CH 30

30.1.0 3. 1 weber is the same as: A) 1 V⋅s B) 1 T⋅s C) 1 T/m D) 1 V/s E) 1 T/m2

A Difficulty: E Section: 30-1

30.1.0 5. The magnetic flux ΦB through a surface: A) is the amount of magnetic field piercing the surface. B) is the magnetic field multiplied by the area. C) does not depend on the area involved. D) is the line integral of the magnetic field around the edge of the surface. E) is the amount of magnetic field skimming along the surface.

A Difficulty: E Section: 30-1

30.1.1 6. The normal to a certain 1.0 m2 area makes an angle of 60° with a uniform magnetic field. The magnetic flux through this area is the same as the flux through a second area that is perpendicular to the field if the second area is: A) 0.50 m2 B) 0.87 m2 C) 1.0 m2 D) 1.2 m2 E) 2.0 m2

A Difficulty: E Section: 30-1

30.1.10 38. A circular loop of wire is positioned half in and half out of a square region of constant uniform magnetic field directed into the page, as shown. To induce a clockwise current in this loop: A) move it in +x direction B) move it in +y direction C) move it in -x direction D) move it in -y direction E) increase the strength of the magnetic field

A Difficulty: E Section: 30-1

30.1.11 42. At a particular instant of time the total magnetic flux through a stationary conducting loop is less in magnitude than the flux associated with an externally applied field. This might occur because: A) the applied field is normal to the loop and increasing in magnitude B) the applied field is normal to the loop and decreasing in magnitude C) the applied field is parallel to the plane of the loop and increasing in magnitude D) the applied field is parallel to the plane of the loop and decreasing in magnitude E) the applied field is tangent to the loop

A Difficulty: E Section: 30-1

30.3.2 55. The unit "henry" is equivalent to: A) volt⋅second/ampere B) volt/second C) ohm D) ampere⋅volt/second E) ampere⋅second/volt

A Difficulty: E Section: 30-4

31.1.3 6. Consider the mechanical system consisting of two springs and a block, as shown. Which one of the five electrical circuits (I, II, III, IV, V) is the analog of the mechanical system? A) I B) II C) III D) IV E) V

A Difficulty: E Section: 31-1

30.1.7 27. A merry-go-round has an area of 300 m2 and spins at 2 rpm about a vertical axis at a place where the Earth's magnetic field is vertical and has a magnitude of 5 × 10-5 T. The emf around the rim is: A) 0 V B) 0.5 mV C) 3.1 mV D) 15 mV E) 190 mV

A Difficulty: M Section: 30-1

30.1.7 22. A rectangular loop of wire is placed perpendicular to a uniform magnetic field and then spun around one of its sides at frequency f. The induced emf is a maximum when: A) the flux is zero B) the flux is a maximum C) the flux is half its maximum value D) the derivative of the flux with respect to time is zero E) none of the above

A Difficulty: M Section: 30-1

30.2.1 46. A rod of length L and electrical resistance R moves through a constant uniform magnetic field B; both the magnetic field and the direction of motion are parallel to the rod. The force that must be applied by a person to keep the rod moving with constant velocity v is: A) 0 B) BLv C) BLv/R D) B2L2v/R E) B2L2v2/R

A Difficulty: M Section: 30-2

30.5.3 66. An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to an ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. The current reaches half its final value at a time of: A) 2.8 ms B) 4.0 ms C) 3.0 s D) 170 s E) 250 s

A Difficulty: M Section: 30-6

30.6.10 76. An inductor with inductance L and a resistor with resistance R are wired in series to an ideal battery with emf E. A switch in the circuit is closed at time t = 0, at which time the current is zero. A long time after the switch is thrown the potential differences across the inductor and resistor are: A) 0, E B) E, 0 C) E/2, E/2 D) (L/R) E, (R/L) E E) unknown since the rate of change of the current is not given

A Difficulty: M Section: 30-6

31.1.1 3. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the energy stored in the magnetic field of the inductor is a maximum is: A) T/4 B) T/2 C) T D) 3T/2 E) 2T

