1. d. According to the right-hand rule, the magnetic force on a positive charge carrier is to the right.

2. No. The charge carriers in the wire move parallel to $\vec{B}$. There’s no magnetic force on a charge moving parallel to a magnetic field. 

3. ${\mathit{F}}_2\mathbf{=}{\mathit{F}}_4\mathbf{>}{\mathit{F}}_1\mathbf{=}{\mathit{F}}_3\mathbf{.}$ $\vec{F}{}_1$ is zero because there’s no field. $\vec{F}{}_3$ is also zero because there’s no current around the loop. The charge carriers in both the right and left edges are pushed to the bottom of the loop, creating a motional emf but no current. The currents at 2 and 4 are in opposite directions, but the forces on the segments in the field are both to the left and of equal magnitude.

4. Clockwise. The wire’s magnetic field as it passes through the loop is into the page. The flux through the loop decreases into the page as the wire moves away. To oppose this decrease, the induced magnetic field needs to point into the page.

5. d. The flux is increasing into the loop. To oppose this increase, the induced magnetic field needs to point out of the figure. This requires a ccw induced current. Using the right-hand rule, the magnetic force on the current in the left edge of the loop is to the right, away from the field. The magnetic forces on the top and bottom segments of the loop are in opposite directions and cancel each other.

6. b or f. The potential decreases in the direction of increasing current and increases in the direction of decreasing current.

7. ${\mathit{\tau }}_{\mathbf{C}}\mathbf{>}{\mathit{\tau }}_{\mathbf{A}}\mathbf{>}{\mathit{\tau }}_{\mathbf{B}}\mathbf{.}$ $\tau =L/R$, so smaller total resistance gives a larger time constant. The parallel resistors have total resistance R/2. The series resistors have total resistance 2R.

1. $2.0\times {10}^4\text{m}\text{/}\text{s}$

3. 0.10 T, into the page

5. $0\text{T}{\text{m}}^2$

7. $3.8\times {10}^{-4}\text{T}{\text{m}}^2$

9.

1. Yes, right to left

2. No

11.

1. $8.7\times {10}^{-4}\text{Wb}$

2. Clockwise

13.

1. 20 mA, ccw

2. 20 mA, ccw

3. 0 A

15. Decreasing, 7.8 T/s

17.

1. $1.6\times {10}^{-3}(1+t)\text{A}$

2. $9.4\times {10}^{-3}\text{A,}1.7\times {10}^{-2}\text{A}$

19.

21. 1.3 T

23. 2400

25. 1.0 ms

27. 0.20 J

29. 250 kHz to 360 kHz

31. $3.8\times {10}^{-18}\text{F}$

33. $30\text{nF}$

35. $1.7\times {10}^{-4}\text{s}$

37. 1.6 A, 0.0 A, $-1.6\text{A}$

39. 8.7 T/s

41. $\epsilon =2\beta \pi r_0^{2}B{e}^{-2\beta t}$

43.

1. 32 A

2. 1.3 m/s

45. $44\mu \text{A}$

47. $-15\mu \text{A}$

49. 0.15 T

51. 4.0 nA

53.

1. Ccw

2. 15 A

55.

1. 0.20 A

2. 4.0 mN

3. 11 K

57.

1. $\text{(}4.9\times {10}^{-3}\text{)}f\text{ sin(}2\pi ft)\text{ A}$

2. $4.1\times {10}^2\text{Hz}$, no

59.

1. ${\displaystyle \frac{{\epsilon }_{\text{bat}}}{Bl}}$

2. $\text{0}\text{.98 m/s}$

61. 3.9 μC

63. $(R^2/2r)(dB/dt)$

65. 3.0 s

67. 0.75 A

69.

1. $1.9\times {10}^{-4}\text{T}$

2. $92\text{Ω}$

71.

1. $6.3\times {10}^{-7}\text{s}$

2. 0.050 mA

73. 2.0 mH, $0.13\mu F$

75.

1. 50 V

2. Close $S_1\text{ at }t=0\text{ s, open }{S}_1\text{ and close }{S}_2\text{ at }t=0.0625\text{ s,}\text{then open }{S}_2\text{ at} t=0.1875\text{ s}$

77.

1. $I_0=\text{Δ}{V}_{\text{bat}}/R$

2. $I=I_0(1-e^{-t/(L/R)})$

79. 0.72 mH

81. 1.0 mA

83.

• a. $v_0{e}^{-bt}\text{, where }b=l^2{B}^2/\left(mR\right)$

• b.

  

  Full Alternative Text

85. $1.6\times {10}^2\text{A}\text{/}\text{s}$