3 14. In a thundercloud there may be an electric charge of +40 C near the top of the cloud and −40 C near the bottom of the clo ud. These charges are separated by about 2.0 km. What is the electric force between these two sets of charges? ( ke = 8.99  109 N·m2/C2) a. 3.6  106 N c. 3.6  107 N b. 3.6  104 N d. 3.6  105 N ANS: A PTS: 1 DIF: 2 15. An electron is sent at high speed toward a gold nucleus (charge +79 e). What is the electrical force acting on the electron when it is 3.0  10−13 m away from the gold nucleus? ( e = 1.6  10−19 C, ke = 8.99  109 N·m2/C2) a. 2.1  10−6 N c. 0.20 N b. 2.0  10−4 N d. 20 N ANS: C PTS: 1 DIF: 2 16. Two electrons are separated by one cm. What is the ratio of the electric force to the gravitational force between them? ( me = 9.11  10−31 kg, ke = 8.99  109 Nm2/C2, G = 6.67  10-11 Nm2/kg2, and e = 1.6  10−19 C) a. 1.3  1020 c. 2.3  102 b. 4.2  1042 d. 3.1  1022 ANS: B PTS: 1 DIF: 2 17. Two equal charges, each Q, are separated by some distance. What third charge would need to be placed half way between the two charges so that the net force on each charge would be zero? a. −Q/8 c. −Q/4 b. −Q d. −Q/2 ANS: C PTS: 1 DIF: 2 18. A 6.0 -mC charge is placed at the origin and a second charge is placed on the x axis at x = 0.30 m. If the resulting force on the second charge is 5.4 N in the positive x direction, what is the val ue of its charge? a. 9.0 nC c. 9.0 C b. –9.0 nC d. –9.0 C ANS: A PTS: 1 DIF: 2 19. A 6.00 -C charge is placed at the origin and a second charge is placed on the x axis at x = 0.300 m. If the resulting force on the second charge is 6.40 N in the neg ative x direction, what is the force on the charge at the origin? a. 6.40 N in the negative x direction b. 0 N c. 6.40 N in the positive x direction d. not able to be determined until the second charge is known ANS: C PTS: 1 DIF: 2 20. Two identica l spheres each carry a charge of −40.0 µC. The spheres are separated by a distance of 2.00 m. What is the electric force between the spheres? ( ke = 8.99  109 N·m2/C2) a. 43.2 N (attractive) c. 3.60 N (repulsive) b. 14.4 N (repulsive) d. 7.19 N (attractive) ANS: C PTS: 1 DIF: 2 21. Two identical iron spheres have equal positive charges and the force between them when they are 1 m apart is 4 N. What percentage of the electrons has been removed from each sphere if each sphere has 1 mole (6  1023) of iron atoms? ( ke = 8.99  109 Nm2/C2, the atomic number of iron is 26, and the electron charge is −1.6  10−19 C) a. 8  10−10 % c. 0.001% b. 0.000002% d. 4  10−10 % ANS: A PTS: 1 DIF: 3 22. Two identical balls have the same amount of charge, but the charge on ball A is positive and the charge on ball B is negative. The balls are placed on a smooth, level, frictionless table whose top is an insulator. Which of the following is true? a. They will move together with constant acceleration. b. Since the force on A is equal but opposite t o the force on B, they will not move. c. Since the force on both balls is negative, they will move in the negative direction. d. None of the above is correct. ANS: D PTS: 1 DIF: 2 23. If two 1.0 -C charges have a force between them of 1.0 N, what is their separation? a. c. b. 1.0 m d. ANS: C PTS: 1 DIF: 2 24. Two point charges, one and the other , form a dipole separated by a distance 2 L. A third charge Q is placed midway between these two charges. If the only charge that is negative is , what is the force on Q? a. toward the c. toward the b. toward the q d. toward the q ANS: C PTS: 1 DIF: 2 25. Two point charges, one and the other , form a dipole separated by a distance d. A third charge Q is placed midway between these two charges.If the distance between the q and the is then doubled with the Q staying midway between the other two, what happens to the force on Q? a. It halves. c. It stays the same. b. It reduces by a factor of 8. d. It quarters. ANS: D PTS: 1 DIF: 2 17.3 The Electric Field 26. Three equal positive charges are placed on the x-axis, one at the origin, one at x = 2 m, and the third at x = 4 m. Of the following points, which has the greatest magnitude electric field? a. x = 1 m b. x = 3 m c. x = 5 m d. The electric field has the same magnitude at all three positions. ANS: C PTS: 1 DIF: 2 27. Charges q, q, and –q are placed on the x axis at x = 0, x = 2 m, and x = 4 m, respectively. At which of the following points does the electric field have the greatest magnitude? a. x = 3 m b. x = 1 m c. x = 5 m d. The electric field has the same magnitude at all three positions. ANS: A PTS: 1 DIF: 3 28. The beam of electrons that hits the screen of an oscilloscope is moved up and down by: a. varying the electron’s charge. b. electrical charges on deflecting plates above and below the beam. c. gravity. d. a phosphorescent coating. ANS: B PTS: 1 DIF: 1 29. Two point charges each have a value of 30.0 mC and are separated by a distance of 3 .00 cm. What is the electric field midway between the two charges? ( ke = 8.99  109 N·m2/C2) a. 40.5  107 N/C c. zero b. 20.3  107 N/C d. 10.1  107 N/C ANS: C PTS: 1 DIF: 2 30. Two point charges are separated by 10.0 cm and have charges of +1.00 µC and −1.00 µC, respectively. What is the electric field at a point midway bet ween the two charges? ( ke = 8.99  109 N·m2/C2) a. 14.4  106 N/C c. 28.8  106 N/C b. zero d. 7.19  106 N/C ANS: D PTS: 1 DIF: 2 31. Electric field is dimensionally equivalent to which of the following? a. N/C2 c. Nm2/C2 b. Nm/C d. N/C ANS: D PTS: 1 DIF: 1 32. An electron with a charge value of 1.6  10−19 C is moving in the presence of an electric field of 