A Difficulty: M Section: 31-1

30.3.2 53. A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with magnitude that is changing linearly with time. If r is the radial distance from the cylinder axis, the magnitude of the induced electric field inside the cylindrical region is proportional to: A) R B) r C) r2 D) 1/r E) 1/r2

B Difficulty: E Section: 30-3

1. The emf that appears in Faraday's law is: A) around a conducting circuit B) around the boundary of the surface used to compute the magnetic flux C) throughout the surface used to compute the magnetic flux D) perpendicular to the surface used to compute the magnetic flux E) none of the above

B Difficulty: E Section: 30-1

30.1.10 33. A long straight wire is in the plane of a rectangular conducting loop. The straight wire initially carries a constant current i in the direction shown. While the current i is being shut off, the current in the loop is: A) zero B) clockwise C) counterclockwise D) clockwise in the left side and counterclockwise in the right side E) counterclockwise in the left side and clockwise in the right side

B Difficulty: E Section: 30-1

30.1.4 7. Suppose this page is perpendicular to a uniform magnetic field and the magnetic flux through it is 5.0 Wb. If the page is turned by 30° around an edge the flux through it will be: A) 2.5 Wb B) 4.3 Wb C) 5.0 Wb D) 5.8 Wb E) 10 Wb

B Difficulty: E Section: 30-1

30.1.5 13. The emf developed in a coil X due to the current in a neighboring coil Y is proportional to the: A) magnetic field in X B) rate of change of magnetic field in X C) resistance of X D) thickness of the wire in X E) current in Y

B Difficulty: E Section: 30-1

30.1.7 19. The graph shows the magnitude B of a uniform magnetic field that is perpendicular to the plane of a conducting loop. Rank the four regions indicated on the graph according to the magnitude of the emf induced in the loop, from least to greatest. A) 1, 2, 3, 4 B) 2, 4, 3, 1 C) 4, 3, 1, 2 D) 1, 3, 4, 2 E) 4, 3, 2, 1

B Difficulty: E Section: 30-1

30.1.7 23. A copper hoop is held in a vertical east-west plane in a uniform magnetic field whose field lines run along the north-south direction. The largest induced emf is produced when the hoop is: A) rotated about a north-south axis B) rotated about an east-west axis C) moved rapidly, without rotation, toward the east D) moved rapidly, without rotation, toward the south E) moved rapidly, without rotation, toward the northwest

B Difficulty: E Section: 30-1

30.1.9 30. A square loop of wire lies in the plane of the page. A decreasing magnetic field is directed into the page. The induced current in the loop is: A) counterclockwise B) clockwise C) zero D) up the left edge and from right to left along the top edge E) through the middle of the page

B Difficulty: E Section: 30-1

30.2.3 50. An electric field is associated with every: A) magnetic field B) time-dependent magnetic field C) position-dependent magnetic field D) object moving in a magnetic field E) conductor moving in a magnetic field

B Difficulty: E Section: 30-3

31.1.1 4. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the energy stored in the electric field of the capacitor is a maximum is: A) T/4 B) T/2 C) T D) 3T/2 E) 2T

B Difficulty: E Section: 31-1

30.1.11 43. The circuit shown is in a uniform magnetic field that is into the page. The current in the circuit is 0.20 A. At what rate is the magnitude of the magnetic field changing? Is it increasing or decreasing? A) 0 T/s B) 140 T/s, decreasing C) 140 T/s, increasing D) 420 T/s, decreasing E) 420 T/s, increasing

B Difficulty: M Section: 30-1

30.1.5 17. A car travels northward at 75 km/h along a straight road in a region where Earth's magnetic field has a vertical component of 0.50 × 10-4 T. The emf induced between the left and right side, separated by 1.7 m, is: A) 0 V B) 1.8 mV C) 3.6 mV D) 6.4 mV E) 23 mV

B Difficulty: M Section: 30-1

30.2.2 48. As a loop of wire with a resistance of 10 Ω moves in a non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5 mJ/s. The induced emf in the loop is: A) 0 V B) 0.22 V C) 0.28 V D) 2.0 V E) cannot be calculated from the given data

B Difficulty: M Section: 30-2

30.2.2 49. Which statement about eddy currents is false? A) They can be prevented by cutting a slot in a solid conducting plate, to prevent electrons from being able to make a complete circuit. B) The mechanical energy that is lost when eddy currents are created returns when the eddy currents cease. C) They can be used as a passive braking system, as no external power source is needed if permanent magnets are used. D) They are created in solid conducting plates as they move in and out of magnetic fields. E) The faster the conductor moves, the larger the eddy currents will be.

