Sol-Ch26 - CHAPTER 26 E xercises 1(a C = 0 A/d = 50 pF(b Q...

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Exercises 1. (a) C = ϵ 0 A/d = 50 pF; (b) Q = CV = 600 pC 2. (a) C/L = 2π ϵ 0 /ln(b/a) = 24.1 pF; (b) Q = CV = 1.45 nC 3. (a) A = Cd/ ϵ 0 = 54.2 cm 2 ; (b) V = W/C = 167 V; (c) E = V/d = 8.33 × 10 5 V/m 4. (a) V = Ed = 24 V; (b) C = Q/V = 2.5 nF (c) A = Cd/ ϵ 0 = 0.226 m 2 5. (a) σ = ϵ 0 E = –8.85 × 10 – 19 C/m 2 ; (b) C = R 1 R 2 /k(R 2 – R 1 ) = 91.7 mF; (c) 712 µF for the earth 6. Given λ =4 nC/m. λ = Q/L = CV/L = 2π ϵ 0 V/ln(b/a) From ln(b/a) = 2π ϵ 0 V/ λ = 0.375, find b = 1.45 mm 7. “Effective area” is 4A, so C = 4 ϵ 0 A/d 8. (a) d = ϵ 0 A/C = 2.21 cm, ths V = Ed = 66.3 kV (b) Q = CV = 1.59 µC 9. C = (1.6 × 10 –7 C) /20 V = 8 nF 10. C = R 1 R 2 /k(R 2 – R 1 ) = 66.7 pF, Q = CV =0.8 nC 11. Q 1 ’ + Q 2 ’ = 80 µC; Q 1 ’/C 1 = Q 2 ’/C 2 Q 1 ’ = 32 µC, Q 2 ’ = 48 µC, V 1 = V 2 = 8V 12. C = 6 ϵ 0 a/d , where A = (πR 2 /2)(1 – θ /180) (a) 33.4 pF; (b) 25.1 pF; (c) 8.35 pF CHAPTER 26
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13. (a) C = R 1 R 2 /k(R 2 – R 1 ) = 4.58 pF; (b) N = CV/e = 1.43 × 10 8 14. (a) Ceq =0.0714 µF, Q 1 = Q 2 = 0.857 µC, V 1 = 8.57 V, V 2 = 3.43 V (b) V 1 = V 2 = 12V, Q 1 = 1.2 µC, Q 2 = 3 µC 15. From 12.4 = 10 + (1/4 + 1/C 1 ) –1 , find C 1 = 6 µF 16. From 1/2.77 = 1/4 + 1/(2 + C 2 ), find C 2 = 7 µF 17. (a) Two in parallel with two in series; (b) Four in series 18. C = 15/41 µF = 0.366 µF 19. Q 1 ’ + Q 2 ’ = 48 µC; Q 1 ’/C 1 = Q 2 ’/C 2 Q 1 ’ = 16 µC, Q 2 ’ = 32 µC; 8 V for both 20. Q 1 ’+ Q 2 ’ = 240 µC; Q 1 ’/C 1 = Q 2 ’/C 2 Q 1 ’ = 60 µF, Q 2 ’ = 180 µF, V = 30V for both 21. (a) Q 1 ’ + Q 2 ’ = 86 µC; Q 1 ’/C 1 = Q 2 ’/C 2 Q1’ = 32.25 µC, Q 2 ’ = 53.75 µC, V = 10.75 V for both; (b) Q 1 ’ + Q 2 ’ = 14; Q 1 ’/C 1 = Q 2 ’/C 2 Q 1 ’ = 5.25 µC, Q 2 ’ = 8.75 µC, V = 1.75 V for both 22. 17 values (µF) : 4/7, 2/3, 4/5, 6/7, 1,10/7, 4/3, 12/7, 2, 7/3,
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