23 (b) 1 (p. 192) 1. (a) F (b) F 2. (a) C C B B B A (b) 2 (p. 196) 1. (a) T (b) F (c) T 2. (a) W 4. 3 (p. 205) 1. A A 2. (a) F (b) T 3. 4. (a) (b) Z 3. (a)
2 23 (b) 4. (a) B X = µ 0I = (4π 10 7 )(1.5) X 2π(0.045) = 6.67 μt B Y = µ 0I = (4π 10 7 )(1.5) Y 2π(0.015) = 20 μt (b) B X = µ 0I = (4π 10 7 )(2) X 2π(0.02) = 20 μt B Y = µ 0I = (4π 10 7 )(2) Y 2π(0.04) = 10 μt 5 (p. 213) 1. A B = µ 0 ni B ni 5. (a) A ni 2. (a) F (b) (b) F (c) T 6. (a) 3. 6 (p. 220) (b) 1. X Y Z 2. (a) (b) (c) 3. (a) 4 (p. 209) 1. (a) T B = µ 0 ni (b) 4. (a) (b) (b) F L R (c) F B = µ 0I B 1 r 2. (a) (b) (c) 3. (a) (b) 7 (p. 227) 1. (a) X (b) F = LI B F L = I B 0.024 0.01 = 3B B = 0.8 T
23 3 2. F L = µ 0I 1 I 2 = (4π 10 7 )(15)(3) 2π(0.2) = 4.5 10 5 N m 1 3. (a) F L = I B sinθ = (1)(1)(sin90 ) = 1 N m 1 (b) F L = (1)(1)(sin30 ) = 0.5 N m 1 (c) F L = (1)(1)(sin60 ) = 0.866 N m 1 4. (III) < (IV) < (I) = (II) 8 (p. 230) 1. (a) X Y (b) F = ( 1.60 10 19) (1)(0.5)(1) = 8 10 20 N (c) (d) F = ( 1.60 10 19) (1)(0.5)(sin45 ) = 5.66 10 20 N 11 (p. 247) 1. (a) F θ (b) (i) (ii) (iii) 1 2 3 θ = 0 θ = 90 0 < θ < 90 2. τ max = N I B A = (1)(1.2)(0.4)(50 10 4 ) = 2.4 10 3 N m 9 (p. 235) 1. (b) I = 0 F X = 0 F Y = 0 F net = 0 τ net = 0 (c) X Y F X = F 0 F Y = F 0 F net = 0 τ net = τ 0 2. 3. 4. 5. 10 (p. 244) 1. (a) F (b) F (b) T (c) F f = 1 T T = 2π B m q 2. (a) (b) (c) 23.1 (p. 198) 1. (a) (c) T (d) T (e) T 2. (a) F = qvb sinθ = ( 1.60 10 19) (1)(0.5)(1) = 8 10 20 N
4 23 (b) 8. (a) 2. D 3. C (b) B > C > A 9. (a) 4. C 5. (a) (b) 6. (a) T X (b) T X Y (b) A C (c) 10. (a) (c) F Z 7. (a) (b) (c) (b)
23 5 11. B C B C (c) 2. (a) (b) 12. (a) (c) (b) 23.2 (p. 213) 1. (a) 3. D 4. (a) (b) 5. (a) P S (b) P S (b) (c) P S 6. (a) A B A B (b) C X C C
6 23 7. (a) B X = µ 0I = (4π 10 7 )(1) 2π(0.6) = 0.333 μt X P 12. (a) (b) (c) (d) 13. (a) (b) cosθ = 0.5/0.6 B res = 2B X cosθ = 2 ( 0.333 10 6) (0.5/0.6) = 0.556 μt 8. (a) +z (b) (b) 14. (a) 9. (a) (b) (c) 10. ( ) N B P = B Q = µ 0 I L = ( 4π 10 7)( ) 11 20 10 2 (3) = 207 μt B R = 1 2 B Q = 104 μt 11. (a) ni B = µ 0 ni P (b) Y X (b) 15. (a) (b) 16. (a) (i) (ii) (b)
23 7 23.3 (p. 236) 1. (a) (b) 1000 7. (a) y (b) (b) (c) x LI B = mg sinθ B = mg sinθ I L (c) 2. B 3. D 4. F = LI B sinθ = ( 8 10 2 sin50 ) (2)(0.05)(sin50 ) = 0.008 N 5. (a) F Q P (b) F L (c) T 6. (a) LIB = mg ( 5 10 3 ) (9.81) B = ( 20 10 2 ) (5) = 49.1 mt 8. (a) (b) 9. (a) Z F X L = µ ( 0I X I Y 4π 10 7 ) (1)(1) = = 2π(0.6) 3.33 10 7 N m 1 cosθ = 0.5/0.6 F L = 2 ( FX L ) cosθ = 2 ( 3.33 10 7) (0.5/0.6) = 5.56 10 7 N m 1 (b) F = LI B B = (F /L)/I = 5.56 10 7 /1 = 0.556 μt 23.2 7 10. (a) PQ QR RS SP
