Physics 202 Spring 2010 Practice Questions for Chapters 21-24

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1 Note: Answer key is at end. Physics 202 Spring 2010 Practice Questions for Chapters A uniformly positively charged spherical conductor is placed midway between two identical uncharged conducting spheres. How would the charges in the middle sphere be distributed? A) The positive charges stay uniformly distributed on the surface of the middle sphere. B) There are more positive charges near the top and bottom of the sphere compared to the sides next to the two other spheres. C) There are more positive charges near the sides of the spheres that are next to the other two spheres compared to the other regions of the sphere. D) There are more positive charges near the front and back of the sphere compared to the sides next to the two other spheres. E) None of these is correct. 2. Two small spheres, each with mass m = 5.0 g and charge q, are suspended from a point by threads of length L = 0.30 m. What is the charge on each sphere if the threads make an angle θ = 20 with the vertical? A) C B) C C) C D) C E) C Page 1 of 40

2 3. Charges q 1 and q 2 exert repulsive forces of 10 N on each other. What is the repulsive force when their separation is decreased so that their final separation is 80% of their initial separation? A) 16 N B) 12 N C) 10 N D) 8.0 N E) 6.4 N 4. Two positive charges (+8.0 mc and +2.0 mc) are separated by 300 m. A third charge is placed at distance r from the +8.0 mc charge in such a way that the resultant electric force on the third charge due to the other two charges is zero. The distance r is A) 0.25 km B) 0.20 km C) 0.15 km D) 0.13 km E) 0.10 km 5. Point charges of C and C are placed 12 cm apart. A third point charge of C halfway between the first two point charges experiences a force of magnitude A) N B) N C) N D) zero E) N 6. A charge 2Q is located at the origin while a second charge Q is located at x = a. Where should a third charge be placed so that the net force on the charge is zero? A) x < 0 B) 0 < x < a C) x > a D) x < 0 or 0 < x < a E) 0 < x < a or x > a Page 2 of 40

3 7. If all the charges are 15 cm from the origin (the crossing point of the vertical and horizontal lines) in the above figure and Q = +3.0 µc, then calculate the magnitude of the net force on a charge of +Q placed at the origin. A) 22.8 N B) 10.2 N C) 26.0 N D) 187 N E) none of the above 8. Three charges are located at 100-m intervals along a horizontal line: a charge of 3.0 C on the left, 2.0 C in the middle, and 1.0 C on the right. What is the electric field on the horizontal line halfway between the 3.0 C and 2.0 C charges? A) N/C to the left B) N/C to the right C) N/C to the left D) N/C to the right E) N/C to the left Page 3 of 40

4 9. Three charges Q 1, Q 2, and Q 3, each equal to C, are in a straight line. The distance between neighboring charges is 60 nm. The magnitude of the electric field at P, which is 80 nm from Q 2 on a line at right angles to the line between Q 1 and Q 3, is A) N/C B) 16 N/C C) 2.0 N/C D) N/C E) N/C 10. Three charges, each of Q = C, are arranged at three of the corners of a 20-nm square as shown. The magnitude of the electric field at D, the fourth corner of the square, is approximately A) N/C B) N/C C) N/C D) 30 N/C E) N/C Page 4 of 40

5 11. The electric field at point A is zero. What is charge Q 1? A) +32 µc B) 32 µc C) The field cannot be zero at A for any value of Q 1. D) +16 µc E) 16 µc 12. Charges Q 1 = q and Q 2 = +4q are placed as shown. Of the five positions indicated by the numbered dots, the one at which the electric field is zero is A) 1 B) 2 C) 3 D) 4 E) Two charges Q 1 and Q 2 are a distance d apart. If the electric field is zero at a distance of 3d/4 from Q 1 (towards Q 2 ), then what is the relation between Q 1 and Q 2? A) Q 1 = Q 2 /9 B) Q 1 = 9Q 2 C) Q 1 = Q 2 /3 D) Q 1 = 3Q 2 E) Q 1 = 4Q 2 /3 Page 5 of 40

