10.0 C N = = = electrons C/electron C/electron. ( N m 2 /C 2 )( C) 2 (0.050 m) 2.
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1 Electric Forces and Fields Section Review, p. 633 Givens Chapter q 10.0 C q 10.0 C N electrons C/electron C/electron Practice 17A, p q C q 8.0 C r 5.0 c F k Cq 1q r F 30 N ( N /C )( C) (0.050 ). r 0.30 q C q C a. F k Cq 1q r F N ( N /C )( C)( C) (0.30 ) q C q C b. F k Cq 1q r ( N /C )( C) (0.30 ) N 3. q C r 0.1 q 4.3 C 4. q C q 50.0 C F 175 N a. F k Cq1q ( N /C )( C)( C) r (0.1 ) F 16 N q C c. N electrons C/electron C/electron q C d. N electrons C/electron C/electron r k Cq1 q ( N /C )( C)( C) F r c 175 N Section One Pupil s Edition Ch. 17 1
2 Practice 17B, p. 639 Givens 1. q C at x 0 c q 1.5 C at x 3.0 c q 3.0 C at x 5.0 c F 1, k Cq1q ( r 1,) F,3 k Cqq3 ( r,3) F 1,3 k Cq1q3 ( r 1,3) ( N /C )( C)( C) (0.030 ) ( N /C )( C)( C) (0.00 ) ( N /C )( C)( C) (0.050 ) F 1,tot F 1, + F 1,3 ( N) + (43 N) 47 N N 67 N 43 N F 1,tot 47 N, along the negative x-axis F,tot F 1, + F,3 ( N) + (67 N) 157 N F,tot 157 N, along the positive x-axis F 3,tot F,3 + F 1,3 (67 N) (43 N) N F 3,tot N, along the negative x-axis. q C q 6.0 C q 3.4 C q C r 1, r,4 r 3,4 r 1,3 15 c a. r 1,4 r,3 (1 5 c ) + ( 15 c ) r 1,4 r,3 1 c F 1, k Cq1q ( r 1,) F 1,3 k Cq1q3 ( r 1,3) 0 c + 0 c 44 0 c ( N /C )( C)( C) (0.15 ) ( N /C )( C)( C) (0.15 ) 7. N.9 N F 1,4 k Cq1q4 ( r 1,4) ( N /C )( C)( C) (0.1 ) F 1,x (7. N) + (5.5 N)(cos 45 ) 7. N N 11.1 N 5.5 N F 1,y (.9 N) (5.5 N)(sin 45 ).9 N 3.9 N 6.8 N F 1,tot (F 1, x ) + ( F 1, y ) ( N ) + ( 6. 8 N ) 1 3 N N F 1,tot 16 9 N 13.0 N q tan F 1,tot b. F,1 7. N (See a.) F,3 k Cqq3 ( r,3) F,4 k Cqq4 ( r,4) 13.0 N, 31 below the positive x-axis ( N /C )( C)( C) (0.1 ) ( N /C )( C)( C) (0.15 ).9 N N Ch. 17 Holt Physics Solution Manual
3 F,x (7. N) + (.9 N)(cos 45 ) 7. N +.1 N 5.1 N F,y ( N) + (.9 N)(sin 45 ) N +.1 N 4 N F,tot (F, x ) + ( F, y ) (5.1 N ) + ( 4 N ) 6 N N F,tot 61 0 N 5 N q tan F,tot 5 N, 78 above the negative x-axis c. F 4,1 5.5 N (See a.) F 4, N (See b.) F 4,3 k Cq4q3 ( r 4,3) ( N /C )( C)( C) (0.15 ) F 4,x (5.5 N)(cos 45 ) + (8.6 N) 3.9 N N 4.7 N F 4,y (5.5 N)(sin 45 ) ( N) 3.9 N N 18 N F 4,tot (F 4, x ) + ( F 4, y ) (4.7 N ) + ( 18 N ) N N F 4,tot 34 0 N 18 N q tan F 4,tot 18 N, 75 below the positive x-axis 8.6 N Practice 17C, p q C at the origin q C at x 1.5 q C ( r 1q3 1,3) k Cqq3 ( r,3) q1 q (r 1, 3) (r, 3) P C C ( 1. 5 P) ( C)(P ) ( C)(1.5 P) P 9 C (1.5 P) C P 1.1 (0.707)(P) (1.707)(P) 1.1 P 0.64 fro q 1, or x 0.64 Section One Pupil s Edition Ch. 17 3