8 23 (b) QR SP F = F RS F PQ = µ 0I 1 I 2 L µ 0I 1 I 2 L RS PQ ( 4π 10 7 ) (2.5)(12)(0.75) = 2π = 37.5 μn ( ) 1 0.10 1 0.10 + 0.50 (c) 37.5 μn 11. (a) NlI B (b) (c) 15. (a) F = NLI B = (50)(0.09)(0.4)(0.2) = 0.36 N (b) QR = F v = (0.36)(2) = 0.72 W 23.4 (p. 248) PQ = 0 ( F v) = 2 0.72 = 1.44 W 1. C 2. B 3. A v B F v B 4. (a) (b) (c) 5. (a) F E = qe F B = qvb (b) 12. (a) N I Bl 2 (b) 0 13. (a) F (b) F (c) T 14. (a) Q (b) τ = N I B A sinϕ = (20)(0.5)(0.4) ( 0.03 2 π ) sin90 = 1.13 10 2 N m 1 Q 6. (a) F E = F B qe = qvb v = E B
23 9 (b) (i) (ii) 7. (a) X Y (b) mv 2 = qvb r v = qbr m = qbd 2m 11. (a) Q P r = mv qb (b) 12. (a) (b) (c) 13. (a) I = Q/t = (5 10 9 )/(0.1) = 5 10 8 A (b) r = mv qb m q 8. (a) 5 cm (c) (i) (ii) r min = mv min qb v min = r min B q m = (0.05)(0.003) ( 1.76 10 4) = 2.64 m s 1 (b) 2.5 cm ( = 1 2 r min) v max = 1 2 v min = 1.32 m s 1 9. mg h X 10. (a) 2 5 = 10 s T = 2πm Bq (b) m = qbt 2π = (2 10 10 )(0.5)(10) 2π = 1.59 10 10 kg (p. 253) 1. B A B C D 2. A (3) P Q (1) (2) B 3. D (1) (2) (3) B = µ 0 ni n I
10 23 4. A B B 2B µ 0 ni 1 2 µ 0nI 5. A 6. D 7. D T = 2πm qb T r 8. D X Y Z F /L I Z F + 3F = 4F 9. C 10. C Y X X 11. C P Q S O R R O ( 12. D B = µ N ) 0 L I N L D N/L (p. 255) 13. 14. (a) (b) (c) 6 10 3 T (1M) ( B = µ N ) 0 L I I = BL µ 0 N = (6 10 3 )(60 10 2 ) (4π 10 7 )(500) (1M) = 5.73 A (d) 15. 16. (a) (b) (c) (2A)
23 11 17. (a) (b) (c) (b) (c) (i) (ii) (iii) 20. (a) 18. (a) (i) 1A 1A (ii) 1A (b) (i) (ii) F L = µ 0I 1 I 2 = (4π 10 7 )(1 10 6 )(1 10 6 ) 2π(1) 2 10 5 N (1M+1A) (c) 19. (a) (i) = (b) I II III IV V VI 1A 2A (c) qvb = mv2 r v = qbr m = (1.60 10 19 )(0.5)(0.5/2) 5.80 10 25 (1M) = 3.45 10 4 m s 1 (d) 3.45 10 4 m s 1 21. (a) 1A 1A (ii) 1A (iii) 1A 1A 1A
12 23 (b) (i) F = LI B (1M) B = F LI = 8.0 10 3 (12 10 3 )(5.8) = 0.115 T 0.1 T (ii) (c) 0.3 T 0.1 T (d) 22. (a) = (b) (i) AB (ii) (1) = LI B = (0.015)(0.030)(0.060) = 2.7 10 5 N (2) = F d = (2.7 10 5 )(0.015) = 4.05 10 7 N m (c) (i) F = QvB (1M) Q = F vb = 2.0 10 13 (4.5 10 6 )(0.14) = 3.17 10 19 C (ii) F = mv 2 /r r = mv2 F = (2.7 10 26 )(4.5 10 6 ) 2 2.0 10 13 = (1M) 2.73 m (iii) r = mv qb r m 23. (a) B = µ 0I = (4π 10 7 )(25) 2π(0.0060) (1M) = 8.33 10 4 T (b) (i) (ii) F l = µ 0I 1 I 2 = (4π 10 7 )(25)I = 5.0 10 6 I r (iii) = (5.70 10 3 )(9.81) = (1M) 0.0559 N m 1 (1M) 24. (a) (i) F = qvb = (1.60 10 19 )(1.2 10 7 )(0.01) (1M) = 1.92 10 14 N (ii) 1A (b) (c) (p. 259) mv 2 = qvb r v r = qb m = (1M) 0.6 10 7 m s 1 1. C W X Z Y W X Y Z W X 2. D v = E/B r = m q v B 3. (a) (b) (i) (ii) (c) 5.0 10 6 I = 0.0559 0.0060 (1M) I = 67.1 A