20 (p.7). (a) T (b) T (c) T (d) F 2. B 3. 3 (p.4). D 2. C D A B D B D B D 3. (a) F (b) F (c) T 4. 2 (p.0) 4 (p.23). (a) B (b) A P 2. (a) F (b) T 3. 4. 5. 6. (a) (b).6 0 9.6 0 9 0 0. (a) X Y (b) X Y Z 2. (a) T (b) F (c) F 3. A A B A B 4. 5.
2 20 5 (p.29). (a) F Qq r 2 ()() 2 9 0 9 N (b) Q 2 r 2 F ( 2 )() Q 0 5 C 2. (a) F (b) F 3. 7 (p.42). (a) T (b) F (c) T 2. (a) A (b) (c) 4. (a) 4 (b) (c) 2/9 5. (a) F ( q 2 r 2 + q2 (2r ) 2 ) 5 4 ( ) q2 r 2 (b) F 0 ( ) (c) F 2 q2 cos45 ( ) 2 r 2 q2 r 2 (c) > (a) > (b) 6 (p.34). (a) T (b) T F qe E (c) F 2. (a) T E F /q + C (b) F (c) F 3. E F q 0.05 24 0 6 625 N C 3. (a) F (b) F X 8 (p.60). (a) T (b) F (c) T r 2 (d) F 2. (a) E 0 Q r 2 0 r a r 0 2 + 2 2r 0 E a Q E 0 ra 2 2 (b) r b r 0 2 + 2 2 5r 0 E b Q E 0 r 2 b 5 (c) r c r 0 2 + 3 2 0r 0 E c Q E 0 rc 2 0 (d) r d r 0 2 + 4 2 7r 0 E d Q E 0 r 2 d 7
20 3 3. (a) E: F: q: (b) Q r 2 E: Q: r : (c) 2. (a) (i) (ii) (b) (i) 4. (a) C (b) A 4πε Q + 0 r+ 2 4 0 6 Q r 2 (0.5 2 5 2 ) 2 Q ( 2 5 2 ) 2 5. (a) KE F d qe d ev (b) KE F (d/2) ev /2 (c) KE 20. (p.4) F (d/2) ev /2. (a) (b) Q 6 μc (ii) 3. B 4. (a) (b) (c) 5. C Q S S R R 6. (a) (b) 7. (a) (b) 0 9.60 0 9 6.25 0 9 6.25 09 6.25 0 5 0 24 8. (a)
4 20 (b) 9. (a) (b) 0. (a) (b) 20.2 (p.23). (a) (b) (c) (d) 2. (a) (b) (c) (d) 3. (a) (b) (c) (d) (c) (d) (a) (b) (b) (d) (a) (c) 4. (a) 3 0 9 C (b) 5. (a) 0.5 0 9 C (b) 0 9 + ( 2 0 9 ) 0 9 C 0.5 0 9 + ( 0.5 0 9 ) 0 9 C 6. (a) A B A B B B A A B C B (b) B A 7.
20 5 8. 9. (a) (b) (c) 20.3 (p.30). F Q Q 2 r 2 (9 0 9 ) (3 0 7 ) 2 0.3 2 9 0 3 N 2. F Q Q 2 r 2 9 0 9 (9 0 9 ) (5 0 3 ) 2 d 5 0 4 m 3. (a) (b) d 2 F 2 q 2 ( 0. 2 +0. 2 0.5) 2 3.6 0 2 q 2 (c) 45 F 4 q 2 ( 0. 2 +0. 2 0.5) 2 cos45 5.09 0 2 q 2 (d) (b) 3.6 0 2 q 2 4. (a) T A (b) F (c) F sinθ 0.05 0.2 θ 4.48 (2) () T cosθ mg () T sinθ Q 2 r 2 (2) tanθ Q 2 r 2 mg tan4.48 (9 0 9 ) Q2 0. 2 (0 5 )(9.8) Q 5.3 0 9 C 7. (a) +q +2q +q +2q Q +q d qq d 2 2 qq ( d) 2 ( d) 2 2d 2 0 d 2 + 2d d 0.44 m 2.4 +q 0.44 m Q (b) 8. (a) 5. D mg + Q 2 d 2 6.
