Chapter 33 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 22. M = ((mu_0)a/2pi)ln((d+a)/d) 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) 47. ANSWER IN BACK IS WRONG IN SOME EDITIONS correct answer is (V²L)/(2R²) 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. (a) $52.56 (b) 67.8 M$ 4. 0.417 A 18. (a) t = (n+(1/2))8.33 ms + 2.78 ms; n = 0 to infinity (b) peak voltage = 217 V; t = (n+(1/2))8.33 ms - 1.39 ms; n = 0 to infinity 28. (a) X_C = 637 Ohms X_L = 12.6 Ohms Z = 626 Ohms (b) X_C = 31.8 Ohms X_L = 251 Ohms Z = 225 Ohms (c) X_C = 1.59 Ohms X_L = 5027 Ohms Z = 5025 Ohms 40. C = 1/2(pi)fR; L = R/2(pi)f 47. ANSWERS IN BOOK ARE WRONG IN SOME EDITIONS (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 4. z(x,t)=(3.09 cm)sin(kx+delta)cos(wt+phi) k=(pi/120)cm^-1; delta=+(pi/2) or -(pi/2) w=(2pi)s^-1; phi= -0.886 rad or 2.276 rad (the +delta goes with -phi and vice versa) (w here stands for omega) 13. at x=1.0 m, y = Asin(0.3 rad - (0.02 s^-1)t); at x=12.0 m, y = Asin(3.6 rad - (0.02 s^-1)t); graph each 14. (a) 2.09 m (b) 0.318 Hz (c) .4 m (d) 3.14 s (e) 3 m^{-1} 23. k=23 m^-1; f=48 Hz Chapter 15 8. (a) proof (b) A = 10 cm; f = 1.5 Hz Chapter 35 16. B = (0.667nT)cos(kz-wt) in the -i direction with k = .0314 rad/m and w = 9.42 M rad/s; where w stands for omega 32. <u> = 2.90 nJ/m³ ; Erms = 18.1 V/m; Brms = 60.4 nT 52. I = (I_0)0.096 = (0.000127 C^2/Js)E_0^2