Page 596 - Engineering Electromagnetics, 8th Edition

578 ENGINEERING ELECTROMAGNETICS

9
9.23 (a) E N1 = 10 cos(10 t)a z V/m E t1 = 10.39
9
(30a x + 20a y ) cos(10 t) V/m l 5l
9
D N1 = 200 cos(10 t)a z pC/m 2 D t1 = ν < t < 4ν : V 1 = 0.44 V 0
9
(600a x + 400a y ) cos(10 t) pC/m 2 3l 13l
9
(b) J N1 = 40 cos(10 t)a z mA/m 2 J t1 = < t < : V 2 =−0.15 V 0
9
(120a x + 80a y ) cos(10 t) mA/m 2 ν 4ν
9 5l 21l
(c) E t2 = (30a x + 20a y ) cos(10 t) V/m D t2 = < t < : V 3 = 0.049 V 0
9
(300a x + 200a y ) cos(10 t) pC/m 2 ν 4ν
9
J t2 = (30a x + 20a y ) cos(10 t) mA/m 2 7l < t < 29l : V 4 =−0.017 V 0
9 ◦ ν 4ν
(d) E N2 = 20.3 cos(10 t + 5.6 )a z V/m D N2 =
9
203 cos(10 t + 5.6 )a z pC/m 2 J N2 = Voltages in between these times are zero.
◦
9
20.3 cos(10 t + 5.6 )a z mA/m 2 10.41
◦
1
9.25 (b) B = t − z c a y T H = µ 0
t − z c a y A/m l

E = (ct − z)a x V/m D = 0 (ct − z)a x C/m 2 0 < t < : V L = 0
2v
l 3l V 0
Chapter 10 < t < : V L = 2
10.1 γ = 0.094 + j2.25 2ν 2ν
3l
α = 0.094 Np/m t > : V L = V 0
β = 2.25 rad/m 2ν
λ = 2.8m 10.43
Z 0 = 93.6 − j3.64
8
10.3 (a)96 pF/m (b)1.44 × 10 m/s 0 < t < 2l/ν : V R L = V 0 /2
(c)3.5 rad/m (d) =−0.09, s = 1.2 t > 2l/ν : V R L = 3V 0 /4
10.5 (a)83.3nH/m, 33.3 pF/m (b)65cm 0 < t < l/ν : V R g = 0, I B = 0
10.7 7.9 mW t > l/ν : V R g = V 0 /4, I B = 3V 0 /4Z 0
10.9 (a) λ/8(b) λ/8 + mλ/2
2
2
10.11 (a) V /R L (b) R L V /(R +
0
0
√
2
2
2
R L ) (c) V /R L (d)(V /R L )exp(−2 RG) Chapter 11
0
0
10.13 (a)6.28 × 10 rad/s (b)4 cos(ωt − πz)A 11.3 (a)0.33 rad/m (b) 18.9 m
8
3
(c)0.287 1.28 rad (d)57.5exp[ j(πz + 1.28)] V (c) −3.76 × 10 a z V/m
8
(e) 257.5 36 V 11.5 (a) ω = 3π × 10 sec −1 ,λ = 2m,
◦
10.15 (a)104V(b)52.6 − j123 V and β = π rad/m (b) − 8.5a x − 9.9a y A/m
10.17 P 25 = 2.28 W, P 100 = 1.16 W (c) 9.08 kV/m
10.19 16.5 W 11.7 β = 25m −1 ,η = 278.5 , λ = 25 cm,
8
3
10.21 (a) s = 2.62 (b) Z L = 1.04 × 10 + v p = 1.01 × 10 m/s, R = 4.01,µ R = 2.19,
8
j69.8 (c) z max =−7.2mm and H(x, y, z, t) = 2 cos(8π × 10 t − 25x)a y +
8
10.23 (a)0.037λ or 0.74m(b)2.61 (c)2.61 5 sin(8π × 10 t − 25x)a z A/m 7
(d)0.463λ or 9.26 m 11.9 (a) β = 0.4π rad/m, λ = 5m, v p = 5 × 10 m/s,
7
10.25 (a) 495 + j290 (b) j98 and η = 251 (b) −403 cos(2π × 10 t) V/m
−7
t) A/m
(c)1.61 cos(2π × 10
10.27 (a)2.6(b)11 − j7.0mS(c)0.213λ 11.11 (a) 0.74 kV/m (b) −3.0 A/m
10.29 47.8 + j49.3 11.13 µ = 2.28 × 10 −6 H/m, = 1.07 × 10 −11 F/m,

10.31 (a)3.8cm(b)14.2cm and = 2.90 × 10 −12 F/m

10.33 (a) d 1 = 7.6cm, d = 17.3cm(b) d 1 = 11.15 (a) λ = 3 cm, α = 0(b) λ = 2.95 cm,
1.8cm, d = 6.9cm α = 9.24 × 10 −2 Np/m (c) λ = 1.33 cm,
10.35 (a)39.6cm(b)24pF α = 335 Np/m
2
10.37 V L = (1/3)V 0 (l/v < t < ∞) and is zero for 11.17 S z (z = 0) = 315a z W/m , S z (z = 0.6) =
t < l/ν. I B = (V 0 /100) A for 0 < t < 2l/v and 248a z W/m 2
is (V 0 /75) for t > 2l/v