300 N/C. What force does the electron experience? a. 2.3  10−22 N c. 6.4  10−17 N b. 4.8  10−17 N d. 1.9  10−21 N ANS: B PTS: 1 DIF: 2 33. Charges of 4.0 µC and −6.0 µC are placed at two corners of an equilateral triangle with sides of 0.20 m. At the third corner, what is the electric field magnitude created by these two charges? ( ke = 8.99  109 N·m2/C2) a. 3.1  106 N/C c. 4.8  106 N/C b. 1.2  106 N/C d. 4.5  106 N/C ANS: B PTS: 1 DIF: 3 34. The average distance of the electron from the proton in the hydrogen atom is 0.51  10−10 m. What is the electric field from the proton’s charge at the location of the electron? ( ke = 8.99  109 Nm2/C2, e = 1.6  10−19 C) a. 8.8  10−8 N/C c. 3.2  102 N/C b. 1.0  106 N/C d. 5.5  1011 N/C ANS: D PTS: 1 DIF: 2 35. Two point charges are placed along a horizontal axis with the following values and positions: +3.0 µC at x = 0 c m and −6.0 µC at x = 20 cm. At what point along the x axis is the electric field zero? a. 8.0 cm c. −38 cm b. −48 cm d. −69 cm ANS: B PTS: 1 DIF: 3 36. A proton initially moves left to right long the x axis at a speed of 2.00  104 m/s. It moves int o an electric field, which points in the negative x direction, and travels a distance of 0.200 m before coming to rest. What acceleration magnitude does the proton experience? a. 2.67  1012 m/s2 c. 6.67  106 m/s2 b. 9.33  109 m/s2 d. 1.00  109 m/s2 ANS: D PTS: 1 DIF: 2 37. A proton initially moves left to right long the x axis at a speed of 2.00  103 m/s. It moves into an electric field, which points in the negative x direction, and travels a distance of 0.300 m before coming to rest. If the prot on's mass and charge are 1.67  10−27 kg and 1.60  10−19 C, respectively, what is the magnitude of the electric field? a. 13.9 N/C c. 28.3 N/C b. 0.0696 N/C d. 0.104 N/C ANS: B PTS: 1 DIF: 2 38. Two charges, + Q and −Q, are located two meters apart a nd there is a point along the line that is equidistant from the two charges as indicated. Which vector best represents the direction of the electric field at that point? a. Vector E C b. The electric field at that point is zero. c. Vector E B d. Vector EA ANS: D PTS: 1 DIF: 2 39. A charge of +2 C is at the origin. When charge Q is placed at 2 m along the positive x axis, the electric field at 2 m along the negative x axis becomes zero. What is the value of Q? a. −7 C c. −8 C b. −3 C d. −6 C ANS: C PTS: 1 DIF: 2 40. An electron with a speed of 2.0  106 m/s moves into a uniform electric field of 325 N/C that is parallel to the electron’s motion. How long does it take to bring the electron to rest? ( me = 9.11  10−31 kg, e = 1.6  10−19 C) a. 3.5  10−8 s c. 2.3  10−8 s b. 2.3  10−6 s d. 1.2  10−7 s ANS: A PTS: 1 DIF: 2 41. In x-ray machines, electrons are subjected to electric fields as great as 4.0  105 N/C. Find an electron’s acceleration in this f ield. ( me = 9.11  10−31 kg, e = 1.6  10−19 C) a. 1.1  1017 m/s2 c. 3.6  108 m/s2 b. 7.0  1016 m/s2 d. 4.6  1010 m/s2 ANS: B PTS: 1 DIF: 2 42. A proton moving at 6.0  104 m/s is projected at an angle of 30  above a horizontal plane. If an elect ric field of 400 N/C is acting down, 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) a. 7.8  10−6 s c. 7.8  10−7 s b. 1.6  10−6 s d. 3.9  10−6 s ANS: B PTS: 1 DIF: 3 43. Electrons in a particle beam each have a kinetic energy of 3.2  10−17 J. What is the magnitude of the electric field that will stop these electrons in a distance of 0.05 m? ( e = 1.6  10−19 C) a. 2000 N/C c. 200 N/C b. 4000 N/C d. 1000 N/C ANS: B PTS: 1 DIF: 2 44. The electric field in a cathode ray tube is supposed to accelerate electrons from 0 to 1.60  107 m/s in a distance of 4.00 cm. What electric field is required? ( me = 9.11  10−31 kg and e = 1.60  10−19 C) a. 18,200 N/C c. 36,400 N/C b. 9110 N/C d. 72,800 N/C ANS: A PTS: 1 DIF: 2 45. The electric field of a point charge has an inverse _____ behavior. a. r3 c. r b. r2 d. r1/2 ANS: B PTS: 1 DIF: 1 46. The number of electric field lines passing through a unit cro ss sectional area is indicative of: a. field strength. c. field direction. b. charge motion. d. charge density. ANS: A PTS: 1 DIF: 1 47. Two point charges, separated by 1.5 cm, have charge values of +2.0 and −4.0 µC, respectively. Suppose we determine that 10 field lines radiate out from the +2.0 -µC charge. If so, what might be inferred about the −4.0 C charge with respect to field lines? a. 40 radiate in c. 5 radiate out b. 20 radiate out d. 20 radiate in ANS: D PTS: 1 DIF: 2 48. Charge A has 10 electric field lines coming out, charge B has 20 lines coming out, and charge C has 30 lines coming in. Which pair of these charges will have the largest force between them if placed one cm apart? a. A and B c. More information is needed. b. B and C d. C and A ANS: B PTS: 1 DIF: 2 49. Q1 has 27 electric field lines radiating outward and Q 2 has 11 field lines converging inward. What is the ratio Q 1/Q2? a. 27/11 c. −11/27 b. d. −27/11 ANS: D PTS: 1 DIF: 2 50. A ping -pong ball covered with a conducting graphite coating has a mass of 2.5  10−3 kg and a charge of 4.0 µC. What electric field directed upward will exactly balance the weight of the ball? ( g = 9.8 m/s2) a. 6.1  103 N/C c. 5.1  106 N/C b. 2.0  10−7 N/C d. 1.2  104 N/C ANS: A PTS: 1 DIF: 2 51. The combination of two separated point charges of opposite sign but equal magnitude is called an electric: a. magnapole. c. quadrapole. b. dipole. d. monopole. ANS: B PTS: 1 DIF: 1 52. Five equal negative charges are uniformly spaced in a semicircular arc of radius with its center at the origin. The charges