Page 597 - Engineering Electromagnetics, 8th Edition

APPENDIX F Answers to Odd-Numbered Problems 579

8
11.19 (a) ω = 4 × 10 rad/s (b) H(ρ, z, t) = Chapter 13
8
(4.0/ρ) cos(4 × 10 t − 4z)a φ A/m 13.1 (a) 1.14 mm (b) 1.14 mm (c) 1.47 mm
−3 2 2 8
(c) S = (2.0 × 10 /ρ ) cos (4 × 10 t − 4z)a z 13.3 14.2 pF/m, 0.786 µH/m, 0, 0.023 /m
2
W/m (d)P=5.7 kW 13.5 (a) 1.23 (b) 1.99 (c) 1.33
4 2
11.21 (a) H φ1 (ρ) = (54.5/ρ)(10 ρ − 1) A/m 13.7 (a) 2.8 (b)5.85 × 10 −2
(.01 <ρ <.012), H φ2 (ρ) = (24/ρ) A/m
(ρ> .012), H φ = 0(ρ< .01m) 13.9 (a) 4.9 (b) 1.33
(b) E = 1.09a z V/m 13.11 9
4 2
(c) S =−(59.4/ρ)(10 ρ − 1)a ρ W/m 2 13.13 9
(.01 <ρ <.012 m), −(26/ρ)a ρ W/m 2 13.15 1.5 ns
(ρ> 0.12 m) 13.17 (a) 12.8 GHz (b)Yes
11.23 (a)1.4 × 10 −3 /m (b)4.1 × 10 −2 /m 13.19 (a)2.5 GHz < f < 3.75 GHz (air-filled)
(c)4.1 × 10 −1 /m (b)3.75 GHs < f < 4.5 GHz (air-filled)
5
11.25 f = 1 GHz, σ = 1.1 × 10 S/m 13.21 a = 1.1 cm, b = 0.90 cm
3
11.27 (a)4.7 × 10 −8 (b)3.2 × 10 (c)3.2 × 10 3 13.25 72 cm
11.29 (a) H s = (E 0 /η 0 )(a y − ja x )e − jβz 13.27 3.32
2
2
(b) S = (E /η 0 )a z W/m (assuming E 0 is real) 13.29 −1
0
11.31 (a) L = 14.6 λ (b) Left 13.31 (a) θ min = sin (n 3 /n 1 )(b) v p,max = c/n 3
11.33 (a) H s = (1/η)[−18e a x + 15a y ]e − jβz A/m greater than
jφ
(b) S = 275 Re {(1/η )} W/m 2
∗
Chapter 14
14.1 (a) −0.284a x − 0.959a z (b) 0.258
Chapter 12
14.3 (a) − j(1.5 × 10 −2 )e − j1000 a z V/m
12.1 0.01% (b) − j(1.5 × 10 −2 )e − j1000 a y V/m
12.3 0.056 and 17.9 (c) − j(1.5 × 10 −2 )(a y + a z ) V/m
8
12.5 (a)4.7 × 10 Hz (b) 691 + j177 (c) −1.7cm (d) −(1.24 × 10 −2 )(a y + a z ) V/m
12.7 (a) s 1 = 1.96, s 2 = 2, s 3 = 1(b) −0.81 m (e)1.75 × 10 −2 V/m
12.9 (a)6.25 × 10 −2 (b) 0.938 (c) 1.67 14.7 (a) 0.711 (b) 0.178 (c) 0.400
12.11 641 + j501 14.9 (a) 85.4 A (b) 5.03 A
12.13 Reflected wave: left circular polarization; power 14.11 (a) 85.4 A (b) 7.1 A
fraction = 0.09. Transmitted wave: right circular 14.13 (a)0.2e − j1000π V/m (b)0.2e − j1000π j0.5π V/m
e
polarization; power fraction = 0.91 (c)0
12.15 (a) 2.55 (b) 2.14 (c) 0.845 14.15 Primary maxima: θ =±90 , relative magnitude
◦
12.17 2.41 1.00. Secondary maxima: θ =±33.8 and
◦
◦
12.19 (a) d 1 = d 2 = d 3 = 0or d 1 = d 3 = 0, d 2 = λ/2 θ =±146.2 , relative magnitude 0.186.
(b) d 1 = d 2 = d 3 = λ/4 S s = 7.3dB
12.21 (a) Reflected power: 15%. Transmitted power: 14.17 (a)36.5W(b) 4.8 µW
85% (b) Reflected wave: s-polarized. 14.19 ξ = 0, d = λ
Transmitted wave: Right elliptically polarized. 14.21 (a) ±48.2 (b) ±60 ◦
◦

2
12.23 n 0 = (n 1 /n 2 ) n − n 2 2 14.23 (a) +π/2(b)0
1
12.25 0.76(−1.19 dB) 14.25 (a) ξ =−π/2(b) 5.6% of maximum (12.6 dB
12.27 2 down)
12.29 4.3 km 14.29 (a)1.7µW(b) 672 nW