6 20 X X F q 2 d 2 X X F q 2 (2d) 2 4 q 2 F d 2 4 F F (b) X 9. (a) +4 μc 8 μc F Q Q 2 r 2 (9 0 9 ) (4 0 6 )(8 0 6 ) 4.608 N 0.25 2 0. q 2 r 2. A B B Q A Q B r 2 m B g (20.) B A A (2) () Q A Q B d 2 m A g (20.2) r 2 d 2 m A d 2 (3)(0.5)2 m B d 0.866 m 8 μc F 2 4.608cos30 7.98 N (b) (a) 8 μc +4 μc F 4.608 N F Q Q 2 +4 μc +4 μc F 4.608/2 2.304 N 2. X Y Q 5+5 2 5 nc F (5 0 9 ) 2 2 2.25 0 7 N 3. (a) Gm 2 r 2 q 2 r 2 q 2 Gm 2 q 8.6 0 3 C 9. 0 3 4.90 0 24 kg 8.6 0 3.60 0 9 F (F + F )cos60 3.456 N F (F F )sin60.995 N tanθ.995 3.456 θ 30 F 3.456 2 +.995 2 3.99 N x 30 (b) G 6.67 0 N m 2 kg 2, k 9 0 9 N m 2 C 2 G k
20 7 4. 20.5 9 0 8 N mv 2 9 0 8 r r ( 9 0 8) v m (0.5 0 0 )( 9 0 8) (ii) (iii) 2.23 0 6 9 0 3 2.23 06 3 0 8 ( 3 0 8) 7 0 3 c 0.7% 20.4 (p.43). (a) 3. B C F qe 4. C C 5. F E qe q F E E 3.0 0 5 7.30 0 5 4.25 0 C (b) 6. mg qe (c) (0.50 0 3 )(9.8) (40.0 0 6 )E E 23 N C 23 N C 2. (a) (i) E A E B E C (ii) E A < E B (iii) E A > E B ( 0) (b) (i) 7.
8 20 8. (a) 2. C F qe ma a q m E E 3. B x 2 (b) (a) F qe 9. 4. 5. (a) E V d 2 03 25 0 3 80000 N C (b) q mg E (.30 0 9 )(9.8) +.59 0 3 C 80000 (c) 20.5 (p.60). (a) 6. A P B P P E E A E B ( 0 9 0.2 2 3 0 9 0.7 2 ) 70 N C 70 N C (b) 7. Q 8πε 0 d 2 y Q ( 2d) 2 y x 2 Q cos45 2Q +y d 2 d 2 E Q(2 2 ) 8πε 0 d 2 8. +y (c) F c F E m e v 2 ( ) e2 r r 2 v e 2 m e r 9. (a)
20 9 (b) 0. 2 mv2 qv 2 (5 0 9 )( 0 2 ) 2 (.25 0 9 )V V 20 kv 2. D α α α 3. C A B 2 F 4. D E V d 20 03 4 0 2 5.00 0 5 N C v 2 u 2 + 2as 0 ( 0 2 ) 2 + 2a(4 0 2 ) a.25 0 5 m s 2 E ma q (5 0 9 )(.25 0 5 ).25 0 9 5.00 0 5 N C. V 0 qv 0 d ma a qv 0 dm t l v 0 0 0. s y u y t + 2 at 2 d 2 u 0 y t + 2 at 2 0.03 (0.4 0 6 )V 0 2 (0.06)( 0 4 ) (0.)2 V 0 90 V A F T mg 0 (0.05)(9.8) 9.5 N. 9.5 (3 0 6 )(5 0 6 ) d.9 cm d 2 5. B () (2) X 6. B () P q P q A R 2 q B r 2 0 (2) P 7. C Y E Y 0 A B Y A X B Z E Z > E X 8. C F E Q 2 L 2 F 2F E Q 2 2πϵ 0 L 2 (p.65). B () (2) X Y Y Y X