positions in polar coordinates are given by , where the values of are . At the positio n in the 4th quadrant, which statement best describes the direction of the resulting electric field? a. The direction is that of a 4th quadrant angle. b. The direction is that of a 3rd quadrant angle. c. The direction is that of a 1st quadrant angle. d. The direction is that of a 2nd quadrant angle. ANS: D PTS: 1 DIF: 1 53. A ring of charge of radius lies in the x-y plane with its center at the origin.The charge counterclockwise from is uniformly distributed with the total charge equaling Q. The charge counterclockwise from is uniformly distributed with the total charge for this half of the ring equaling . What is the direction of the electric field on the z-axis at the position ? a. It is in the direction. c. It is in the direction. b. It is in the direction. d. It has no direction since there. ANS: C PTS: 1 DIF: 2 17.4 Conductors, Insulators, and the Motion of Electric Charge 54. Two small objects are suspended from threads. When the objects are moved close together, they at tract one another. Which of the following could produce this result? a. One object is negatively charged and the other is uncharged. b. One object is positively charged and the other is uncharged. c. One object is positively charged and the other is nega tively charge. d. All of the above could result in such attraction. ANS: D PTS: 1 DIF: 1 55. When a glass rod is rubbed with silk, which of the following statements best describes what happens? a. Electrons are removed from the rod. c. The silk remai ns neutral. b. Protons are removed from the silk. d. The silk is charged positively. ANS: A PTS: 1 DIF: 1 56. When charging two objects by rubbing them together: a. neither may be a conductor. b. the heat produced by friction is a necessary part of this process. c. they must be made of different material. d. they will sometimes end up with both being positively charged. ANS: C PTS: 1 DIF: 1 57. An uncharged conductor is supported by an insul ating stand. I pass a positively charged rod near the left end of the conductor, but do not touch it. The right end of the conductor will be: a. neutral. c. attracted. b. positive. d. negative. ANS: B PTS: 1 DIF: 1 58. Of the following substances, wh ich one contains the highest density of free electrons? a. glass c. iron b. hard rubber d. amber ANS: C PTS: 1 DIF: 1 59. Which of the following best characterizes electrical conductors? a. high tensile strength c. electric charges move freely b. poor heat conductors d. low mass density ANS: C PTS: 1 DIF: 1 60. Which of the following best characterizes electrical insulators? a. high tensile strength c. good heat conductors b. charges on the surface don’t move d. electric charges move freely ANS: B PTS: 1 DIF: 1 61. If body M, with a positive charge, is used to charge body N by induction, what will be the nature of the charge left on the latter? a. must be positive b. must be equal in magnitude to that on M c. must be negative d. must be greater in magnitude than that on M ANS: C PTS: 1 DIF: 2 62. If body P, with a positive charge, is placed in contact with body Q (initially uncharged), what will be the nature of the charge left on Q? a. must be greater in magnitude than that on P b. must be equal in magnitude to that on P c. must be negative d. must be positive ANS: D PTS: 1 DIF: 1 63. I wish to use a positively charged rod to charge a ball by induction. Which statement is correct? a. The ball is charged as the area of contact between the two increases. b. The ball must be a conductor. c. The ball must be an insulator that is connected temporarily to the ground. d. The charge on the ball will be positive. ANS: B PTS: 1 DIF: 1 64. How can a charged object attract an unch arged object made of non -conducting material? a. The charges in the uncharged object can become polarized. b. The uncharged object must somehow gain a like charge. c. Attraction of an insulator is not possible. d. The uncharged object must somehow gain an unlike charge. ANS: A PTS: 1 DIF: 1 65. The electric field at the surface of a positively charged conductor has a direction characterized by which of the following? a. perpendicular outward and away from the charge b. at a 45 angle to the surface c. tangent to the surface d. perpendicular inward toward the charge ANS: A PTS: 1 DIF: 1 66. The electric field associated with a uniformly charged hollow metallic sphere is the greatest at: a. the center of the sphere. c. infinity. b. the sphere’ s outer surface. d. the sphere’s inner surface. ANS: B PTS: 1 DIF: 1 67. If a conductor is in electrostatic equilibrium near an electrical charge: a. the sum of all forces between the conductor and the charge must be zero. b. the total charge on the conductor must be zero. c. any charges on the conductor must be uniformly distributed. d. the electric field inside the conductor must be zero. ANS: D PTS: 1 DIF: 1 68. A charge Q accumulates on the hollow metallic dome, of radius R, of a Van de Gra aff generator. A probe measures the electric field strength at various points outside the sphere surface. If the probe is initially at a distance 3 R from the sphere's center and then is moved to 5 R, by what factor will the electric field reading change? a. 3/5 c. 5/3 b. (5/3)2 d. (3/5)2 ANS: D PTS: 1 DIF: 2 69. A charge Q accumulates on the hollow metallic dome, of radius R, of a Van de Graaff generator. A probe measures the electric field strength at various points outside the sphere’s surface. By wh at factor will the electric