Answers to Odd-Numbered Problems

Answers to Odd-Numbered Probems CHAPTER.. (a) m;.8 m northward and.4 m eastward; (c).8944 m.5..7. a x + a y + a z.9......5..7..9. Traveing wave progressing in the negative z-direction.. (a) Linear; circuar; (c) eiptica.. Eiptica poarization.5..7..9..... 4a x - 5a y + a z >5; 6 4a x + 4a y + a z dz 4a x - a y > 7 x + y + z = constant v- ya x + xa y 5 cos vt + 6.87 8p P mg.555q a P x + a y + a z N/C - 7 5 p P a i - - 4 i - + 4 - > a y i = 4 * - 7 p P 5 5 a a i = j = - 4 i - + - 4 j - + 4 - > a z - - 4 m >4p a.5. (a).4485 * - 6 sin p * 7 t a x A/m.7..4485 * - 8 df = ; df = m sin p * 7 t A 4p I I dx dy a x.9. (a) 5 * - 5 m >p a z ;.4..4..79m Ia z - v B 4a y + 7a z z 4

44 Answers to Odd-Numbered Probems CHAPTER...855...7..9. >6 4n - - e - ;.85,.9,.7,.7 n - e - >n e - >n.... 6p A.5. - B bv a x + a - b x.7..9... a sin vt - B bv a B bv n x + x x + a - b cos vt x B v sin vt.. (a) ; I - I.5. J J a r for r 6 a and for r 7 a, where r is the radia distance from the axis; r direction circuar to the axis of the wire.7. (a) I>4 ; I>4.9..66 C.. r r>p for r 6 a and r a >P r for r 7 a, where r is the radia distance from the center of the charge, and direction radiay away from the center of the charge...5. - A p > CHAPTER.... z vb sin vt a x (a) za x + xa y + ya z ;.5. * - 7 cos 6p * 8 t - p z a y Wb/m.7..9. B = - vm P E z cos vt a y E = - v m P E z4 sin vt a x E = cos 6p * 8 t - p z a x B = - 7 cos 6p * 8 t - p z a y.. J a + za y for - a 6 z 6, J a - za y for 6 z 6 a, otherwise.. Cur wi have a component in the y-direction in addition to the x-component.5. Cur has ony a z-component

.7..9. (a) x + y + z ;.. (a) - xa z, y; - a z, ; (c), ; (d),.. x - a a ap x for - a 6 x 6 a, otherwise.5. (a) and (c).7. # r =.9. # AS A ds = p, # A =.. CHAPTER 4 Answers to Odd-Numbered Probems 45 4.. (a). A; ; (c). A 4.. (a). cos vt A;. sin vt A; (c).88 sin vt + 45 A 4.5. (a) ;.68 cos vt a y for z = ;; ;.5 cos vt a y for z = ; 4.7. 4.9. 4.5. t - zm corresponds to a wave; t + zm P P + corresponds to a - wave 4.7. 4.9. For Probem 4., E x = h J S t < zm for z and P 4.. Spacing = >4; ampitudes = J S, phase difference = p > J S; 4.. (a) right circuar; eft circuar E 4.5. cos vt + bz a x - sin vt + bz a y 4 4.7. AC A# d = for any C r J a a y for z 6 - a, - J a z + z a b a y for - a 6 z 6, - J a z - 6 z 6 a, - J a a y for z 7 a - r a>p a x for x 6 - a, r x>p a x for - a 6 x 6 a, r a>p a x for x 7 a C = h J S H y = ; E x h for z E =.h cos 6p * 8 t < p z +.5h for z H = ; E x h a y for z + E cos vt + bz a x + sin vt + bz a y 4.5 E ccos a p * 8 t - + sin a p * 8 t - cos p * p z +.48p b a x p z +.48p b a y d z a b a y for 8 t < 4p z4a x

