1. b. $\vec{v}{}_{\text{AB}}$ is parallel to $\vec{B}{}_{\text{A}}$ hence $\vec{v}{}_{\text{AB}}\times \vec{B}{}_{\text{A}}$ is zero. $\vec{E}{}_{\text{B}}=\vec{E}{}_{\text{A}}$ and points in the positive z-direction. $\vec{v}{}_{\text{AB}}\times \vec{E}{}_{\text{A}}$ points down, in the negative y-direction, so $-\vec{v}{}_{\text{AB}}\times \vec{E}{}_{\text{A}}/c^2$ points in the positive y-direction and causes $\vec{B}{}_{\text{B}}$ to be angled upward.

2. $B{}_C>B{}_A>B{}_D>B{}_{\text{B}}$. The induced magnetic field strength depends on the rate dE/dt at which the electric field is changing. Steeper slopes on the graph correspond to larger magnetic fields.

3. e. $\vec{E}$ is perpendicular to $\vec{B}$ and to $\vec{v}$, so it can only be along the z-axis. According to the Ampère-Maxwell law, $d{\text{Φ}}_{\text{e}}/dt$ has the same sign as the line integral of $\vec{B}\cdot d\vec{s}$ around the closed curve. The integral is positive for a cw integration. Thus, from the right-hand rule, $\vec{E}$ is either into the page (negative z-direction) and increasing, or out of the page (positive z-direction) and decreasing. We can see from the figure that $B$ is decreasing in strength as the wave moves from left to right, so $E$ must also be decreasing. Thus $\vec{E}$ points along the positive z-axis.

4. a. The Poynting vector $\vec{S}=(\vec{E}\times \vec{B})/{\mu }_0$ points in the direction of travel, which is the positive y-direction. $\vec{B}$ must point in the positive x-direction in order for $\vec{E}\times \vec{B}$ to point upward.

5. b. The intensity along a line from the antenna decreases inversely with the square of the distance, so the intensity at 20 km is ${\displaystyle \frac{1}{4}}$ that at 10 km. But the intensity depends on the square of the electric field amplitude, or, conversely, $E_0$ is proportional to $I^{1/2}$. Thus $E_0$ at 20 km is ${\displaystyle \frac{1}{2}}$ that at 10 km.

6. $I{}_D>I{}_A>I{}_B=I{}_{\text{C}}$. The intensity depends on ${\text{cos}}^2\theta$ where $\theta$ is the angle between the axes of the two filters. The filters in D have $\theta =0\text{°}$. The two filters in both B and C are crossed $(\theta =90\text{°})$ and transmit no light at all.

1.

1. Along the $-x\text{-axis}$

2. Along the y-axis $(+\text{or}-)$

3. Along the $+x\text{-axis}$

3. $-1.11\times {10}^{-5}ĵ\text{T}$

5. 11 T, inward

7. $17\mu \text{A}$

11. $6.0\times {10}^5\text{V}\text{/}\text{m}$

13.

1. 628 nm

2. $4.77\times {10}^{14}\text{Hz}$

3. 900 V/m

15. $-z\text{-direction}$

17. 980 V/M, 3.3 T

19.

1. $2.2\times {10}^{-6}{\text{W/m}}^2$

2. 0.041 V/m

21. $4.6\times {10}^{-7}\text{T}$

23. $3.3\times {10}^{-6}\text{T}$, $(-1.7\times {10}^{-6}\text{T})î$

25. 66 mW

27. $(-1.73\times {10}^6î+2.0\times {10}^6ĵ)\text{V}\text{/}\text{m}$

29.

1. $(0.10\text{T}\text{,}\text{into}\text{page})$

2. $0\text{V}\text{/}\text{m}\text{,}(0.10\text{T},\text{ into page})$

31. $(-3.2\times {10}^{-14}î-4.8\times {10}^{-14}ĵ)\text{N}$

33.

1. 0.94 V/m

2. 10.0 T

37.

1. 1.0 mT

2. 0.160 mT

39.

1. $5.4\times {10}^{15}\text{N}\text{/}\text{C}s$

2. Opposite

41.

1. $-14.6\text{,}6.8\times {10}^{-2}$

2. $-260î+140ĵ-200\widehat{k}{\text{W/m}}^2$

43.

1. $3.85\times {10}^{26}\text{W}$

2. $589{\text{W/m}}^2$

45. 1.3 m

47. 0.092 V/m

49. $1.8\times {10}^7\text{V}\text{/}\text{m}$

51. 1.3 m

53. $4.9\times {10}^7{\text{W/m}}^2$

55. 0.41 m/s

57. $63\text{°}$

59.

1. $7.9\times {10}^4\text{m}\text{/}\text{s}$

2. $0.81\text{m}\text{/}{\text{s}}^2$

3. 27 h

4. 1.2 GW

61. $16\text{°}$

63. 8.8 h

65. $5.2\mu \text{V}\text{/}\text{m}$