field value at the 2 R distance be changed if the charge value were increased to (5/3) Q? a. 3/5 c. 5/3 b. (5/3)2 d. (3/5)2 ANS: C PTS: 1 DIF: 2 70. A Van de Graaff generator has a spherical dome of radius 12 cm. Operating i n dry air, where “atmospheric breakdown” is at Emax = 3.0  106 N/C, what is the maximum charge that can be held on the dome? ( ke = 8.99  109 Nm2/C2) a. 4.8  10−6 C c. 2.7  10−5 C b. 1.3  10−5 C d. 3.3  10−6 C ANS: A PTS: 1 DIF: 3 17.5 Electric Flux and Gauss’s Law 71. A spherical surface surrounds a point charge at its center. If the charge is quadrupled and if the radius of the surface is doubled, what happens to the electric flux E out of the surface and the magnitude E of the electric fiel d at the surface as a result of these doublings? a. E and E do not change. c. E increases and E remains the same. b. FE increases and E increases. d. E increases and E decreases. ANS: C PTS: 1 DIF: 2 72. An initially uncharged hollow metallic sph ere with radius of 5 cm has a small object with a charge of −10 µC carefully placed at the center of the sphere through a hole in the latter’s surface. With the charge in place, what charge is now present on the outside surface of the sphere? a. zero c. +4000 µC b. −10 µC d. +10 µC ANS: B PTS: 1 DIF: 2 73. An initially uncharged hollow metallic sphere with radius of 5 cm has a small object with a charge of −10 µC carefully placed at the center of the sphere through a hole in the latter’s surface. What charge resides inner surface of the sphere? a. −10 µC c. +10 µC b. zero d. −4000 µC ANS: C PTS: 1 DIF: 2 74. We have an initially uncharged hollow metallic sphere with radius of 5.0 cm. I place a small object with a charge of +40 µC at the center of the sphere through a hole in the surface. Find the electric field present at a point 10 cm from the sphere’s center. ( ke = 8.99  109 Nm2/C2) a. 9.0  106 N/C c. 2.3  106 N/C b. 1.1  106 N/C d. 36  106 N/C ANS: D PTS: 1 DIF: 2 75. We have a hol low metallic sphere with charge +5.0 µC and radius 5.0 cm. We insert a −10 µC charge at the center of the sphere through a hole in the surface. What charge now rests on the outer surface of the sphere? a. +10 µC c. −5 µC b. +5 µC d. +15 µC ANS: C PTS: 1 DIF: 3 76. If a negative charge is placed inside a hollow isolated conductor that is originally neutral and the charge does not touch that conductor at any time: a. both the inner and outer surfaces will become negative. b. both the inner and outer su rfaces will remain neutral. c. the outside surface of the conductor will become positively charged. d. the inside surface of the conductor will become positively charged. ANS: D PTS: 1 DIF: 2 77. A thin uncharged conducting spherical shell has a cha rge q carefully placed at its center through a small hole in the shell. The charge q does not touch the shell. What is the charge on the shell? a. 2q c. q b. 0 d. −q ANS: B PTS: 1 DIF: 1 78. A charge, + Q, is placed inside a balloon and the balloon is inflated. As the radius of the balloon r increases the number of field lines going through the surface of the balloon: a. increases proportional to r2. c. stays the same. b. increases proportional to r. d. decreases as 1/ r. ANS: C PTS: 1 DIF: 1 79. A spherical volume of space has an electric field of intensity 170 N/C directed radially outward from it surface of radius 0.600 m. What is the net charge enclosed within this surface? a. –6.8 nC c. 4.0 nC b. –4.0 nC d. 6.8 nC ANS: D PTS: 1 DIF: 3 80. A closed surface contains the following point charges: 6 C, −4 C, –2 C, –4 C. The electric flux coming out of the surface is: a. 16 C/o. c. –16 C/o. b. –4 C/o. d. 4 C/o. ANS: B PTS: 1 DIF: 2 81. A conducting spherical shell of inner radius and outer radius has a charge Q on it. An additional charge, also Q, is then added to the sphere. What is the resulting charge per unit area on the outer surface of the sphere? a. c. b. No answer given is correct. d. ANS: D PTS: 1 DIF: 2 82. A conducting spherical shell of inner radius and outer radius has a charge Q on it. The flux through a concentric spherical surface of radius is . An additional charge, also Q, is then added to the sphere. What is the change in flux through a concen tric spherical surface of radius when the additional charge is placed on the conducting shell? a. c. b. d. 0 ANS: D PTS: 1 DIF: 3 17.6 Applications: DNA Fingerprinting 83. In an electrophoresis experiment, the terminal speed of a particular DNA fragment is vT . If the experiment is repeated with identical fragments with the voltage between the plates producing the field increased by 50%, what new terminal speed would occur? Choose the closest answer. a. 1.6 vT c. 2.3 vT b. 1.5 vT. d. 0.50 vT ANS: B PTS: 1 DIF: 2 17.7 “Why Is Charge Quantized?” and Other Deep Questions 84. A proton consists of 3 quarks, two with charge +2 e/3 and one with charge –e/3. Of the following, which is closest to the approximate potential energy of the arrangeme nt of the two positive quarks if they are separated by 10–15 m? a. 1 MeV c. 1012 MeV b. 10–19 MeV d. 100 MeV ANS: A PTS: 1 DIF: 2 Chapter 18: Electric Potential MULTIPLE CHOICE 18.1 Electric Potential Energy 1. Case 1: An electron is released from rest in a uniform electric field. Case 2: A proton is released from rest in a uniform electric field of the same magnitude as in case 1. How does the electric potential energy of the charge -field system behave in these cases? a. In case 1 the potential energy increases, but in case 2 it decreases. b. In both cases, the potential energy increases. c. In