B Difficulty: M Section: 30-2

30.4.2 57. A long narrow solenoid has length ℓ and a total of N turns, each of which has cross-sectional area A. Its inductance is: A) µ0N2Aℓ B) µ0N2A/ℓ C) µ0NA/ℓ D) µ0N2 ℓ/A E) none of these

B Difficulty: M Section: 30-4

30.5.2 63. A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel. When the total emf of the combination is 16 V, the rate of change of the current in the larger inductor is: A) 2.0 × 103 A/s B) 3.6 × 103 A/s C) 4.6 × 103 A/s D) 7.0 × 103 A/s E) 8.1 × 103 A/s

B Difficulty: M Section: 30-5

30.6.10 74. An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to a 20-V ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. After a long time the current in the resistor and the current in the inductor are: A) 0 A, 0 A B) 10 A, 10 A C) 2.5 A, 2.5 A D) 10 A, 2.5 A E) 10 A, 0 A

B Difficulty: M Section: 30-6

30.6.10 75. An 8.0-mH inductor and a 2.0-Ω resistor are wired in series to a 20-V ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. Immediately after the switch is thrown the potential differences across the inductor and resistor are: A) 0 V, 20 V B) 20 V, 0 V C) 10 V, 10 V D) 16 V, 4 V E) unknown since the rate of change of the current is not given

B Difficulty: M Section: 30-6

30.6.5 70. When the switch S in the circuit shown is closed, the time constant for the growth of current in R2 is: A) L/R1 B) L/R2 C) L/(R1 + R2) D) L(R1 + R2)/(R1R2) E) (L/R1 + L/R2)/2

B Difficulty: M Section: 30-6

30.7.2 84. A current of 10 A in a certain inductor results in a stored energy of 40 J. When the current is changed to 5 A in the opposite direction, the stored energy changes by: A) 20 J B) 30 J C) 40 J D) 50 J E) 60 J

B Difficulty: M Section: 30-7

30.7.2 85. A 6.0 mH inductor is in a series circuit with a resistor and an ideal battery. At the instant the current in the circuit is 5.0 A the energy stored in the inductor is: A) 0 J B) 7.5 × 10-2 J C) 15 × 10-2 J D) 30 × 10-2 J E) unknown since the rate of change of the current is not given

B Difficulty: M Section: 30-7

30.8.0 88. A 0.20-cm radius cylinder, 3.0 cm long, is wrapped with wire to form an inductor. At the instant the magnetic field in the interior is 5.0 mT, the energy stored in the field is: A) 0 J B) 3.8 × 10-6 J C) 7.5 × 10-6 J D) 7.5 × 10-4 J E) 9.9 J

B Difficulty: M Section: 30-8

30.9.1 90. Two coils have a mutual inductance of 3.5 mH. If the current in one coil is changing at a rate of 4.8 A/s, what is the emf induced in the second coil? A) 7.3 x 10-4 V B) 0.017 V C) 1400 V D) cannot tell without knowing the inductance of the second coil E) cannot tell without knowing the current in the second coil

B Difficulty: M Section: 30-9

31.1.0 2. A charged capacitor and an inductor are connected in series. At time t = 0 the current is zero, but the capacitor is charged. If T is the period of the resulting oscillations, the next time, after t = 0 that the voltage across the inductor is a maximum is: A) T/4 B) T/2 C) T D) 3T/2 E) 2T

B Difficulty: M Section: 31-1

31.1.3 7. A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm and released from rest. In the electrical analog the initial charge on the capacitor is: A) 0.15 C B) 0.25 C C) 8.8 C D) 15 C E) 35 C