6 14. A bob of mass m (m = g), and charge magnitude Q (Q = 50.0 µc) is held by a massless string in a uniform electric field E. If the bob makes an angle of 10.0 degrees with the vertical, then calculate the magnitude of the electric field E and the sign of the bob charge Q. A) N/C and Q is positive. B) N/C and Q is negative. C) N/C and Q is positive. D) N/C and Q is negative. E) N/C and Q is positive. 15. The point P is on the axis of a ring of charge, and all vectors shown lie in the yz plane. The negatively charged ring lies in the xz plane. The vector that correctly represents the direction of the electric field at this point is A) B) C) D) E) Page 6 of 40

7 16. In the diagram, Q 1 = 9.0 µc and Q 2 = 9.0 µc. If Q 2 has a mass of 3.0 g, a uniform electric field of 1.8 kn/c imposed in the positive y direction would give this particle an acceleration in the y direction of approximately A) zero B) 5.4 m/s 2 C) 6.8 cm/s 2 D) 4.5 m/s 2 E) 7.5 cm/s An electron is released from rest in a uniform electric field. If the electric field is 3.65 kn/c, at the end of 15 ns the electron's velocity will be approximately A) m/s B) m/s C) m/s D) m/s E) m/s 18. An electric dipole consists of a positive charge separated from a negative charge of the same magnitude by a small distance. Which, if any, of the diagrams best represents the electric field lines around an electric dipole? A) 1 B) 2 C) 3 D) 4 E) None of these is correct. Page 7 of 40

8 19. Two electric dipoles, p 1 and p 2, are arranged as shown. The first dipole is not free to rotate but the second dipole can rotate in any direction. Which way will p 2 rotate? The directions represent the following: 1 clockwise, 2 counter-clockwise, 3 rotate about axis of the dipole rolling up, and 4 rotate about axis of the dipole rolling down. A) 1 B) 2 C) 3 D) 4 E) None of these is correct. 20. An electric dipole of magnitude 25 p C m makes an angle of 65 with a uniform electric field of magnitude N/C. What is the magnitude of the torque on the dipole? A) N m B) N m C) N m D) N m E) N m Page 8 of 40

9 21. An electric dipole of moment is placed in a uniform external electric field as shown in the diagram. The dipole moment vector is in the positive y direction. The external electric field vector is in the positive x direction. If the dipole is to have minimum potential energy, should be in the A) positive x direction. B) negative x direction. C) positive y direction. D) negative y direction. E) positive z direction. 22. An infinite line charge of linear density λ = 0.30 µc/m lies along the z axis and a point charge q = 6.0 µc lies on the y axis at y = 2.0 m. The x component of the electric field at the point P on the x axis at x = 3.0 m is approximately A) 1.8 kn/c B) 4.2 kn/c C) 0.96 kn/c D) 5.2 kn/c E) 0.64 mn/c 23. A disk of radius 10 cm carries a uniform surface charge density of 6.0 µc/m 2. The electric field on the axis of the disk at a distance of 0.10 cm is approximately A) 0.34 MN/C B) 68 kn/c C) 99 kn/c D) 0.54 MN/C E) 18 kn/c Page 9 of 40

10 24. A conducting circular disk has a uniform positive surface charge density. Which of the following diagrams best represents the electric field lines from the disk? (The disk is drawn as a cross section.) A) 1 B) 2 C) 3 D) 4 E) none of the diagrams 25. An infinite plane lies in the yz plane and it has a uniform surface charge density. The electric field at a distance x from the plane A) decreases linearly with x. B) decreases as 1/x 2. C) is constant and does not depend on x. D) increases linearly with x. E) is undetermined. 26. A uniform line charge of linear charge density λ = 5.00 nc/m extends from x = 0 to x = 10 m. The magnitude of the electric field at the point y = 12 m on the perpendicular bisector of the finite line of charge is A) 18.8 N/C B) 15.3 N/C C) 9.65 N/C D) 4.27 N/C E) 2.88 N/C 27. A uniform circular ring has charge Q and radius r. A uniformly charged disk also has charge Q and radius r. Calculate the ratio of the electric field at a distance of r along the axis of the ring to the electric field at a distance of r along the axis of the disk. A) 1.0 B) 0.60 C) 1.7 D) 0.50 E) 0.85 Page 10 of 40