0 20 9. B A B 3. A 4. B () (2) P R Q S 5. D Q Q 2 Q Q 2 Q Q 3 Q F r 2 F Q2 4F Q3 Q 3 4 Q 2 (p.67) 6. (a) (i) C B A A C (ii) A (b) (i) F A sin45 W A sin60 F B sin5 W B sin60 F A F B W B W A sin45 sin5 2.73W A B 2.73m 0. A k n F ke2 r 2 r ω 2/3 ω r r 3 4 ke2 r 2 mr ω 2. A (3) 2. A () (2) E V 0 d (3) A A AB OB OA OAB mg (ii) B 7. (a) A B (b) (2.0 0 9 )(2.0 0 9 ) (4 0 2 ) 2 2.25 0 5 N F qee F q (c) 2.25 0 5 2.0 0 9 300 N C (M+A)
20 (a) B A B B (b) B A 4πϵ 2.0 0 9 0 (4 0 2 ) 2 300 N C (2M+A) A A A A 8. (a) A (b) A B A B 20. (a) (b) x 8 cm E 0 E Q Q A r 2 Q B 8 2 0 2 2 Q A : Q B 6: (c) A B x 8 cm 2. (a) (i) 9. (a) (b) (c) E Q E r 2 B 0 9 4 N C 0.8 2 AX 2 + 0.8 2.28 m E A Q r 2 sinθ 4 0 9.28 2 0.8.28 4 N C E B Q cosθ 4 0 9 r 2.28 2.28 7 N C E A E B 7 N C (d) 0.28 0 70 0 4 0 3 V 3.7 0 3 V 4.2 0 3 V (ii) tanθ F e mg F qe E V 0 d tanθ qe mg q mg d V 0
2 20 q mg d (b) q mg d q ( 4 0 3)( 0.0 0 3) (9.8)(0.08) +3.4 0 8 C (c) 22. (a) 24. (a) (i) (ii) (b) (i) tanθ 3 3.5 tanθ v x v y v y ( 3 )( 3.5 3 0 7 ) 2.86 0 6 m s (M+A) (ii) t t 0.03 3 0 7 0 9 s v u 0 + at a v t 2.86 06 a 0 9 2.86 05 m s 2 F ma F qe E ma q A A (b) KE 2 m ( v 2 2 v2 ).09 0 7 J (M+A) (c) U q V E V 0 d U qed E.09 0 7 (.60 0 9 )( 2 0 2) 3.4 0 3 N C (d) F ma qe ma a qe m s ut + 2 at 2 s ut + ( ) qe t 2 2 m (.60 0 9 )( 3.4 0 3) 2 0 + 2 t 8.7 0 8 s 9. 0 3 t 2 23. (a) (b) (c) ( 9. 0 3 )( 2.86 0 5) E.60 0 9 6.3 0 3 N C 6.3 kn C 0 25. (a) 2 3 2 2 2 (b) 2 3 26. (a) (b) (i) (ii) A (iii) (c) (i) (ii) (iii)
20 3 3.6 0 6.2 0 9 3.0 0 3 N C (c) F q q 2 r 2 (d) A (.2 0 3.6 0 6 9 ) 2 r 2 r 6 0 2 m (d) A 27. (a) A 28. (a) (a) T F W (b) A A A (i) (b) A A A (i) tanθ W F (ii) F qe E V d tanθ F W qe mg qv mg d mg d tanθ q V ( 0.07 0 3 ) (9.8)(0.)(tan2 ) 4000 6.00 0 0 C W T cos20 F T sin20 F W tan20 (ii) E F q 3.6 0 6 N (c) θ
4 20 (p.7). A A B B A B 2. B 3. (a) (b) (c) (d) 4. (a) d 0. sin20 0.0342 m qed (0.5 0 6 )(2.38 0 4 )(0.0342).22 0 4 J (b) h 0. 0. cos20 0.00603 m mg h (0.00)(9.8)(0.00603) 5.92 0 5 J (c)