B Difficulty: M Section: 31-1

30.1.10 31. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries a constant current i, as shown. While the wire is being moved toward the loop, the current in the loop is: A) zero B) clockwise C) counterclockwise D) clockwise in the left side and counterclockwise in the right side E) counterclockwise in the left side and clockwise in the right side

C Difficulty: E Section: 30-1

30.1.10 32. A long straight wire is in the plane of a rectangular conducting loop. The straight wire carries an increasing current in the direction shown. The current in the loop is: A) zero B) clockwise C) counterclockwise D) clockwise in the left side and counterclockwise in the right side E) counterclockwise in the left side and clockwise in the right side

C Difficulty: E Section: 30-1

30.1.10 34. A rectangular loop of wire is placed midway between two long straight parallel conductors as shown. The conductors carry currents i1 and i2 as indicated. If i1 is increasing and i2 is constant, then the induced current in the loop is: A) zero B) clockwise C) counterclockwise D) depends on i1 - i2 E) depends on i1 + i2

C Difficulty: E Section: 30-1

30.1.10 35. You push a permanent magnet with its north pole away from you toward a loop of conducting wire in front of you. Before the north pole enters the loop the current in the loop is: A) zero B) clockwise C) counterclockwise D) to your left E) to your right

C Difficulty: E Section: 30-1

30.1.10 39. The figure shows a bar moving to the right on two conducting rails. To make an induced current i in the direction indicated, a constant magnetic field between the rails should be in what direction? A) Right B) Left C) Into the page D) Out of the page E) Impossible, cannot be done with a constant magnetic field

C Difficulty: E Section: 30-1

30.1.10 40. A square loop of wire moves with a constant speed v from a field-free region into a region of uniform B field, as shown. Which of the five graphs correctly shows the induced current i in the loop as a function of time t? A) I B) II C) III D) IV E) V

C Difficulty: E Section: 30-1

30.1.4 8. A 2.0 T uniform magnetic field makes an angle of 30° with the z axis. The magnetic flux through a 3.0 m2 portion of the xy plane is: A) 2.0 Wb B) 3.0 Wb C) 5.2 Wb D) 6.0 Wb E) 12 Wb

C Difficulty: E Section: 30-1

30.1.5 11. Faraday's law states that an induced emf is proportional to: A) the rate of change of the magnetic field B) the rate of change of the electric field C) the rate of change of the magnetic flux D) the rate of change of the electric flux E) zero

C Difficulty: E Section: 30-1

30.7.2 83. In each of the following operations, energy is expended. The LEAST percentage of returnable electrical energy will be yielded by: A) charging a capacitor B) charging a storage battery C) sending current through a resistor D) establishing a current through an inductor E) moving a conducting rod through a magnetic field

C Difficulty: E Section: 30-7

30.1.5 16. A rod lies across frictionless rails in a uniform magnetic field B, as shown. The rod moves to the right with speed v. In order for the emf around the circuit to be zero, the magnitude of the magnetic field should: A) not change B) increase linearly with time C) decrease linearly with time D) increase quadratically with time E) decrease quadratically with time

C Difficulty: M Section: 30-1

30.1.7 25. The diagram shows a circular loop of wire that rotates at a steady rate about a diameter O that is perpendicular to a uniform magnetic field. The maximum induced emf occurs when the point X on the loop passes: A) a B) b C) c D) d E) e

C Difficulty: M Section: 30-1

30.3.1 51. A cylindrical region of radius R = 3.0 cm contains a uniform magnetic field parallel to its axis. If the electric field induced at a point R/2 from the cylinder axis is 4.5 × 10-3 V/m the magnitude of the magnetic field must be changing at the rate of: A) 0 T/s B) 0.30 T/s C) 0.60 T/s D) 1.2 T/s E) 2.4 T/s