11 28. Consider a uniform electric field = (5.0 kn/c). What is the flux of this field through a square of side 20 cm in a plane parallel to the yz plane? A) 0.10 kn m 2 /C B) 0.20 kn m 2 /C C) 0.40 kn m 2 /C D) 0.50 kn m 2 /C E) 0.13 kn m 2 /C 29. An electric field is = (400 N/C) for x > 0 and = ( 400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = 15 cm. What is the flux through the curved surface of the cylinder? A) zero B) 1.3 kn m 2 /C C) 0.25 kn m 2 /C D) 1.3 N m 2 /C E) 0.13 MN m 2 /C 30. An electric field is = (400 N/C) for x > 0 and = ( 400 N/C) for x < 0. A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = 15 cm. What is the net charge inside the cylinder? A) zero B) 22 nc C) 0.22 nc D) 4.5 nc E) 2.2 µc 31. A cube of side 3.56 cm has a charge of 9.11 µc placed at its center. Calculate the electric flux through one side of the cube. A) N. m 2 /C B) N. m 2 /C C) N. m 2 /C D) N. m 2 /C E) N. m 2 /C Page 11 of 40

12 32. A horizontal surface of area m 2 has an electric flux of 123 N. m 2 /C passing through it at an angle of 25 to the horizontal. If the flux is due to a uniform electric field, calculate the magnitude of the latter. A) 907 N. m 2 /C B) 423 N. m 2 /C C) N. m 2 /C D) N. m 2 /C E) 383 N. m 2 /C 33. A rod of infinite length has a charge per unit length of λ (= q/l). Gauss's law makes it easy to determine that the electric field strength at a perpendicular distance r from the rod is, in terms of k = (4πε 0 ) 1, A) kλ/r 2 B) kλ/r C) 4πkλ/r D) 2kλ/r E) zero 34. A hollow metal sphere has a total charge of 100 µc. If the radius of the sphere is 50 cm, the electric field intensity at a distance of 3.0 m from the surface of the sphere is approximately A) N/C B) N/C C) N/C D) N/C E) N/C Page 12 of 40

13 35. A sphere of radius 8.0 cm carries a uniform volume charge density ρ = 500 nc/m 3. What is the electric field at r = 8.1 cm? A) 0.12 kn/c B) 1.5 kn/c C) 0.74 kn/c D) 2.3 kn/c E) 12 kn/c 36. An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density ρ = 200 nc/m 3. What is the electric field at r = 3.9 cm? A) zero B) 0.44 kn/c C) 57 N/C D) 0.11 kn/c E) 0.23 kn/c 37. An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density ρ = 200 nc/m 3. What is the electric field at r = 4.1 cm? A) zero B) 0.11 kn/c C) 57 N/C D) 0.44 kn/c E) 0.23 kn/c Page 13 of 40

14 38. An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density σ = 12 nc/m 2. The electric field at r = 6.1 cm is approximately A) 0.81 kn/c B) zero C) 1.3 kn/c D) 12 kn/c E) 0.56 kn/c 39. A spherical shell of radius 9.0 cm carries a uniform surface charge density σ = 9.0 nc/m 2. The electric field at r = 4.0 cm is approximately A) 0.13 kn/c B) 1.0 kn/c C) 0.32 kn/c D) 0.75 kn/c E) zero 40. A spherical shell of radius 9.0 cm carries a uniform surface charge density σ = 9.0 nc/m 2. The electric field at r = 16 cm is approximately A) 0.32 kn/c B) 1.0 kn/c C) zero D) 0.13 kn/c E) 0.53 kn/c Page 14 of 40

