```
Chapter 30
2. drawing
20. drawing
12. (mu_0)h/2 parallel to sheet; perp to current
32. (a) 171 microT; 137 microT
(b) 0.138 microWb
(c) rate of heat production = 1.54 J/s
38. 168 nT
40. B_square = (mu_0)(2sqrt2)I/(pi)L;
B_square/B_circle = 0.9
46. for ratio of 0.90, x = 0.270 R;
for ratio of 0.10, x = 1.91 R
52. zero
54. (a) 25 V/s
(b) 5.65 Nm²/Cs; 5 microA
58. (mu_0)h²/2  attractive
62. 0.603 N attractive
Chapter 31
4. 92.3 nW
6. graph
12. at t = 0, I = 0; at t = T/4, I is clockwise;
at t = T/2, I = 0; at t = 3T/4, I is clockwise
16. Br_0(alpha)/R_0(1+(beta)t);
clockwise looking down with B out of page,
and current loop in plane of page
30. 24.1 microV away from the wire
42. I'=(2(pi)r²(mu_0)nI_0/Rt_0)e^(-t/t_0)
44. inside E = -R(mu_0)n(omega)I_0cos(omega t)/4;
outside E = -R(mu_0)n(omega)I_0cos(omega t)/4
46. R = 11.3 cm
50. 3.59 m/s
54. (a) left
(b) counter-clockwise
(c) 1.8 A
Chapter 32
12. 9.29 x 10^{-24} Am²
Chapter 33
2. L/volume = (mu_0)n²
8. L_eq = L_1 + L_2
18. L = ((mu_0)N²h/2(pi))ln((R+w)/R);
for R>>w, L = (mu_0)N²A/l
32. (a) L = 9.01 mH
(b) U = 11.3 microJ
40. (a) u_B = (mu_0)I²r²/8(pi²)a^4
(b) U_B/length = (mu_0)I²/16(pi)
42. 351 - 3510 ohms
46. I=(V/R)e^(-Rt/L)
50. 1.52x10^{13} Hz
52. Imax = q/sqrt(LC); t_max = (n+(1/2))(pi)sqrt(LC)
where n=0-infinity
56. 1.79 ohms
60. proof; E = Q_0²/2C
62. Imax = 224 mA; Qmax = 200 microC; Imin = Qmin = 0
64. proof
Chapter 34
2. 67.8 M\$
4. 0.417 A
18. (a) t = (n+(1/2))8.33 ms + 2.78 ms;
n = 0 to infinity
(b) t = (n+(1/2))8.33 ms - 1.39 ms;
n = 0 to infinity
40. C = 1/2(pi)fR; L = R/2(pi)f
47. ANSWER IN BOOK IS WRONG!!
(a) (EMF_m)²R/2(omega²)L²
--> 0 as omega --> infinity
(b) (1/2)(EMF_m)²R(omega²)C²
--> 0 as omega --> 0
NOTE: the book uses V_0 for what I call EMF_m
Chapter 14
14. (a) 2.09 m
(b) 0.318 Hz
(c) .4 m
(d) 3.14 s
(e) 3 m^{-1}
Chapter 15
8. (a) proof
(b) A = 10 cm; f = 1.5 Hz
Chapter 35
12. proof
16. B = (0.667nT)cos(kz-wt) in the -i direction
with k = .0314/m and w = 9.42 M rad/s;
where w stands for omega
22. E = 0.268 V/m @ 5 km, B = 0.894 nT;
E = 0.0134 V/m @ 100 km, B = 44.7 pT
24. 3.33 mN
26. 192 W/m²
32. <u> = 2.90 nJ/m³ ; Erms = 18.1 V/m;
Brms = 60.4 nT
45. ANSWERS IN BOOK ARE WRONG! At least according
to the picture in my copy of the text.  The