261 Odd Problem Solution

# 261 Odd Problem Solution - APPENDIX E ANSWERS TO SELECTED...

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APPENDIX E – ANSWERS TO SELECTED PROBLEMS Author’s note: “Selected” problems are odd-numbered end-of-chapter problems that have an answer (as opposed to a proof). The answers to problems created by Hayt and Kemmerly were determined by working all problems myself and comparing results to rough solutions generated by them before their deaths. An answer would not be released until there was agreement and the work was checked. If results disagreed, the problem would be re-worked and checked until results were certain. Answers to my own problems (in Chapters 11-14) were subjected to similar scrutiny, and were in most cases classroom tested before inclusion in the text. Despite this system, errors are likely to exist. I would greatly appreciate your contacting me or the publisher as these are found. — J.A. Buck Chapter 1 1.1. ) a. )0 . 92 a x + 0 . 36 a y + 0 . 14 a z b. ) 48.6 c. ) 580 . 5 a x + 3193 a y 2902 a z . 1.3. ) (7.8, -7.8, 3.9) 1.5. ) a. )48 a x + 36 a y + 18 a z ) 0 . 26 a x + 0 . 39 a y + 0 . 88 a z c. . 59 a x + 0 . 20 a y 0 . 78 a z d. ) 100 = 16 x 2 y 2 + 4 x 4 + 16 x 2 + 16 + 9 z 4 1.7. ) a. ) 1) the plane z = 0 , with | x | < 2, | y | < 2; 2) the plane y = 0 , with | x | < 2, | z | < 2; 3) the plane x = 0 , with | y | < 2, | z | < 2; 4) the plane x = π/ 2 , with | y | < 2, | z | < 2. ) the plane 2 z = y , with | x | < 2, | y | < 2, | z | < 1. c. ) the plane y = 0 , with | x | < 2, | z | < 2. 1.9. ) a. . 6 a x + 0 . 8 a y )53 c. )26 1.11. ) a. ) ( 0 . 3 , 0 . 3 , 0 . 4 ) ) 0.05 c. ) 0.12 d. )78 1.13. ) a. ) ( 0 . 93 , 1 . 86 , 2 . 79 ) ) ( 9 . 07 , 7 . 86 , 2 . 21 ) c. ) ( 0 . 02 , 0 . 25 , 0 . 26 ) 1.15. ) a. ) ( 0 . 08 , 0 . 41 , 0 . 91 ) ) ( 0 . 30 , 0 . 81 , 0 . 50 ) c. ) 30.3 d. ) 32.0 1.17. ) a. ) ( 0 . 664 , 0 . 379 , 0 . 645 ) ) ( 0 . 550 , 0 . 832 , 0 . 077 ) c. ) ( 0 . 168 , 0 . 915 , 0 . 367 ) 1.19. ) a. ) ( 1 /ρ) a ρ . . 5 a ρ ,or0 . 41 a x + 0 . 29 a y 1.21. ) a. ) 6 . 66 a ρ 2 . 77 a φ + 9 a z ) 0 . 59 a ρ + 0 . 21 a φ 0 . 78 a z c. ) 0 . 90 a ρ 0 . 44 a z 1.23. ) a. ) 6.28 ) 20.7 c. ) 22.4 d. ) 3.21 1.25. ) a. )1 . 10 a ρ + 2 . 21 a φ ) 2.47 c. . 45 a r + 0 . 89 a φ 1.27. ) a. ) 2.91 ) 12.61 c. ) 17.49 d. ) 2.53 1.29. ) a. . 59 a r + 0 . 38 a θ 0 . 72 a φ . 80 a r 0 . 22 a θ 0 . 55 a φ c. . 66 a r + 0 . 39 a θ 0 . 64 a φ 1

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Chapter 2 2.1. )4 . 0 × 10 4 N 2.3. )2 1 . 5 a x µ N 2.5. ) a. . 58 a x 0 . 15 a y + 5 . 51 a z b. ) 6 . 89 or 22 . 11 2.7. ) 159 . 7 a ρ + 27 . 4 a φ 49 . 4 a z 2.9. ) a. ) (x + 1 ) = 0 . 56 [ (x + 1 ) 2 + (y 1 ) 2 + (z 3 ) 2 ] 1 . 5 )1 . 69 or 0 . 31 2.11. ) a. ) 1 . 63 µ C ) 30 . 11 a x 180 . 63 a y 150 . 53 a z c. ) 183 . 12 a ρ 150 . 53 a z d. ) 237 . 1 2.13. ) a. )82 . 1pC . 24 cm 2.15. ) a. )3 . 35 × 10 2 C . 24 × 10 6 C / m 3 2.17. ) a. )57 . 5 a y 28 . 8 a z V / m )23 a y 46 a z 2.19. ) a. )7 . 2 a x + 14 . 4 a y kV / m . 9 a x + 9 . 8 a y + 4 . 9 a z kV / m 2.21. ) 126 a y µ N / m 2.23. ) a. )8 . 1kV / m ) 8 . / m 2.25. ) 3 . 9 a x 12 . 4 a y 2 . 5 a z V / m 2.27. ) a. ) y 2 x 2 = 4 xy 19 )0 . 99 a x + 0 . 12 a y 2.29. ) a. ) 12.2 ) 0 . 87 a x 0 . 50 a y c. ) y = ( 1 / 5 ) ln cos 5 x + 0 . 13 2.31. ) ρ 3 = 364 sin 3 φ Chapter 3 3.1. ) a. ) Penny: + 5 nC; nickel: 0; dime: 0; can: 5nC ) Coins: same as at start; can: 2nC 3.3. ) a. . 25 nC )9 . 45 pC 3.5. ) 360 C 3.7. ) a. . 0 × 10 9 nC . 2 × 10 4 nC / m 2 3.9. ) a. ) 164 pC ) 130 nC / m 2 c. )32 . / m 2 3.11. ) a. b .) D ρ = 10 15 2 π 2 ρ h sin ( 2000 πρ) + 2 π h 1 10 3 ρ cos ( 2000 ii C / m 2 ( 1mm <ρ< 1 . 5mm ) c .) D ρ = 2 . 5 × 10 15 πρ C / m 2 (ρ > 1 . ) 3.13. ) a. ) D r (r < 2 ) = 0; D r (r = 3 ) = 8 . 9 × 10 9 C / m 2 ; D r (r = 5 ) = 6 . 4 × 10 10 C / m 2 . ) ρ s 0 =− ( 4 / 9 ) × 10 9 C / m 2 . 2
3.15. ) a. )[ ( 8 πL)/ 3][ ρ 3 1 10 9 ] µ C where ρ 1 is in meters. b. )4 3 1 10 9 )/( 3 ρ 1 C / m 2 where ρ 1 is in meters.

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261 Odd Problem Solution - APPENDIX E ANSWERS TO SELECTED...

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