15 Use the following to answer questions An infinite slab of thickness 2d lies in the xz plane. The slab has a uniform volume charge density ρ. 41. The electric at y = b where 0 < b < d is A) 4πkρb B) 2πkρb C) 4πkρ/b D) 2πkρ/b E) 4πkρ/b Which diagram best represents the electric field along the y axis? A) 1 B) 2 C) 3 D) 4 E) none of the diagrams Page 15 of 40

16 43. A non-conducting pipe has a uniform charge density of 50 C/m 3. The inner radius of the pipe is 25 cm, while the outer radius is 35 cm. Calculate the magnitude of the electric field at r = 30 cm. A) N/C B) N/C C) N/C D) N/C E) N/C 44. The electric field for an infinite plane of charge is discontinuous by the amount at a point where there is a surface charge density σ. A) ε 0 /σ B) σ/ε 0 C) ε 0 /σ 2 D) ε 0 2 /σ 2 E) σ 2 /ε 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) m/s B) m/s C) m/s D) m/s E) m/s 46. The electric field in a region is given by where the units are in V/m. What is the potential from the origin to (x, y) = (2, 0) m? A) 8 V B) 8 V C) 16/3 V D) 24/3 V E) 11 V Page 16 of 40

17 47. A lithium nucleus with a charge of 3( ) C and a mass of 7( ) kg, and an alpha particle with a charge of 2( ) C and a mass of 4( ) 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 48. A charge of 2.0 mc is located in a uniform electric field of intensity 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 49. Two parallel horizontal plates are spaced 0.40 cm apart in air. You introduce an oil droplet of mass 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 Page 17 of 40

18 50. 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 C at a point midway between the plates is approximately A) N B) N C) N D) N E) N 51. 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) 3.0 MV C) 15 kv D) 0.30 kv E) None of these is correct. Page 18 of 40

19 Use the following to answer questions Two equal positive charges are placed x m apart. The equipotential lines are at 100 V intervals. 52. The potential for line c is A) 100 V B) +100 V C) 200 V D) +200 V E) zero 53. The work required to move a third charge, q = e, from the +100 V line to b is A) 100 ev B) +100 ev C) 200 ev D) +200 ev E) zero 54. The potential a distance R from a unit positive point charge is found to be V. If the distance between the charge and the point at which the potential is measured is tripled and is now 3V, the potential becomes A) V/3 B) 3V C) V/9 D) 9V E) 1/V 2 Page 19 of 40

20 55. Two charges Q 1 and Q 2 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? (Q 1 = C and Q 2 = C) A) J B) J C) J D) J E) J 56. 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 Page 20 of 40

21 57. 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) The electric potential in a region of space is given by V(x) = 50 V + (15 V/m) x. The electric field in this region is A) 50 V B) (15 V/m)x C) (50 V/m + 15 V/m) D) (15 V/m) E) (15 V/m) 59. The electric potential in a region of space is given by V(x, y, z) = (10 V/m) x + (20 V/m) y + (30 V/m) z The x-component of the electric field in this region is A) (10 V/m) B) (10 V/m) C) (20 V/m) D) (20 V/m) E) (30 V/m) Page 21 of 40

22 60. If the potential V of an array of charges versus the distance from the charges is as shown in graph 1, which graph shows the electric field E as a function of distance r? A) 2 B) 3 C) 4 D) 5 E) The electric potential is known to be a function of x only; i.e., v = V(x). The electric field at a position x 1 is given by A) V(x 1 ) B) C) D) E) 62. The graph that best represents the electric potential of a uniformly charged spherical shell as a function of the distance from the center of the shell is A) 1 B) 2 C) 3 D) 4 E) 5 Page 22 of 40