case 1 the potential energy decre ases, but in case 2 it increases. d. In both cases, the potential energy decreases. ANS: D PTS: 1 DIF: 2 2. An electron and a proton are each released from rest in the same uniform electric field. The electron moves a distance delectron and the proto n moves a distance dproton as each particle’s kinetic energy increases by 1.6 eV. How do delectron and dproton compare? a. delectron > dproton b. delectron = dproton c. delectron < dproton d. The answer depends on the direction of the electric field. ANS: B PTS: 1 DIF: 3 3. An electron (charge −1.6  10−19 C) moves on a path perpendicular to the direction of a uniform electric field of strength 3.0 N/C. How much work is done on the electron as it moves 20 cm? a. 1.6  10−20 J c. 4.8  10−20 J b. −4.8  10−20 J d. zero ANS: D PTS: 1 DIF: 2 4. A proton (+1.6  10−19 C) moves 10 cm on a path in the direction opposite to a uniform electric field of strength 3.0 N/C. How much work is done on the proton by the electrical field? a. 4.8  10−20 J c. zero b. 1.6  10−20 J d. −4.8  10−20 J ANS: D PTS: 1 DIF: 2 5. A free electron is in an electric field. With respect to the field, it experiences a force acting: a. perpendicular. c. parallel. b. along a constant potential line. d. anti-parallel (opp osite in direction). ANS: D PTS: 1 DIF: 1 6. In which case does an electric field do positive work on a charged particle? a. A negative charge moves opposite to the direction of the electric field. b. A positive charge completes one circular path aro und a stationary positive charge. c. A positive charge is moved to a point of higher potential energy. d. A positive charge completes one elliptical path around a stationary positive charge. ANS: A PTS: 1 DIF: 1 7. If the distance between two negati ve point charges is increased by a factor of two, the resultant potential energy is what factor times the initial potential energy? a. 2 c. 1/4 b. 1/2 d. 4 ANS: B PTS: 1 DIF: 1 8. Which of the following characteristics are held in common by both grav itational and electrostatic forces when dealing with either point masses or charges? a. potential energy is a function of distance of separation b. forces are conservative c. inverse square distance law applies d. all of the above choices are valid ANS: D PTS: 1 DIF: 1 9. Two point charges of values +3.4 C and +6.6 C, respectively, are separated by 0.20 m. What is the potential energy of this 2 -charge system? ( ke = 8.99  109 Nm2/C2) a. +1.0 J c. −0.75 J b. −5.0 J d. +0.50 J ANS: A PTS: 1 DIF: 2 10. Consider two charged spheres, one with charge +2 C and the other with −2 C. A proton (a positively charged particle) is at the point halfway between the spheres. What is not zero? a. the potential energy of the proton b. the work to move the pro ton from infinity to that point c. the force on the proton d. all of the three above are zero ANS: C PTS: 1 DIF: 1 11. Two protons, each of charge 1.60  10−19 C, are 3.00  10−5 m apart. What is the change in potential energy if they are brought 1. 00  10−5 m closer together? ( ke = 8.99  109 N·m2/C2) a. 3.84  10−24 J c. 1.15  10−23 J b. 3.20  10−16 J d. 3.20  10−19 J ANS: A PTS: 1 DIF: 2 12. Two particles each have the same mass but particle #1 has four times the charge of particle #2. Pa rticle #1 is accelerated from rest through a potential difference of 10 V and attains speed v. Particle #2 is accelerated from rest also through a potential difference of 10 V. What speed does particle #2 attain? a. 2v c. v/4 b. v/2 d. ANS: B PTS: 1 DIF: 2 13. Two charges, each of charge q, are separated by a distance d. The distance between the charges is doubled. If the original potential energy of the arrangement was 40 mJ, by how much does the potential energy change when the charges are moved t o the increased distance? a. It decreases by more than 20 mJ. c. More information is needed. b. It decreases by less than 20 mJ d. It decreases by 20 mJ. ANS: A PTS: 1 DIF: 2 18.2 Electric Potential: Voltage 14. Two equal positive charges are separa ted by d. Then one of the charges is replaced by a negative charge of the same magnitude. Take the potential at infinity to be zero. In which situation is the potential higher midway between the charges; is this value of potential zero? a. the first situat ion; no c. the second situation; no b. the first situation; yes d. the second situation; yes ANS: A PTS: 1 DIF: 2 15. A proton (+1.6  10−19 C) moves 10 cm along the direction of an electric field of strength 4.0 N/C. The electrical potential differe nce between the proton’s initial and ending points is: a. 4.8  10−19 V. c. 0.044 V. b. 0.40 V. d. 6.4  10−19 V. ANS: B PTS: 1 DIF: 2 16. If an electron is accelerated from rest through a potential difference of 300 V, find its approximate speed at the end of this process. ( e = 1.6  10−19 C; me = 9.1  10−31 kg) a. 2.5  107 m/s c. 1.0  107 m/s b. 2.1  107 m/s d. 1.4  107 m/s ANS: C PTS: 1 DIF: 2 17. The unit of electrical potential, the volt, is dimensionally equivalent to: a. J/C. c. FC. b. JC. d. C/J. ANS: A PTS: 1 DIF: 1 18. The quantity of electrical potential, the volt, is dimensionally equivalent to: a. force/charge. c. force  charge. b. electric field/distance. d. electric field  distance. ANS: D PTS: 1 DIF: 1 19. A uniform electric field, with a magnitude of 600 N/C, is directed parallel to the positive x axis. If the potential at x = 4.0 m is 1000 V, what is the potential at x = 2.0 m? a. −800 V c. 2800 V b. 2200 V d. 1600 V ANS: B PTS: 1 DIF: 2 20. A uniform e lectric field, with a magnitude