C Difficulty: M Section: 30-3

30.4.0 56. A 10-turn ideal solenoid has an inductance of 3.5 mH. When the solenoid carries a current of 2.0 A the magnetic flux through each turn is: A) 0 Wb B) 3.5 × 10-4 Wb C) 7.0 × 10-4 Wb D) 7.0 × 10-3 Wb E) 7.0 × 10-2 Wb

C Difficulty: M Section: 30-4

30.4.3 58. A flat coil of wire, having 5 turns, has an inductance L. The inductance of a similar coil having 20 turns is: A) 4L B) L/4 C) 16L D) L/16 E) L

C Difficulty: M Section: 30-4

30.5.2 61. A 3.5 mH inductor and a 4.5 mH inductor are connected in series and a time varying current is established in them. When the total emf of the combination is 16 V, the emf of the larger inductor is: A) 2.3 V B) 7.0 V C) 9.0 V D) 28 V E) 36 V

C Difficulty: M Section: 30-5

30.6.10 77. The diagrams show three circuits with identical batteries, identical inductors, and identical resistors. Rank them according to the current through the battery just after the switch is closed, from least to greatest. A) 3, 2, 1 B) 2 and 3 tie, then 1 C) 1, 3, 2 D) 1, 2, 3 E) 2, 3, 1

C Difficulty: M Section: 30-6

30.6.10 79. A 6.0 mH inductor is in a circuit. At the instant the current is 5.0 A and its rate of change is 200 A/s, the rate with which the energy stored in the inductor is increasing is: A) 7.5 × 10-2 W B) 3.0 W C) 6.0 W D) 120 W E) 240 W

C Difficulty: M Section: 30-7

30.7.2 86. A 6.0-mH inductor and a 3.0-Ω resistor are wired in series to a 12-V ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. 2.0 ms later the energy stored in the inductor is: A) 0 J B) 9.6 × 10-3 J C) 1.9 × 10-2 J D) 2.5 × 10-2 J E) 3.8 × 10-2 J

C Difficulty: M Section: 30-7

31.1.3 8. A 150-g block on the end of a spring with a spring constant of 35 N/m is pulled aside 25 cm and released from rest. In the electrical analog the maximum charge on the capacitor is 0.25 C. The maximum current in the LC circuit is: A) 0.025 A B) 0.12 A C) 3.8 A D) 5.3 A E) 40 A

C Difficulty: M Section: 31-1

30.1.0 2. 1 weber is the same as: A) 1 V/s B) 1 T/s C) 1 T/m D) 1 T⋅m2 E) 1 T/m2

D Difficulty: E Section: 30-1

30.1.10 41. As an externally generated magnetic field through a certain conducting loop increases in magnitude, the field produced at points inside the loop by the current induced in the loop must be: A) increasing in magnitude B) decreasing in magnitude C) in the same direction as the applied field D) directed opposite to the applied field E) perpendicular to the applied field

D Difficulty: E Section: 30-1

30.1.4 10. In the experiment shown: A) there is a steady reading in G as long as S is closed B) a motional emf is generated when S is closed C) the current in the battery goes through G D) there is a current in G just after S is opened or closed E) since the two loops are not connected, the current in G is always zero

D Difficulty: E Section: 30-1

30.1.5 12. If the magnetic flux through a certain region is changing with time: A) energy must be dissipated as heat B) an electric field must not exist at the boundary C) a current must flow around the boundary D) an emf must exist around the boundary E) a magnetic field must exist at the boundary

D Difficulty: E Section: 30-1

30.1.5 15. Coils P and Q each have a large number of turns of insulated wire. When switch S is closed, the pointer of galvanometer G is deflected toward the left. Now that S is closed, to make the pointer of G deflect toward the right one could: A) move the slide of the rheostat R quickly to the right B) move coil P toward coil Q C) move coil Q toward coil P D) open S E) do none of the above

D Difficulty: E Section: 30-1

30.1.7 21. The four wire loops shown have edge lengths of either L, 2L, or 3L. They will move with the same speed into a region of uniform magnetic field B directed out of the page. Rank them according to the maximum magnitude of the induced emf, least to greatest. A) 1 and 2 tie, then 3 and 4 tie B) 3 and 4 tie, then 1 and 2 tie C) 4, then 2 and 3 tie, then 1 D) 1, then 2 and 3 tie, then 4 E) 1, 2, 3, 4

