Page 593 - Engineering Electromagnetics, 8th Edition

APPENDIX F Answers to Odd-Numbered Problems 575

2
2
2.27 (a) y − x = 4xy − 19 (b)0.99a x + 0.12a y 4.7 (a)90(b)82
2.29 (a) 12.2 (b) −0.87a x − 0.50a y 4.9 (a)8.14V(b) 1.36 V
(c) y = (1/5) ln cos 5x + 0.13 4.11 1.98 kV
4.13 576 pJ
Chapter 3 4.15 −68.4V
2
3.1 (a) ¯ F = [Q 1 Q 2 /4π 0 R ] because a r 4.17 (a) −3.026V(b) −9.678 V
(b) Same as part (a) 4.19 .081 V
(c)0
(d)Force will become attractive! 4.21 (a) −15.0V(b) 15.0 V
3.3 (a) 0.25 nC (b) 9.45 pC (c)7.1a x + 22.8a y − 71.1a z V/m
(d) 75.0 V/m
3.5 360 nC (e) −0.095a x − 0.304a y + 0.948a z
3.7 (a)4.0 × 10 −9 nC (b)3.2 × 10 −4 nC/m 2 ( f )62.8a x + 202a y − 629a z pC/m 2
2
3.9 (a) 164 pC (b) 130 nC/m (c) 32.5 nC/m 2 4.23 (a) −48ρ −4 V/m (b) −673 pC/m (c) −1.96 nC
3
3.11 D = 0(ρ< 1 mm); 4.25 (a) V p = 279.9V, E p =−179.9a ρ − 75.0a φ V/m,
2
10 −15 D p =−1.59a ρ − .664a φ nC/m , ρ vp =
D ρ = 2 [sin(2000πρ) + 2π[1 −
3
2π ρ −443 pC/m (b) −5.56 nC
3
10 ρ cos(2000πρ)]]C/m 2 (1 mm <ρ < 1.5 mm); 4.27 (a)5.78V(b) 25.2 V/m (c) 5.76 V
2.5×10 −15 2 4.29 1.31 V
D ρ = C/m (ρ> 1.5 mm)
πρ
3.13 (a) D r (r < 2) = 0; D r (r = 3) = 8.9 × 4.31 (a) 387 pJ (b) 207 pJ
2
2
10 −9 C/m ; D r (r = 5) = 6.4 × 10 −10 C/m 2 4.33 (a)(5 × 10 −6 )/(4πr )a r C/m 2
(b) ρ s0 =−(4/9) × 10 −9 C/m 2 (b)2.81J(c) 4.45 pF
3
3.15 (a) [(8π L)/3][ρ − 10 −9 ] µC where ρ 1 4.35 (a)0.779 µJ(b)1.59 µJ
1
3
is in meters (b)4(ρ − 10 −9 )/(3ρ 1 )µC/m 2
1
where ρ 1 is in meters
Chapter 5
(c) D ρ (0.8 mm) = 0; D ρ (1.6 mm) = 3.6 ×
2
10 −6 µC/m ; D ρ (2.4 mm) = 3.9 × 10 −6 µC/m 2 5.1 (a) −1.23 MA (b)0(c)0,asexpected
3.17 (a) 0.1028 C (b) 12.83 (c) 0.1026 C 5.3 (a)77.4A(b)53.0a r A/m 2
3.19 113 nC 5.5 (a) −178.0A(b)0(c)0
2
3.21 (a) 8.96 (b) 71.67 (c) −2 5.7 (a) mass flux density in (kg/m − s) and mass
3
3
3
3.23 (b) ρ v0 = 3Q/(4πa )(0 < r < a); density in (kg/m )(b) −550 g/m − s
7
3
3
D r = Qr/4πa ) and ∇ · D = 3Q/(4πa ) 5.9 (a) 0.28 mm (b)6.0 × 10 A/m 2
2
(0 < r < a); D r = Q/(4πr ) and 5.11 (a) E = [(9.55)/ρl)]a ρ V/m, V = (4.88)/l V and
∇ · D = 0(r > a) R = (1.63)/l , where l is the cylinder length
3
2
3.25 (a) 17.50 C/m (b)5a r C/m (c) 320π C (not given) (b)14.64/l W
(d) 320π C 5.13 (a) 0.147 V (b) 0.144 V
3
3.27 (a) 1.20 mC/m (b)0(c) −32µC/m 2 5.15 (a)(ρ + 1)z cos φ = 2
2
3.29 (a)3.47C(b) 3.47 C (b) ρ = 0.10, E(.10,.2π, 1.5) =−18.2a ρ +
3.31 −3.91 C 145a φ − 26.7a z V/m (c) 1.32 nC/m 2
2
5.17 (a) D(z = 0) =−(100 0 x)/(x + 4)a z C/m 2
Chapter 4 (c) −0.92 nC
2
4.1 (a) −12 nJ (b)24nJ(c) −36 nJ (d) −44.9nJ 5.19 (a)At0V:2x y − z = 0. At 60 V:
2
(e) −41.8nJ 2x y − z = 6/z (b) 1.04 nC/m 2
4.3 (a)3.1 µJ(b)3.1 µJ (c) −[0.60a x + 0.68a y + 0.43a z ]
4.5 (a)2(b) −2 5.21 (a) 1.20 kV (b) E p = 723a x − 18.9a y V/m