of 600 N/C, is directed parallel to the positive x axis. If the potential at x = 4.0 m is 1000 V, what is the change in potential energy of a proton as it moves from x = 4.0 m to x = 1.0 m? ( qp = 1.6  10−19 C) a. 500 J c. 1.9  10−16 J b. 2.9  10−16 J d. 8.0  10−17 J ANS: B PTS: 1 DIF: 2 21. An electron in a cathode ray tube is accelerated through a potential difference of 10 kV. What kinetic energy does the electron gain in the process? ( e = 1.6  10−19 C) a. 8.0  10−16 J c. 8.0  1022 J b. 1.6  10−15 J d. 1.6  10−16 J ANS: B PTS: 1 DIF: 2 22. If the distance between two isolated parallel plates that are oppositely charged is doubled, the electric field between the plates is essentially unchanged. However, the: a. charge on each plate will double. b. force on a charged particle halfway between the plates will get twice as small. c. potential difference between the plates will double. d. force on a charged particle halfway between the plates will get four times as small. ANS: C PTS: 1 DIF: 2 23. An electron is released from rest at the negative plate of a parallel -plate capacitor. If the distance across the plates is 5.0 mm and the potential difference across the plates is 20 V, with what velocity does the electron hit the positive plate? ( me = 9.1  10−31 kg, e = 1.6  10−19 C) a. 1.3  106 m/s c. 2.7  106 m/s b. 1.0  106 m/s d. 5.3  106 m/s ANS: C PTS: 1 DIF: 2 24. An ion is released from rest and moves due to the force from an electric fiel d from a position in the field having a potential of 14 V to a position having a potential of 8 V. The ion: a. can have either a positive or a negative charge. b. must be neutral. c. must have a positive charge. d. must have a negative charge. ANS: C PTS: 1 DIF: 2 25. A 9.0 -V battery moves 200 mC of charge through a circuit running from its positive terminal to its negative terminal. How much energy was delivered to the circuit? a. 4.5 x 103 J c. 2.2 mJ b. 1.8 J d. 0.18 J ANS: B PTS: 1 DIF: 2 26. Four point charges are on the rim of a circle. The charges are (in C) +0.50, +3.0, −1.0, −0.50. If the electrical potential at the circle’s center due to the +0.5 charge alone is 4.5  104 V, what is the total potential at the center due to the four charges combined? a. 18  104 V c. zero b. 4.5  104 V d. −4.5  104 V ANS: A PTS: 1 DIF: 2 27. Find the electrical potential at 0.055 m from a point charge of 6.0 C. (ke = 8.99  109 Nm2/C2) a. 1.5  105 V c. 9.8  105 V b. 1.2  107 V d. 3.6  105 V ANS: C PTS: 1 DIF: 2 28. Two point charges of values +3.4 C and +6.6 C are separated by 0.20 m. What is the electrical potential at the point midway between the two charges? ( ke = 8.99  109 Nm2/C2) a. +1.8  106 V c. +0.90  106 V b. −0.90  106 V d. +3.6  106 V ANS: C PTS: 1 DIF: 2 29. At what distance from a point charge of 14 C would the electrical potential be 4.2  104 V? (ke = 8.99  109 Nm2/C2) a. 0.76 m c. 3.0 m b. 0.58 m d. 1.7 m ANS: C PTS: 1 DIF: 2 30. A point charge of +3.0 C is located at the origin of a coordinate system and a second point charge of −9.0 C is at x = 1.00 m. What is the electric potential at the x = 0.50 m point? ( ke = 8.99  109 Nm2/C2) a. −5.4  104 V c. 16  104 V b. 11  104 V d. −11  104 V ANS: D PTS: 1 DIF: 2 31. A point charge of +3.0 C is located at the origin of a coordinate system and a second point charge of −9.0 C is at x = 1.0 m. At what point on the x axis is the electrical potential zero? a. +0.33 m c. +0.25 m b. −0.25 m d. +0.75 m ANS: C PTS: 1 DIF: 2 32. When charge Q1 is placed at point P 1, the resulting potential at point P is V1. When Q2 is placed at point P 2 after Q1 is in position at P 1, the resulting potential at P becomes V2. What is the potential at point P if charge Q1 is then removed? a. V1 – V2 c. V1 + V2 b. (V1 + V2)/2 d. V2 – V1 ANS: D PTS: 1 DIF: 2 33. When charges qa, qb, and qc are placed respectively at the corners a, b, and c of a right triangle, the potential at the midpoint of the hypotenuse i s 20 V. When the charge qa is removed, the potential at the midpoint becomes 15 V. When, instead, the charge qb is removed ( qa and qc both in place), the potential at the midpoint becomes 13 V. What is the potential at the midpoint if only the charge qc is removed from the array of charges? a. 12 V c. 7 V b. 8 V d. 5 V ANS: A PTS: 1 DIF: 3 34. When charges qa, qb, and qc are placed respectively at the corners a, b, and c of a right triangle, the potential at the midpoint of the hypotenuse is 20 V. Whe n the charge qa is removed, the potential at the midpoint becomes 15 V. When, instead, the charge qb is removed ( qa and qc both in place), the potential at the midpoint becomes 13 V. What is the potential at the midpoint if both charges qa and qc are remov ed? a. 13 V c. 5 V b. 7 V d. 8 V ANS: B PTS: 1 DIF: 3 35. A solid conducting sphere of 10 cm radius has a net charge of 40 nC. If the potential at infinity is taken as zero, what is the potential at the center of the sphere? a. 360 V c. >3.6  104 V b. 3.6  103 V d. 36 V ANS: B PTS: 1 DIF: 3 36. If a doubly -ionized oxygen atom is accelerated from rest by going through a potential difference of 10 V, what will be the change in its kinetic energy? a. 10 eV c. 20 eV b. 40 eV d. none of the above ANS: C PTS: 1 DIF: 2 37. An electron in a TV picture tube is accelerated through a potential difference of 20 kV before it hits the screen. What is the kinetic energy of the electron in electron volts? (1 eV = 1.6  10−19 J) a. 6.25  1022 eV c. 2.0  104 eV b. 1.0  104 eV d. 3.2  10−22 eV ANS: C PTS: 1 DIF: 1 38. Electrons in an x -ray machine are accelerated