4 Givens. q C q C r 1, 40.0 c q C ( r 1q3 1,3) k Cqq3 ( r,3) q1 q (r 1, 3) (r, 3) C C P ( P) ( C)(P ) ( C)(0.400 P) P C C (0.400 P) P 0.63 (1.58)(P) (.58)(P) 0.63 P c fro q 1 or (40.0 c 4.5 c) 15.5 c fro q 3. q 1 q C e kg F electric F g k C q 1q r e g r k Cq e 1g q ( N /C )( C) 5.07 ( kg)(9.81 /s ) Section Review, p q 1.0 C r 1 c q 3.5 C a. F k Cq 1q r F 4.4 N ( N /C )( C)( C) (0.1 ) 3. q C at x 1.5 q C at x.0 q C at the origin q C c. N electrons C/electron C/electron F 1,3 k Cq1q3 ( r 1,3) F 1, N F,3 k Cqq3 ( r,3) F, N ( N /C )( C)( C) (1.5 ) ( N /C )( C)( C) (.0 ) F 3,tot ( N) ( N) N F 3,tot N, along the negative x-axis Ch Holt Physics Solution Manual
5 4. q C q C r 1, 60.0 c ( r 1q3 1,3) k Cqq3 ( r,3) q1 q (r 1, 3) (r, 3) C C P ( P) ( C)(P ) ( C)(0.600 P) P C C (0.600 P) P (1.41)(P) (.41)(P) P 0.35 fro q c fro q 1 or (60.0 c 35. c) 4.8 c fro q Practice 17D, p q C at the origin q 3.00 C at x For the point y on the y-axis, E 1 k Cq1 r 1 ( N /C )( C) (0.500 ) N/C E k Cq ( N /C )( C) r ( ) + ( ) ( N /C )( C) E ( N /C )( C) E N/C q tan E y ( N/C) ( N/C)(cos 58.0 ) E y ( N/C) ( N/C) N/C E x ( N/C)(sin 58.0 ) N/C E tot (E y ) + ( E x ) ( N /C ) + ( N /C ) E tot ( N C / ) + ( N C / ) E tot N C / N/C j tan E tot N/C, 81.1 above the positive x-axis Section One Pupil s Edition Ch. 17 5
6 Givens. r E N/C, along the positive x-axis q e q p C E k Cq r ( N /C )( C) ( ) E N/C, away fro the proton a. F Eq e ( N/C)( C) F N, along the negative x-axis b. F Eq p ( N/C)( C) F N, along the positive x-axis N/C Section Review, p q C q C r 30.0 c 15.0 c E 1 k C r q 1 E k C r q ( N /C )( C) (0.150 ) ( N /C )( C) (0.150 ) N/C N/C E tot E 1 + E ( N/C) ( N/C) N/C E tot N/C toward the C charge Chapter Review and Assess, pp q 3.5 C q C N electrons C/electron C/electron 18. q 1 q (46)( C) r ()( ) F k Cq 1q r ( N /C )[(46)( C)] [()( )] 19. q 1.5 C q 5.0 C r 5.0 c 0. q 1.0e q 79e r e C F N F k Cq 1q r F 45 N F k Cq 1q r F 91 N ( N /C )( C)( C) (0.050 ) ( N /C )(.0)(79)( C) ( ) Ch Holt Physics Solution Manual
7 1. q nc q 6.0 nc q 3.0 nc r 1, r,3 (1.0 ) + ( 1. 0 ). q 1 q C q C r,1 1.0 r 3,1 r 3, r 1, r,3 F 1, k Cq1q ( r 1,) (1.0 ) + ( 1. 0 ) F 1, N F,3 k Cqq3 ( r,3) F, N F x ( N)(cos 45 ) + ( N)(cos 45 ) F x ( N) + ( N) N F y ( N)(sin 45 ) + ( N)(sin 45 ) F y ( N) + ( N) N F tot (F x ) + ( F y ) ( N ) + ( N ) F tot ( N ) + ( N ) N F tot N q tan ( N /C )( C)( C) (1.4 ) ( N /C )( C)( C) (1.4 ) F tot N, 1 below the positive x-axis r 3,1 r 3, (0.5 0 ) + ( ) 0.86 F 3,1 F 3, k Cq3q1 ( r 3,1) F 3,1 F 3, N ( N /C )( C)( C) (0.86 ) F x F 3,1 cos q + F 3, cos q F x ( N) ( N) F x N N N F y F 3,1 sin q + F 3, sin q F x ( N) ( N) N F tot (F 1 ) + ( F 4 ) ( N ) N q tan 1 0 N N 0 F tot N along the +x-axis Section One Pupil s Edition Ch. 17 7