D Difficulty: E Section: 30-1

30.1.12 44. A copper penny slides on a horizontal frictionless table. There is a square region of constant uniform magnetic field perpendicular to the table, as shown. Which graph correctly shows the speed v of the penny as a function of time t? A) I B) II C) III D) IV E) V

D Difficulty: E Section: 30-2

30.3.2 54. A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with magnitude that is changing linearly with time. If r is the radial distance from the cylinder axis, the magnitude of the induced electric field outside the cylinder is proportional to: A) R B) r C) r2 D) 1/r E) 1/r2

D Difficulty: E Section: 30-3

30.5.2 65. The diagram shows an inductor that is part of a circuit. The direction of the emf induced in the inductor is indicated. Which of the following is possible? A) The current is constant and rightward B) The current is constant and leftward C) The current is increasing and rightward D) The current is increasing and leftward E) None of the above

D Difficulty: E Section: 30-5

30.7.2 87. The quantity (B2/μo) has units of: A) J B) J/H C) J/m D) J/m3 E) H/m3

D Difficulty: E Section: 30-8

31.1.1 5. The electrical analog of a spring constant k is: A) L B) 1/L C) C D) 1/C E) R

D Difficulty: E Section: 31-1

30.7.0 80. An inductance L and a resistance R are connected in series to an ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. The rate of increase of the energy stored in the inductor is a maximum: A) just after the switch is closed B) at the time t = L/R after the switch is closed C) at the time t = 2L/R after the switch is closed D) at the time t = (L/R)ln 2 after the switch is closed E) a long time after the switch is closed

D Difficulty: H Section: 30-7

30.1.7 18. A rectangular loop of wire has area A. It is placed perpendicular to a uniform magnetic field B and then spun around one of its sides at frequency f. The maximum induced emf is: A) BAf/2π B) BAf C) 2BAf D) 2πBAf E) 4πBAf

D Difficulty: M Section: 30-1

30.1.7 26. A single loop of wire with a radius of 7.5 cm rotates about a diameter in a uniform magnetic field of 1.6 T. To produce a maximum emf of 1.0 V, it should rotate at: A) 0 rad/s B) 2.7 rad/s C) 5.6 rad/s D) 35 rad/s E) 71 rad/s

D Difficulty: M Section: 30-1

30.2.0 45. A rod with resistance R lies across frictionless conducting rails in a constant uniform magnetic field B, as shown. Assume the rails have negligible resistance. The magnitude of the force that must be applied by a person to pull the rod to the right at constant speed v is: A) 0 B) BLv C) BLv/R D) B2L2v/R E) B2Lxv/R

D Difficulty: M Section: 30-2

30.2.1 47. As a loop of wire with a resistance of 10 Ω moves in a constant non-uniform magnetic field, it loses kinetic energy at a uniform rate of 5.0 mJ/s. The induced current in the loop is: A) 0 A B) 2.0 mA C) 2.8 mA D) 22 mA E) cannot be calculated from the given data

D Difficulty: M Section: 30-2

30.5.2 62. A 3.5 mH inductor and a 4.5 mH inductor are connected in parallel. The equivalent inductance is: A) 0.13 mH B) 0.51 mH C) 1.0 mH D) 2.0 mH E) 8.0 mH

D Difficulty: M Section: 30-5

30.6.10 78. Immediately after switch S in the circuit shown is closed, the current through the battery is: A) 0 B) V0/R1 C) V0/R2 D) V0/(R1 + R2) E) V0(R1 + R2)/(R1R2)

D Difficulty: M Section: 30-6

30.6.5 71. An inductance L, resistance R, and ideal battery of emf E are wired in series and the circuit is allowed to come to equilibrium. A switch in the circuit is opened at time t = 0, at which time the current is E/R. At any later time t the current i is given by: A) (E/R)(1 - e-Lt/R) B) (E/R)e-Lt/R C) (E/R)(1 + e-Rt/L) D) (E/R)e-Rt/L E) (E/R)(1 - e-Rt/L)