23 Use the following to answer question A ring of radius 5 cm is the yz plane with its center at the origin. The ring carries a uniform charge of 10 nc. A small particle of mass m = 10 mg and charge q 0 = 5 nc is placed at x = 12 cm and released. The speed of the particle when it is a great distance from the ring is A) 1.36 cm/s B) 1.94 cm/s C) 2.63 cm/s D) 3.43 cm/s E) None of these is correct. 64. The graph that represents the electric potential near an infinite plane of charge is A) 1 B) 2 C) 3 D) 4 E) 5 Page 23 of 40

24 65. A copper ring lies in the yz plane, as shown. The magnet's long axis lies along the x axis. Induced current flows through the ring, as indicated in the figure. The magnet A) must be moving away from the ring. B) must be moving toward the ring. C) must be moving either away from or toward the ring. D) is not necessarily moving. E) must remain stationary to keep the current flowing 66. If you were to double the amplitude and halve the frequency of a harmonic (sinusoidal) wave on a string while keeping the wave speed constant, the rate at which energy is delivered by the wave would A) double. B) quadruple. C) be reduced to 50% of its previous value. D) be reduced to 25% of its previous value. E) be unchanged. 67. A charge of 100 nc resides on the surface of a spherical shell of radius 20 cm. The electric potential at a distance of 50 cm from the center of the spherical shell is A) 18 V B) 180 V C) 1800 V D) 18,000 V E) None of these is correct. 68. The potential of a spherical shell carrying 6.0 µc of charge is 540 kv. What is the radius of the shell? A) m B) m C) m D) m E) none of the above Page 24 of 40

25 69. A conducting sphere of radius r 1 = 10 cm and charge q 1 = 2 µc is placed far apart from a second conducting sphere of radius r 2 = 30 cm and charge q 2 = 3 µc. The two spheres are then connected by a thin conducting wire. What is the potential on the surface of the first sphere after the two spheres are connected by the wire? Use the reference V = 0 for r at infinity. A) V B) V C) V D) V E) none of the above 70. The figure shows portions of four equipotential surfaces whose potentials are related as follows: V 1 > V 2 > V 3 > V 4. 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. Page 25 of 40

26 71. 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. 72. 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 73. 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 Page 26 of 40

27 74. A solid conducting sphere of radius r a is placed concentrically inside a conducting spherical shell of inner radius r b1 and outer radius r b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge. The potential for r b1 < r < r b2 is A) B) C) D) E) zero 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 ouside of the shell has a charge of +Q and the ball has a charge of Q. 76. Dielectric breakdown occurs in the air at an electric field strength of E max = V/m. If the maximum charge that can be placed on a spherical conductor is 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 Page 27 of 40

28 77. 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 78. 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. 79. Calculate the change in electrostatic potential energy of a charge, Q = 1 µc, when it is moved from a distance x = 4 m to 2 m from an infinite plane of uniform surface charge density σ = 10 µc/m 2. A) 1.13 J B) J C) 1.69 J D) 2.82 J E) zero 80. 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. Page 28 of 40

29 81. 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. 82. 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/ You want to store excess electrons on the negative plate of a capacitor at 9.0 V. How large a capacitance must you use? A) µf B) 0.18 µf C) 0.18 nf D) 14 pf E) 5.6 pf 84. 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 85. 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) F B) F C) F D) F E) F Page 29 of 40

30 86. A capacitor is constructed by placing a conducting sphere of radius a concentrically inside a thin conducting spherical shell of radius b. Derive an expression for the capacitance of such a capacitor. A) B) C) D) E) It is not possible to construct such a capacitor. 87. 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 true. 88. 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 89. 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 Page 30 of 40

31 90. You attach a 30-pF capacitor across a 1.5-V battery. How much energy is stored in the capacitor? A) J B) J C) J D) J E) J 91. 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 92. A coaxial cable has the inner wire of radius a = 1 mm and the outside shield of radius b = 8 mm. The electric field strength between the wire and the shield is given by A) nj B) 6.69 µj C) 3.34 µj D) 14.5 µj E) zero. The electrostatic energy per meter of the cable is Page 31 of 40