8 Givens 3. q C at y 6.0 q 8.0 C at y 4.0 ( r 1q3 1,3) k Cqq3 ( r,3) C C P ( 10.0 P) ( C)(P ) ( C)(10.0 P) C C P (10.0 P) P 11 (1.1)(P) (.1)(P) 11 P 5. below q 1, or y q 3 is located at y q nc q 5.0 nc r 40.0 c q nc ( r 1q3 1,3) k Cqq3 ( r,3) C C P ( P) ( C)(P ) ( C)(0.400 P) C C P (0.400 P) P 0.33 (0.84)(P) (1.84)(P) 0.33 P c fro q q C q C r 30.0 c 15.0 c E 1 k C r q 1 E k C r q ( N /C )( C) (0.150 ) ( N /C )( C) (0.150 ) N/C N/C E tot ( N/C) ( N/C) N/C E tot N/C toward the C charge Ch Holt Physics Solution Manual
9 39. q C at x 3.0 q.0 C at x 1.0 For E at y.0 on the y-axis, r 1 (.0 ) + ( 3. 0 ) r (.0 ) + ( 1. 0 ) E 1 k Cq1 r 1 E k Cq r q 1 tan ( N /C )( C) (3.61 ) ( N /C )( C) (. ) N/C N/C q tan E x ( N/C)(cos 34 ) ( N/C)(cos 63 ) E x ( N/C) ( N/C) N/C E y ( N/C)(sin 34 ) + ( N/C)(sin 63 ) E y ( N/C) + ( N/C) N/C E tot (E x ) + ( E y ) ( N /C ) + ( N /C ) E tot ( N C / ) + ( N C / ) ( N C / ) N/C q tan E tot N/C, 75 above the positive x-axis 40. q 1 ( protons)(e) q ( electrons)(e) e C Q net q 1 + q [( ) ( )](e) ( )(e) Q net ( )( C) Q net C 41. a /s e kg g of Cu has atos. 1 Cu ato has 9 electrons. a. F e a ( kg)( /s ) N F N, in a direction opposite E b. E F 7 q N N/C C a g of Cu has ( atos)(9 electrons/ato) electrons b. q tot ( electrons)( C/electron) C Section One Pupil s Edition Ch. 17 9
10 Givens 43. q C q 1.5 C q 3.0 C r 1, 3.0 c r,3.0 c a. E at 1.0 c left of q E 1 + E + E 3 r 1 r 1, 1.0 c 3.0 c 1.0 c.0 c r 1.0 c r 3 r, c.0 c c 3.0 c E 1 k Cq1 r 1 E k Cq r ( N /C )( C) (0.00 ) ( N /C )( C) (0.010 ) N/C N/C E 3 k Cq3 ( N /C )( C) r N/C 3 (0.030 ) E tot ( N/C) ( N/C) + ( N/C) E tot N/C along the positive x-axis q 4.0 C b. F q 4 E ( C)( N/C) N 44. q nc q 6.0 nc q nc r 1, 0.30 r 1, a. F 1, k Cq1q ( r 1,) F 1, N F 1,3 k Cq1q3 ( r 1,3) F 1, N F 1,tot (F 1, ) + ( F 1, 3 ) F 1,tot ( N /C )( C)( C) (0.30 ) ( N /C )( C)( C) (0.10 ) ( ( N ) + ( N ) 6 N ) + ( N ) N N 45. q 1 ( )(e) q ( )(e) r ()( ) e C kg kg q tan F 1,tot N, 77 below the negative x-axis F b. E N q N/C, 77 below the negative x-axis C F k C q 1q r F N F g F electric G1 r k Cq r q G k 1 C ( N /C )[( )( C)] [()( )] ( N /kg )( kg)( kg) N /C q C Ch Holt Physics Solution Manual
