Physics 202 Spring 2010 Note: Answer key is at end. · PDF filePage1of40% Physics 202 Spring...

of 40

Physics 202 Spring 2010

Practice Questions for Chapters 21-24 Note: Answer key is at end. 1. 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) 7.9 × 10–7 C B) 2.9 × 10–7 C C) 7.5 × 10–2 C D) 6.3 × 10–13 C E) 1.8 × 10–7 C

of 40

3. Charges q1 and q2 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 4.0 × 10–8 C and –2.0 × 10–8 C are placed 12 cm apart. A third point

charge of 3.0 × 10–8 C halfway between the first two point charges experiences a force of magnitude

A) 4.5 × 10–3 N B) 2.0 × 10–3 N C) 1.5 × 10–3 N D) zero E) 5.0 × 10–3 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

of 40

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) 2.2 × 107 N/C to the left B) 1.8 × 107 N/C to the right C) 1.8 × 107 N/C to the left D) 3.2 × 106 N/C to the right E) 4.0 × 106 N/C to the left

of 40

9. Three charges Q1, Q2, and Q3, each equal to 6.4 × 10–19 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 Q2 on a line at right angles to the line between Q1 and Q3, is

A) 1.2 × 10–8 N/C B) 16 N/C C) 2.0 N/C D) 1.9 × 1010 N/C E) 1.2 × 108 N/C 10. Three charges, each of Q = 3.2 × 10–19 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) 1.4 × 107 N/C B) 1.0 × 1011 N/C C) 3.6 × 1010 N/C D) 30 N/C E) 1.8 × 107 N/C

of 40

11. The electric field at point A is zero. What is charge Q1?

A) +32 µC B) –32 µC C) The field cannot be zero at A for any value of Q1. D) +16 µC E) –16 µC 12. Charges Q1 = –q and Q2 = +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) 5 13. Two charges Q1 and Q2 are a distance d apart. If the electric field is zero at a distance

of 3d/4 from Q1 (towards Q2), then what is the relation between Q1 and Q2? A) Q1 = Q2 /9 B) Q1 = 9Q2 C) Q1 = Q2 /3 D) Q1 = 3Q2 E) Q1 = 4Q2 /3

of 40

14. A bob of mass m (m = 0.500 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) 1.73 × 101 N/C and Q is positive. B) 9.81 × 101 N/C and Q is negative. C) 9.81 × 101 N/C and Q is positive. D) 1.73 × 101 N/C and Q is negative. E) 1.80 × 10–1 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)

of 40

16. In the diagram, Q1 = 9.0 µC and Q2 = –9.0 µC. If Q2 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/s2 C) 6.8 cm/s2 D) 4.5 m/s2 E) 7.5 cm/s2 17. 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) 9.6 × 106 m/s B) 3.9 × 103 m/s C) 3.1 × 108 m/s D) 5.5 × 103 m/s E) 7.4 × 106 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.

of 40

19. Two electric dipoles, p1 and p2, are arranged as shown. The first dipole is not free to rotate but the second dipole can rotate in any direction. Which way will p2 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 3.0 × 10–6 N/C. What is the magnitude of the torque on the dipole?

A) 3.2 × 10–16 N · m B) 6.2 × 10–16 N · m C) 1.4 × 10–15 N · m D) 6.8 × 10–16 N · m E) 7.5 × 10–16 N · m

of 40

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/m2. 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

of 40

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/x2. 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

of 40

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 · m2/C B) 0.20 kN · m2/C C) 0.40 kN · m2/C D) 0.50 kN · m2/C E) 0.13 kN · m2/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 · m2/C C) 0.25 kN · m2/C D) 1.3 N · m2/C E) 0.13 MN · m2/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) 1.03 × 106 N.m2/C B) 2.58 × 105 N.m2/C C) 8.13 × 108 N.m2/C D) 1.72 × 105 N.m2/C E) 1.35 × 108 N.m2/C

of 40

32. A horizontal surface of area 0.321 m2 has an electric flux of 123 N.m2/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.m2/C B) 423 N.m2/C C) 1.10 × 10–3 N.m2/C D) 2.36 × 10–3 N.m2/C E) 383 N.m2/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 = (4πε0)–1,

A) kλ/r2 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) 3.0 × 105 N/C B) 2.6 × 105 N/C C) 1.0 × 105 N/C D) 7.4 × 104 N/C E) 3.6 × 106 N/C

of 40

35. A sphere of radius 8.0 cm carries a uniform volume charge density ρ = 500 nC/m3. 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/m3. 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/m3. 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

of 40

38. An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density σ = 12 nC/m2. 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/m2. 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/m2. 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

of 40

Use the following to answer questions 41-42. 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/b2 42. Which diagram best represents the electric field along the y–axis?

A) 1 B) 2 C) 3 D) 4 E) none of the diagrams

of 40

43. A non-conducting pipe has a uniform charge density of 50 C/m3. 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) 5.2 × 109 N/C B) 2.6 × 1011 N/C C) 8.2 × 1010 N/C D) 4.7 × 1011 N/C E) 4.9 × 1010 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) ε0/σ B) σ/ε0 C) ε0/σ2 D) ε0

2/σ2 E) σ2/ε0 45. 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/s B) 2.8 × 106 m/s C) 6.2 × 107 m/s D) 7.7 × 1015 m/s E) 5.3 × 107 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

of 40

47. 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 48. 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 49. 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

of 40

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 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 N C) 1.6 × 10–18 N D) 4.8 × 10–16 N E) 3.2 × 10–14 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.

of 40

Use the following to answer questions 52-53. 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/V2

of 40

55. 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 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

of 40

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) 5 58. 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)

of 40

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) 6 61. The electric potential is known to be a function of x only; i.e., v = V(x). The electric

field at a position x1 is given by A) V(x1) 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

of 40

Use the following to answer question 63.

63. 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 q0 = 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

of 40

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) 1.0 × 101 m B) 1.0 × 102 m C) 3.2 × 10–1 m D) 1.0 × 10–1 m E) none of the above

of 40

69. A conducting sphere of radius r1 = 10 cm and charge q1 = 2 µC is placed far apart from a second conducting sphere of radius r2 = 30 cm and charge q2 = 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) 1.12 × 105 V B) 1.80 × 105 V C) 2.25 × 105 V D) 2.70 × 105 V E) none of the above 70. 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.

of 40

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

of 40

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 rb1 < r < rb2 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 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

of 40

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/m2.

A) 1.13 J B) 0.565 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.

of 40

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 1/4. 83. 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 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) 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

of 40

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

of 40

90. 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 J B) 4.5 × 10–11 J C) 6.7 × 10–11 J D) 3.4 × 10–8 J E) 4.5 × 10–8 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

. The electrostatic energy per meter of the cable is

A) 0.328 nJ B) 6.69 µJ C) 3.34 µJ D) 14.5 µJ E) zero

of 40

Use the following to answer questions 93 and 94.

93. 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 94. 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 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.

of 40

96. 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 97. 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. 98. 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.

of 40

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. 100. 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 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

of 40

102. 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 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 ε0 = 8.85 × 10–12 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.

of 40

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. 106. 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.

of 40

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

of 40

Answer Key - practice questions for chapters 21-24 1. 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

of 40

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

of 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

Physics 202 Spring 2010 Note: Answer key is at end. · PDF filePage1of40% Physics 202 Spring...

Documents

Transcript of Physics 202 Spring 2010 Note: Answer key is at end. · PDF filePage1of40% Physics 202 Spring...