46 Answers to Odd-Numbered Probems 4.9. (a) Same as in Figure 4.7, except dispaced to the eft by ms; 75.4 V m for n - > 6 ƒ z ƒ 6 n and - 7.7 V/m for n - 6 ƒ z ƒ 6 n - >, n =,,,... ; (c).z> ƒ z ƒ A/m for n - 6 ƒ z ƒ 6 n - > and -.z> ƒ z ƒ A/m for n - > 6 ƒ z ƒ 6 n, n =,,,... 4.. mv/m CHAPTER 5 5.. (a).74 * - 4 V/m,.74 * - 6 V,.74 * - 5 Æ;.857 * - 4 V/m,.857 * - 6 V,.857 * - 5 Æ; (c) 5 V/m,.5 V, 5 Æ 5...545 * - 9 s 5.5. (a) - 8.667 * - 7 sin p * 9 t A; -.778 * - 6 sin p * 9 t A; (c) - 4.444 * - 5 sin p * 9 t A 5.7. (a) P E (4a x + a y + a z ); 8P E (a x + a y + a z ); 5.9. (c).5e (a x - a y - a z ) 5...5 * - 6 sin p z A H y 5.. z = g H y 5.5..8 Np/m, 4.756 * - rad/m,.5 * 8 m/s,.5 m, (6. + j8.5) Æ 5.7. ƒeƒ B a >m,.75 * - 8 A-m E =.76e <.44z cos a p * 6 t <.976z + p 8 b a x for z H = ;.5e <.44z cos (p * 6 t <.976z) a y for z 5.9. 6.9 m,.97:, 9 out of phase 5.. (a) MHz; 5 m; (c).5 * 8 m/s; (d) 4P ; (e) 6p cos(6p * 7 t -.4p z) a y A/m 5.. (a) Same as in Figure 4.7; 75.4 V/m for (n - >) 6 z 6 n and - 7.7 V/m for (n - ) 6 z 6 (n - >), n =,,, Á ; (c).6z> z A/m for (n - ) 6 z 6 (n - >) and -.z> z A/m for (n - >) 6 z 6 n, for n =,,, Á 5.5. (a). Np/m, 8.7 rad/m,.54 * 8 m/s,.54 m, 4.5 Æ; p * - Np/m, p * - rad/m, 7 m/s, m, p ( + j) Æ 5.7. E (4a x + a y - 6a z ), H (4a x - a y ) 5.9. 5.. P Yes

5.. 5.5. p cos px sin p * 9 t a y ; (c) sin p * p 9 t a z on both sheets 5.7. (a) 4; 6; (c) 4>9 5.9. CHAPTER 6 6.. xa x + ya y + za z (a) yza x + zxa y + xya z x + y + z ; 6.. 6.5. 5 (5a x + a y + 4a z ). 6.7. Q>p P 6.9. V = - 5 5 p P a [ - 4 (i - i = ) + y ] - > E = - 5 5 p P a [ - 4 (i - ) + ] - > a y - > 4P V 6.. (a) - ; 9d a x d b kx 6.. V = - 6P + kd x 8P for - d 6 x 6 d P (d - t) +P (t - x) 6.5. (a) V P (d - t) +P t for 6 x 6 t, 6.7. 4 D E E E r = - E cos (vt + bz) a x, H r = E h cos (vt + bz) a y E = E sin vt sin bz a x, H = E h [J S ] z = = E h P (d - x) P (d - t) +P t V for t 6 x 6 d P (d - t) P (d - t) +P t V ; m m m + m a i = d b w cos vt a x (c) P P w P (d - t) +P t Answers to Odd-Numbered Probems 47 cos vt cos bz a y [r s ] x = =, [r s ] x = d = 4P V d 6.9. Y in = jv Pw equivaent circuit is a series combination of d a + v mp b; C = Pw d and md L, where L = w

48 Answers to Odd-Numbered Probems 6.. Z in = jvmd jvms a - b; equivaent circuit consists of an inductor L in w parae with a resistor R where L = md>w and R = d>sw 6.. (a) p cos (p * 6 t -.p z) V;.5 cos (p * 6 t -.p z) A; (c).5p cos (p * 6 t -.p z) W 6.9. =.49m, c =.P, g =.s; exact vaues are.49m,.855p, and.855s, respectivey 6.. m, 9P, 9s 9 CHAPTER 7 7.. (a) =.78 * - 6 H/m, g = 4.54 * - 6 S/m; (5.7 + j) Æ 7.. V (z) = A cos bz, Ī(z) = - j A sin bz; Z in = - jz Z cot b 7.5. (a).686 m;.586 m 7.7. (a) 5 Æ; 8.9 V,.76 A 7.9. (a) 8 m/s; 6 m, * - 6, j.79 Æ; m,, ; 8m,.5, q 7.. 9 (a) (c) 8 P i 6 P i; 6 P i; 7.. 7.7. 7.9. 5 Æ -.5 S,.667.4,.9 7.. (a) 4 V for - 4 6 z 6 6 m, otherwise; otherwise; A for 6 z 6 m, - A for - 8 m 6 z 6, (c) for 6 t 6. ms, 4 V for t 7. ms; (d) for 6 t 6. ms, - A for t 7. ms 7.. (a) 6 V, A; 67.5 V,.9 A; (c) - 7.5 V,. A 7.5. 4 4 [V ] t =. m s V 6 (a) z, m 8 [I] t =.4 m _ s A z, m [V ] z = m V [I] z = 4 m A 4..4 t, ms..5 t, ms (c) (d)