D Difficulty: M Section: 30-6

30.6.8 72. An inductance L, resistance R, and ideal battery of emf E are wired in series and the circuit is allowed to come to equilibrium. A switch in the circuit is opened at time t = 0, at which time the current is E/R. At any later time t the potential difference across the resistor is given by: A) E(1 - e-Lt/R) B) Ee-Lt/R C) E(1 + e-Rt/L) D) Ee-Rt/L E) E(1 - e-Rt/L)

D Difficulty: M Section: 30-6

30.6.9 73. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the circuit is closed at time t = 0, at which time the current is zero. At any later time t the emf of the inductor is given by: A) E(1 - e-Lt/R) B) Ee-Lt/R C) E(1 + e-Rt/L) D) Ee-Rt/L E) E(1 - e-Rt/L)

D Difficulty: M Section: 30-6

31.1.3 9. Which of the following has the greatest effect in decreasing the oscillation frequency of an LC circuit? Using instead: A) L/2 and C/2 B) L/2 and 2C C) 2L and C/2 D) 2L and 2C E) none of these

D Difficulty: M Section: 31-1

30.1.0 4. The units of motional emf are: A) volt/second B) volt⋅meter/second C) volt/tesla D) tesla/second E) tesla⋅meter2/second

E Difficulty: E Section: 30-1

30.1.10 36. A vertical bar magnet is dropped through the center of a horizontal loop of wire, with its north pole leading. At the instant when the midpoint of the magnet is in the plane of the loop, the induced current in the loop, viewed from above, is: A) maximum and clockwise B) maximum and counterclockwise C) not maximum but clockwise D) not maximum but counterclockwise E) essentially zero

E Difficulty: E Section: 30-1

30.1.10 37. A circular loop of wire rotates about a diameter in a magnetic field that is perpendicular to the axis of rotation. Looking in the direction of the field at the loop the induced current is: A) always clockwise B) always counterclockwise C) clockwise in the lower half of the loop and counterclockwise in the upper half D) clockwise in the upper half of the loop and counterclockwise in the lower half E) sometimes clockwise and sometimes counterclockwise

E Difficulty: E Section: 30-1

30.1.4 9. A uniform magnetic field makes an angle of 30° with the z axis. If the magnetic flux through a 1.0 m2 portion of the xy plane is 5.0 Wb then the magnetic flux through a 2.0 m2 portion of the same plane is: A) 2.5 Wb B) 4.3 Wb C) 5.0 Wb D) 5.8 Wb E) 10 Wb

E Difficulty: E Section: 30-1

30.1.5 14. In the circuit shown, there will be a non-zero reading in galvanometer G: A) only just after S is closed B) only just after S is opened C) only while S is kept closed D) never E) only just after S is opened or closed

E Difficulty: E Section: 30-1

30.1.8 29. A magnet moves inside a coil. Consider the following factors: I. strength of the magnet II. number of turns in the coil III. speed at which the magnet moves Which can affect the emf induced in the coil? A) I only B) II only C) III only D) I and II only E) I, II, III

E Difficulty: E Section: 30-1

30.3.2 52. A cylindrical region of radius R contains a uniform magnetic field parallel to its axis. The field is zero outside the cylinder. If the magnitude of the field is changing at the rate dB/dt, the electric field induced at a point 2R from the cylinder axis is: A) 0 B) 2R dB/dt C) R dB/dt D) (R/2) dB/dt E) (R/4) dB/dt

E Difficulty: E Section: 30-3

30.7.0 81. The stored energy in an inductor: A) depends, in sign, upon the direction of the current B) depends on the rate of change of current C) is proportional to the square of the inductance D) has units J/H E) is none of the above

E Difficulty: E Section: 30-7

30.8.2 89. In the diagram, assume that all the magnetic field lines generated by coil 1 pass through coil 2. Coil 1 has 100 turns and coil 2 has 400 turns. Then: A) the currents will be the same in the two coils B) the emf around coil 1 will be 1/4 the emf around coil 2 C) the current in coil 1 will be 1/4 the current in coil 2 D) the emfs will be the same in the two coils E) none of the above