from rest through a potential difference of 80,000 V. What is the kinetic energy of each of these electrons in eV? a. 128 eV c. 80 eV b. 40 eV d. 80 keV ANS: D PTS: 1 DIF: 1 39. There is a hollow, conducting, uncharged sphere with a negative charge inside the sphere. Consider the electrical potential at the inner and outer surfaces of the sphere. Which of the follo wing is true? a. The potentials on both surfaces are equal but not zero. b. The potentials on both surfaces are zero. c. The potential on the inner surface is greater. d. The potential on the outer surface is greater. ANS: A PTS: 1 DIF: 2 40. Which of the following were found from Millikan’s oil drop experiment? a. the weight, and hence the mass, of the electron b. all of the above c. that quarks have charges that are fractions of the electronic charge d. the value of the electron’s quantized c harge ANS: D PTS: 1 DIF: 1 41. A solid metal sphere of radius r is inside a metal concentric spherical shell of inner radius 2 r and outer radius 3 r. A charge is place on the solid metal sphere and it is found that the potential at its surface is (at r) and that the potential at the outer surface of the spherical shell is (at 3r). In terms of and , what is the potential at the inner surface of the metal shell (at 2 r)? a. c. b. d. ANS: B PTS: 1 DIF: 2 18.3 Equipotential Lines and Surf aces 42. Equipotential surfaces around a point charge are a. spherical. c. planar. b. cylindrical. d. none of these choices. ANS: A PTS: 1 DIF: 1 43. If the plane x = 4 m is an equipotential surface, in which of the following directions can the ele ctric field be in the region immediately adjacent to this plane? a. the positive y direction b. both the positive and negative z directions c. the positive x direction d. more than one of these choices ANS: C PTS: 1 DIF: 2 44. Suppose two equipoten tial surfaces are the planes x = 3 m and x = 5 m. If the potential at the x = 3 m surface is 10 V and the potential at the x = 5 m surface is 50 V, what is the magnitude of the electric field between the two surfaces? a. 40 N/C c. 15 N/C b. 20 N/C d. 10 N /C ANS: B PTS: 1 DIF: 2 45. Suppose two charges, one positive and one negative, are separated by a distance d. Where can two equipotential surfaces at different potentials intersect in the region near the charges? a. halfway between the charges if th e charges have the same magnitude b. closer to the smaller negative charge than the larger positive charge if the charges are not equal c. Equipotential surfaces at different potentials cannot intersect. d. closer to the smaller positive charge than the larger negative charge if the charges are not equal ANS: C PTS: 1 DIF: 2 18.4 Capacitors 46. Three capacitors have capacitances C1 < C2 < C3. If these capacitors are connected in series, which of the following is true for the resulting equivalent ca pacitance? a. Ceq < C1 c. Ceq = (C1 + C2 + C3)/3 b. Ceq > C3 d. None of the above is always correct. ANS: A PTS: 1 DIF: 1 47. A capacitor is attached across a battery and charged. Then the battery is removed leaving the capacitor charged. The positiv e lead of the capacitor is then connected to one lead of a previously uncharged identical capacitor, and then the other lead of the charged capacitor is connected to the other lead of the second capacitor. How does the energy E0 stored in the originally ch arged capacitor compare to the energy Ef stored in the connected capacitors? a. E0 = 2Ef c. E0 = 4Ef b. E0 < Ef d. E0 = Ef ANS: A PTS: 1 DIF: 2 48. At which location will the electric field between the two parallel plates of a charged capacitor be th e strongest in magnitude? a. near the positive plate b. near the negative plate c. midway between the two plates nearest their center d. midway between the two plates at their ends ANS: C PTS: 1 DIF: 1 49. The unit of capacitance, the farad, is dim ensionally equivalent to which of the following? a. J/V c. VC b. C/V d. V/C ANS: B PTS: 1 DIF: 1 50. Decreasing the voltage across the two plates of a capacitor will produce what effect on the capacitor? a. decrease charge c. decrease capacitance b. increase capacitance d. increase charge ANS: A PTS: 1 DIF: 1 51. A 0.50 -F capacitor is connected to a 400 V battery. Find the charge on the capacitor. a. 2.0  10−4 C c. 1.0  10−4 C b. 0.020 C d. 1.2  10−12 C ANS: A PTS: 1 DIF: 1 52. A parallel -plate capacitor has a capacitance of 20 µF. What potent ial difference across the plates is required to store 22  10−5 C on this capacitor? a. 2.2  10-2 V c. 11 V b. 1.4  10−8 V d. 70 V ANS: C PTS: 1 DIF: 2 53. If two parallel, conducting plates have equal positive charge, the electric field lines will : a. leave one plate and go straight to the other plate. b. enter both plates from infinity. c. leave both plates and go to infinity. d. none of the above. ANS: C PTS: 1 DIF: 1 54. A 20 -F capacitor is attached across a 1000 -V power supply. What is the net charge on the capacitor? a. 20 mC c. 10 mC b. 40 mC d. none of these choices ANS: D PTS: 1 DIF: 1 55. Doubling the voltage across a parallel -plate capacitor does not double which of the following? a. the electric field between the plates c. the energy stored b. the charge d. both a and b ANS: C PTS: 1 DIF: 2 56. Increasing the separation of the two charged parallel plates of a capacitor, which are disconnected from a battery, will produce what effect on the capacitor? a. increase charge c. decrease capacitance b. decrease charge d. increase capacitance ANS: C PTS: 1 DIF: 1 57. Three capacitors of 1.0, 1.5, and 3.0 