32 Use the following to answer questions 93 and You connect three capacitors as shown in the diagram below. The effective capacitance of this combination when C 1 = 5.0 µf, C 2 = 4.0 µf, and C 3 = 3.0 µf is approximately A) 0.44 µf B) 2.3 µf C) 3.5 µf D) 5.2 µf E) 12 µf 94. You connect three capacitors as shown in the diagram. C 1 = 5.0 µf, C 2 = 4.0 µf, and C 3 = 3.0 µf. If you apply 12 V between points A and B, the energy stored in C 3 will be approximately A) 0.16 mj B) 41 µj C) 0.12 mj D) 0.41 mj E) 16 mf 95. 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. Page 32 of 40

33 96. You connect two capacitors C 1 = 15 pf and C 2 = 30 pf in series across a 1.5-V battery. The potential difference across capacitor C 1 is approximately A) 0.50 V B) 1.0 V C) 1.5 V D) 0.33 V E) 0.67 V 97. If C 1 < C 2 < C 3 < C 4 for the combination of capacitors shown, the equivalent capacitance A) is less than C 1. B) is more than C 4. C) is between C 2 and C 3. D) is less than C 2. E) could be any value depending on the applied voltage. 98. If C 1 < C 2 < C 3 < C 4 for the combination of capacitors shown, the equivalent capacitance A) is less than C 1. B) is more than C 4. C) is between C 2 and C 3. D) is more than C 2. E) could be any value depending on the applied voltage. Page 33 of 40

34 99. 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 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) C B) C C) C D) C E) C 101. If all the four capacitors have equal values of 50 µf then calculate the equivalent capacitance of the circuit shown. A) 50 µf B) 30 µf C) 75 µf D) 100 µf E) 83 µf Page 34 of 40

35 102. A capacitor, C 1 = 5.0 µf, is charged up to 8 V. It is then connected to a second uncharged capacitor C 2 = 2.5 µf. The charge on C 1 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 103. 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 ε 0 = F/m.) A) 43 nf B) 0.16 µf C) 0.58 µf D) 2.0 µf E) 7.3 µf 104. 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. Page 35 of 40

36 105. 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 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 107. 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. Page 36 of 40

37 108. 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 109. The space between the inner wire of radius a = 1 mm of a co-axial cable and the conducting shield of radius b = 8 mm is made of nylon (κ = 4.2). A potential difference of 20 V is maintained between the wire and the shield. The energy stored per meter of the cable is A) 1.12 nj/m B) 22.5 nj/m C) 44.9 nj/m D) 5.36 nj/m E) 2.68 nj/m 110. 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 Page 37 of 40

38 Answer Key - practice questions for chapters C 2. B 3. A 4. B 5. A 6. C 7. C 8. C 9. D 10. A 11. A 12. A 13. B 14. A 15. A 16. B 17. A 18. D 19. B 20. D 21. A 22. D 23. A 24. C 25. C 26. E 27. B 28. B 29. A 30. C 31. D 32. A 33. D 34. D 35. B 36. B 37. D 38. C 39. E 40. A 41. A 42. D 43. B 44. B Page 38 of 40

39 45. A 46. C 47. B 48. C 49. E 50. E 51. E 52. D 53. E 54. A 55. A 56. C 57. E 58. E 59. B 60. D 61. E 62. B 63. C 64. A 65. B 66. E 67. C 68. D 69. A 70. E 71. C 72. A 73. A 74. C 75. D 76. B 77. A 78. C 79. A 80. D 81. A 82. B 83. C 84. E 85. A 86. A 87. C 88. A 89. C 90. A Page 39 of 40

40 91. C 92. D 93. B 94. C 95. D 96. B 97. B 98. A 99. D 100. E 101. B 102. A 103. C 104. A 105. E 106. E 107. B 108. C 109. B 110. B Page 40 of 40

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