E Difficulty: E Section: 30-9

30.1.7 20. A changing magnetic field pierces the interior of a circuit containing three identical resistors. Two voltmeters are connected as shown. V1 reads 1 mV across R. V2 reads the voltage across the other two resistors, which is: A) 0 V B) 1/3 mV C) 1/2 mV D) 1 mV E) 2 mV

E Difficulty: M Section: 30-1

30.1.7 24. A 10 turn conducting loop with a radius of 3.0 cm spins at 60 revolutions per second in a magnetic field of 0.50 T. The maximum emf generated is: A) 0.014 V B) 0.085 V C) 0.53 V D) 0.85 V E) 5.3 V

E Difficulty: M Section: 30-1

30.1.7 28. One hundred turns of insulated copper wire are wrapped around an iron core of cross-sectional area 0.100 m2. The circuit is completed by connecting the coil to a 10-Ω resistor. As the magnetic field along the coil axis changes from 1.00 T in one direction to 1.00 T in the other direction, the total charge that flows through the resistor is: A) 0.01 C B) 0.02 C C) 0.2 C D) 1 C E) 2 C

E Difficulty: M Section: 30-1

30.4.3 59. A 10-turn ideal solenoid has an inductance of 4.0 mH. To generate an emf of 2.0 V the current should change at a rate of: A) 0 A/s B) 0.5 A/s C) 50 A/s D) 250 A/s E) 500 A/s

E Difficulty: M Section: 30-5

30.5.2 60. A 3.5 mH inductor and a 4.5 mH inductor are connected in series. The equivalent inductance is: A) 0.13 mH B) 0.51 mH C) 1.0 mH D) 2.0 mH E) 8.0 mH

E Difficulty: M Section: 30-5

30.5.2 64. An inductor with inductance L and an inductor with inductance 2L are connected in parallel. When the rate of change of the current in the larger inductor is 2000 A/s the rate of change of the current in the smaller is: A) 400 A/s B) 1000 A/s C) 1600 A/s D) 2000 A/s E) 4000 A/s

E Difficulty: M Section: 30-5

30.6.3 67. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the circuit is closed at time t = 0, at which time the current is zero. At any later time t the current i is given by: A) (E/R)(1 - e-Lt/R) B) (E/R)e-Lt/R C) (E/R)(1 + e-Rt/L) D) (E/R)e-Rt/L E) (E/R)(1 - e-Rt/L)

E Difficulty: M Section: 30-6

30.6.4 68. An inductance L, resistance R, and ideal battery of emf E are wired in series. A switch in the circuit is closed at time t = 0, at which time the current is zero. At any later time t the potential difference across the resistor is given by: A) E(1 - e-Lt/R) B) Ee-Lt/R C) E(1 + e-Rt/L) D) Ee-Rt/L E) E(1 - e-Rt/L)

E Difficulty: M Section: 30-6

30.6.4 69. If both the resistance and the inductance in an LR series circuit are doubled the new inductive time constant will be: A) twice the old B) four times the old C) half the old D) one-fourth the old E) unchanged

E Difficulty: M Section: 30-6

30.7.2 82. An inductance L and a resistance R are connected in series to an ideal battery. A switch in the circuit is closed at time t = 0, at which time the current is zero. The energy stored in the inductor is a maximum: A) just after the switch is closed B) at the time t = L/R after the switch is closed C) at the time t = L/R2 after the switch is closed D) at the time t = 2L/R after the switch is closed E) a long time after the switch is closed

E Difficulty: M Section: 30-7

1. An LC circuit has an inductance of 15 mH and a capacitance of 10 μF. At one instant the charge on the capacitor is 25 μC. At that instant the current is changing at the rate: A) 0 A/s B) 1.7 × 10-7 A/s C) 5.9 × 10-3 A/s D) 3.8 × 10-2 A/s E) 170 A/s

E Difficulty: M Section: 31-1