Page 594 - Engineering Electromagnetics, 8th Edition

576 ENGINEERING ELECTROMAGNETICS

2
2
2 1.5
5.23 (a) 289.5 V (b) z/[(x − 1) + y + z ] − ( f ) V (φ) = 28.7φ + 194.9V, E =−(28.7)/ρa φ
2
2
2
2 1.5
z/[(x + 1) + y + z ] = 0.222 V/m, D =−(28.7 0 )/ρa φ C/m , ρ s = (28.7 0 )/
2
5.25 (a)4.7 × 10 −5 S/m (b)1.1 × 10 −3 S/m ρ C/m , Q b = 122 pC (g) 471 pF
(c)1.2 × 10 −2 S/m 6.41 (a) 12.5 mm (b) 26.7 kV/m
2
2
5.27 (a) 6.26 pC/m (b) 1.000176 (c) 4.23 (with given ρ s = 1.0 µC/m )
◦
◦
5.29 (a) E = [(144.9)/ρ]a ρ V/m, D = 6.43 (a) α A = 26.57 ,α B = 56.31 (b) 23.3 V
2
(3.28a ρ )/ρ nC/m (b) V ab = 192 V, χ e = 1.56 6.45 (a) 833.3r −.4 V(b) 833.3r −.4 V
(c) [(5.0 × 10 −29 )/ρ]a ρ C · m
5.31 (a)80 V/m (b) −60a y − 30a z V/m (c) 67.1 V/m Chapter 7
2
(d) 104.4 V/m (e)40.0 ( f ) 2.12 nC/m (g) 2.97 7.1 (a) −294a x + 196a y µA/m
◦
2
nC/m (h)2.12a x − 2.66a y − 1.33a z nC/m 2 (b) −127a x + 382a y µA/m
2
(i)1.70a x − 2.13a y − 1.06a z nC/m ( j)54.5 ◦ (c) −421a x + 578a y µA/m
5.33 125a x + 175a y V/m 7.3 (a)
5.35 (a) E 2 = E 1 (b) W E1 = 45.1 µJ, W E2 = 338 µJ I a
H = 1 − a φ A/m
2
Chapter 6 2πρ ρ + a 2
6.1 b/a = exp(2πd/W) (b)1/ 3
√
6.3 barium titanate 7.5
6.5 451 pF
2
6.7 (a) 3.05 nF (b) 5.21 nF (c) 6.32 nF (d) 9.83 nF I 2 2
|H|= −
2
2
6.9 (a) 143 pF (b) 101 pF 2π y + 2y + 5 y − 2y + 5
6.11 (a) 53.3 pF (b) 41.7 pF 1/2
(y − 1) (y + 1) 2
6.13 K 1 = 23.0,ρ L = 8.87 nC/m, a = 13.8m, + −
2
2
C = 35.5pF y − 2y + 5 y + 2y + 5
2
2
6.15 (a) 47.3 nC/m (b) −15.8 nC/m (c) 24.3 pF/m 2
6.17 Exact value: 57 pF/m 7.7 (a) H = I/(2π z)(a x − a y ) A/m
(b)0
6.19 Exact value: 11 0 F/m 7.9 −1.50a y A/m
6.21 (b) C ≈ 110 pF/m (c) Result would not change. 7.11 2.0 A/m, 933 mA/m, 360 mA/m, 0
6.23 (a) 3.64 nC/m (b) 206 mA 7.13 (e) H z (a <ρ < b) = k b ; H z (ρ> b) = 0
6.25 (a) −8V(b)8a x − 8a y − 24a z V/m 7.15 (a)45e −150ρ a z kA/m 2
2
2
(c) −4xz(z + 3y ) C/m 3 (b)12.6[1 − (1 + 150ρ 0 )e −150ρ 0 ]A
2 3
2
2
(d) xy z =−4(e) y − 2x = 2 and (c) 2.00 [1 − (1 + 150ρ)e −150ρ ] A/m
2
2
3x − z = 2( f )No ρ
2
2
2
6.27 f (x, y) =−4e 2x + 3x , V (x, y) = 3(x − y ) 7.17 (a)2.2 × 10 −1 a φ A/m (just inside), 2.3 ×
−2
6.29 (b) A = 112.5, B =−12.5or 10 a φ A/m (just outside)
−1
A =−12.5, B = 112.5 (b)3.4 × 10 −1 a φ A/m −1
2
3
6.31 (a) −106 pC/m (b) ±0.399 pC/m (depending on (c)1.3 × 10 a φ A/m (d) −1.3 × 10 a z A/m
which side of the surface is considered) 7.19 (a) K =−Ia r /2πr A/m (θ = π/2) 2
√
2
6.33 (a) yes, yes, yes, no (b)At the 100 V surface, no (b) J = Ia r /[2πr (1 − 1/ 2)] A/m (θ< π/4)
(c) H = Ia φ /[2πr sin θ] A/m (π/4 <θ <π/2)
for all. At the0V surfaces, yes, except for V 1 + 3. √
(c) Only V 2 is (d) H = I(1 − cos θ)a φ /[2πr sin θ(1 − 1/ 2)]
6.35 (a) 33.33 V (b) [(100)/3]a z + 50a y V/m 7.21 A/m (θ< π/4) 2
3
6.37 (a) 1.01 cm (b) 22.8 kV/m (c) 3.15 (a) I = 2πba /3A(b) H in = bρ /3a φ A/m
3
(c) H out = ba /3ρ a φ A/m
4
3
6.39 (a)(−2.00 × 10 )φ + 3.78 × 10 V 2
4
(b) [(2.00 × 10 )/ρ]a φ V/m 7.23 (a)60ρa z A/m (b)40π A(c)40π A
4
(c)(2.00 × 10 0 /ρ)a φ C/m 2 7.25 (a) −259A(b) −259 A
2
3
4
(d) [(2.00 × 10 )/ρ] C/m 2 7.27 (a)2(x + 2y)/z a x + 1/z a z A/m
(e) 84.7 nC (b) same as part (a)(c)1/8A