Answers to Odd-Numbered Probems 49 7.7. 6 V, V t ms.5 I, A t ms.5 z.5 9 z (a) [V ] z,v 4 t, ms (c) 7.9..46 V 7.. (a) 4 V for - 6 z 6 ; - A for - 6 z 6, A for 6 z 6 ; * - 6 J; (c) Votage across 6 Æ =4 V for 6 t 6 ms, V for 6 t 6 ms, otherwise;votage across Æ =4 V for 6 t 6 ms, otherwise; (d) * - 6 J 7.. [V] z, V [V] z, V 7 5.4 5 4.4.6 7 t.5.8 4.5.4 6 t 7.5. (a) 8.4 Æ; 48.4 Æ CHAPTER 8 8.. 8...5p (a x + a y ) a x + a y + 8.5. (a) Yes; a z 4p (a y - a z ) cos [6p * 7 t -.p (y + z)]

44 Answers to Odd-Numbered Probems 8.7. (a) 8 m, 4 m (a x + a z ); 8.9. cm 8.. 6 MHz, 54 MHz 8.. 8.5. 8.7. (a).kv,.44kv ; kv, kv ; (c).kv,.88kv 8.9. 8.. TE,, TE,, TE,, TE,, and TM, 6.5 cm,.5 cm 8.. 55.5 MHz (TE,,, TE,, ), 4. MHz (TE,,, TM,, ), 559. MHz (TE,,, TE,,, TE,,, TE,, ) 8.5. (a) 4.8 ; 48.6 8.7. 8.9. 8.. CHAPTER 9 9.. 9.5..p cos p *. 7 t A 9.7. (a).57 * - V/m; 9.9.. W 9.. (D R rad )>(D R rad ) 9.. 9.5. 7 8.694 9.7..5 W 9.9. (a) E u =- hbli sin u sin (vt - 8p r R rad = p (L>), D =.5 9.. - p 4, cos a p 4 cos c - p 8 b 9.. 9.5. TE, mode; sin p x sin a p t -.5769 * 8 m/s E r = -.76E a y cos [6p * 8 t + p (x - z)] E t =.884E a y cos [6p * 8 t - p (x + z)] 75.5 cos a p cos cb ` cos c cos a p 4 cos c - p 4 b ` 8p zb a y R rad =.5 Æ, 8P rad 9 =.7546 W br), H f = E u h ; 9.7. ccos a p cos ubdnsin u, where u is the ange from the vertica, D =.84 9.9. 4 9...587 V 9...6 A

CHAPTER Answers to Odd-Numbered Probems 44.. (a) 5 * 8 m/s; 5 m; (c).5..7.. 4.4.9..7 db.. (a) K f V >T for T 6 t 6.T,- K f V >T for.4t 6 t 6.5T, otherwise K b V V (, t).t.4t.5t T T.T.4T.5T t K b V (c) V (.8, t) K b V.8T.9T T.T.T.6T.7T t K b V.. (a) -.K b V (z>) for.9 6 z 6 ; K b V for 6 z 6.9, K b V ( - z>) for.9 6 z 6 ; (c) K b V for 6 z 6.9, K b V ( -.z>) for.9 6 z 6.5. =-.5, t =.6748.9. (a).654 * - V/m; R rad =.677 * - Æ, 8P rad 9 =.4 W APPENDIX A A.. A.. A.5. A.7. APPENDIX B - a x + a y + a z Equa -, a z a r + 6a z B.. (a) - sin f a z, cos f;, except at r = ; (c) except at r =, B.. r r a r r b + r f + z B.5. (a) - r (sin u a r - cos u a u ); cos u a r - sin u a u