F are connected in series. Find the combined capacitance. a. 0.50 F c. 5.0 F b. 1.0 F d. 5.5 F ANS: A PTS: 1 DIF: 2 58. If three 3.0 -µF capacitors are connected in parallel, what is the combined capacitance? a. 0.46 F c. 9.0 F b. 1.0 F d. 0.75 F ANS: C PTS: 1 DIF: 1 59. Two capacitors with capacitances of 1.5 C and 0.25 F, respectively, are connected in parallel. The system is connected to a 40 -V battery. What charge accumulates on the 1.5 -F capacitor? a. 100 C c. 60 C b. 75 C d. 33 C ANS: C PTS: 1 DIF: 2 60. Two capacitors with capacitances of 1.0 C and 0.50 F, respectively, are connecte d in series. The system is connected to a 150 V battery. What charge accumulates on the 1.0 -F capacitor? a. 50 C c. 100 C b. 150 C d. 33 C ANS: A PTS: 1 DIF: 2 61. Two capacitors, with CA greater than CB, are connected in series with a battery. Which of the following is true? a. There is more charge stored on CB. b. There is the same charge stored on each capacitor. c. There is the same potential difference across both capacitors. d. There is more charge stored on CA. ANS: B PTS: 1 DIF: 2 62. Two capacitors with CA greater than CB, are connected in parallel with a battery. Which of the following is true? a. There is the same charge stored on each capacitor. b. There is the same potential difference across both capacitors. c. There is mor e potential difference across CB. d. There is more potential difference across CA. ANS: B PTS: 1 DIF: 2 63. What is the equivalent capacitance between points a and b? All capacitors are 2.0 F. a. 1.2 µF b. 0.25 µF c. 4.0 µF d. 0.60 µF ANS: A PTS: 1 DIF: 2 64. If C = 48 µF, determine the equivalent capacitance for the combination shown. a. 32 µF c. 24 µF b. 48 µF d. 28 µF ANS: A PTS: 1 DIF: 2 65. If C = 14 µF, what is the equivalent capacitance for the combination shown? a. 5.8 µF c. 8.2 µF b. 6.5 µF d. 7.0 µF ANS: D PTS: 1 DIF: 2 66. What is the equivalent capacitance of the combination shown? a. 25 µF c. 29 µF b. 10 µF d. 40 µF ANS: B PTS: 1 DIF: 1 67. What is the equivalent capacitance of the combination shown? a. 4.6 µF b. 100 µF c. 12 µF d. 24 µF ANS: D PTS: 1 DIF: 2 68. Four identical 4 -mF capacitors are connected together electrically. What is the least possible capacitance of the combination? a. 4 mF c. 1/8 mF b. 1 mF d. 1/4 mF ANS: B PTS: 1 DIF: 2 69. Four identical 4 -mF capacitors are connected together electrically. What is the greatest possible capacitance of the combination? a. 16 mF c. 4 mF b. 8 mF d. 1 mF ANS: A PTS: 1 DIF: 2 70. Using a 1 -mF capacitor, a 2 -mF capacitor, and a 3 -mF capacitor, which of the following capacitances cannot be made by a combination that uses all three? (Hint: At most only 2 combinations must be considered to determine the correct answer.) a. 6/11 mF c. 11/3 mF b. 6 mF d. 7 mF ANS: D PTS: 1 DIF: 3 71. A 6.0 -F capacitor is attached to a 20 -V power supply. How much energy is stored in the capacitor? a. 2.0  10−3 J c. 2.0  10−4 J b. 5.2  10−4 J d. 1.2  10−3 J ANS: D PTS: 1 DIF: 2 72. A 0.50 -F capacitor is connected to a 400 -V battery. What potential energy is stored in the capacitor? a. 0.020 J c. 1.0  10−4 J b. 0.040 J d. 1.2  10−12 J ANS: B PTS: 1 DIF: 1 73. Two capacitors with capacitances of 1.5 F and 0.25 F, respectively, are connected in parallel. The system is connected to a 100 -V bat tery. What electrical potential energy is stored in the 1.5 -F capacitor? a. 1.2  10−3 J c. 0.50  10−3 J b. 1.9  10−3 J d. 7.5  10−3 J ANS: D PTS: 1 DIF: 2 74. Two capacitors with capacitances of 1.0 F and 0.50 F, respectively, are connected in series. The system is connected to a 50 -V battery. What electrical potential energy is stored in the 1.0 -F capacitor? a. 5.6  10−4 J c. 0.065  10−3 J b. 4.3  10−3 J d. 1.4  10−4 J ANS: D PTS: 1 DIF: 3 75. If C1 = 25 µF, C2 = 20 µF, C3 = 10 µF, and V0 = 42 V, determine the energy stored by C3. a. 3.6 mJ c. 1.8 mJ b. 0.32 mJ d. 0.40 mJ ANS: C PTS: 1 DIF: 3 76. A pair of parallel plates, forming a capacitor, are charged. The plates are pulled apart to triple the original separation, the c harges on the plates remaining the same. What is the ratio of the final energy stored to the original energy stored? a. 1/9 c. 1/3 b. 1.5 d. 3 ANS: D PTS: 1 DIF: 2 77. A pair of parallel plates, forming a capacitor, are connected to a battery. Whil e the capacitor is still connected to the battery maintaining a constant voltage, the plates are pulled apart to triple their original distance. What is the ratio of the final energy stored to the original energy stored? a. 1/9 c. 3 b. 1/3 d. 1 ANS: B PTS: 1 DIF: 2 78. A parallel plate capacitor has the voltage applied to it doubled. Is the force between the plates attractive or repulsive, and what happens to the force between the plates when the voltage is doubled? a. The force is attractive and it q uadruples. b. The force is attractive and it doubles. c. The force is repulsive and it halves. d. There is no force between the plates since the net charge is zero on the capacitor. ANS: A PTS: 1 DIF: 3 79. Capacitor #1 has parallel plates of lengt h L and width W, plate separation d, and is filled with dielectric with constant .Capacitor #2 has parallel plates of length 2 L and width 2 W, plate separation 2 d, and is filled with dielectric with constant 2 . If a voltage V is applied to capacitor #1 an d a voltage 2 V is applied to capacitor #2, which capacitor stores more energy and by what factor? a. Capacitor #2 by a factor of 8 b. Capacitor #2 by a factor of 16 c. Capacitor #1 by a factor of 4 d. Both capacitors store the same energy.