11 g q 5.0 L 30.0 c ΣF y 0 N, so F g F T,y F T (cos 5.0 ) ΣF x 0 N, so F electric F T,x F T (sin 5.0 ) F el ec tric FT( sin 5. 0 ) tan 5.0 Fg F T ( cos 5. 0 ) r tan 5.0 g r ()(0.300 )(sin 5.0 ) q r g( a n 5.0 ) t kc [()(0.300 )(sin 5.0 )] q ( kg)(9.81 /s )(tan 5.0 ) N /C q C 49. e kg p kg a. F Eq g E e eg q E e b. E p pg q ( kg)(9.81 /s ) C N/C, downward ( kg)(9.81 /s ) C E p N/C upward N/C N/C 50. q nc q 6.0 nc q nc r 1,3 r, r,3 r 1, ( N /C )( C) E 1 ( r1,4) 670 N/C (0.0 ) ( N /C )( C) E ( r,4) 150 N/C (0.60 ) r 3,4 (0. 0 ) + ( ) r 3, ( N /C )( C) E 3 ( r3,4) 110 N/C (0.63 ) q tan E x (150 N/C) (110 N/C)(cos 18 ) 150 N/C ( N/C) E x 50 N/C E y (670 N/C) + (110 N/C)(sin 18 ) 670 N/C + 34 N/C E y N/C E tot (E x ) + ( E y ) ( 50 N /C ) + ( N /C ) ( N C / ) + ( N C / ) E tot j tan ( ) N C / N/C E tot N/C, ( ) above the negative x-axis Section One Pupil s Edition Ch
12 51. E 50 N/C t 48 ns a F qe v i 0 /s e kg p kg v f a t q E t For the electron, v f,e q E t ( C)(50 N/C)( s) e kg /s For the proton, v f,p q E t ( C)(50 N/C)( s) p kg /s 5. q C r 1.0 a. Because the doe is a closed conducting surface, E 0.0 N/C inside the doe. b. E k Cq ( N /C )( C) r (1.0 ) N/C c. E ( 4r) ( N /C )( C) (4.0 ) N/C 53. E N/C r.0 q E r kc ( N/C)(.0 ) ( N /C ) C 54. E N/C p kg 55. E N/C 56. q 5.0 C r.0 a. F qe ( C)( N/C) F N b. a /s p kg N F qe ( C)( N/C) N E 1 E E 3 k Cq ( N /C )( C) r N/C (.0 ) E x ( N/C)(sin 60 ) ( N)(sin 60 ) 0.0 N/C E y ( N/C) ( N/C)(cos 60 ) ( N/C)(cos 60 ) E y ( N/C) ( N/C) ( N/C) 0.0 N/C E tot (0.0 N /C ) + ( 0. 0 N /C ) 0.0 N/C Ch Holt Physics Solution Manual
13 57. q 4 C E 610 N/C 58. E 640 N/C v i 0 /s v f /s p kg F electric F g qe g q ( ge 6 C)(610 N/C) 3 kg 9.81 /s F qe ( C)(640 N/C) a. a /s p p kg b. t v f /s a /s s c. x 1 a t (0.5)( /s )( s) x 1 d. KE f 1 p v f (0.5)( kg)( /s) KE f J kg L 30.0 c q 45 ΣF x 0 N F electric F T,x F T,x F electric F T (sin 45 ) ΣF y 0 N F T,y F g F T,y F g F T (cos 45 ) F el ec tric FT( sin 45 ) tan 45 Fg F T ( cos 45 ) F electric (L sin q) + (L sin q) 4k Cq + 5 4L ( sin q) 4L ( sinq) F g g g L 0.0 c E N/C q 15 F el ec tric 5 Fg 4L ( sin tan 45 q)g 5k C q 4L (sin q)g(tan 45 ) q 4L (sin q)g(tan 45 ) L(sin q) g (t a n 5 k C 45 ) (0.10 kg)(9.81 /s q ()(0.300 )(sin 45 ) )(tan 45 ) (5)( N /C ) q C 5kC b. F T, y F g g FT,y g F T co s 15 co s15 qe F T,x F T (sin 15 ) g ( sin 15 ) g(tan 15 ) cos 15 q g(ta n15 ) E ( kg)(9.81 /s )(tan 15 ) N/C C Section One Pupil s Edition Ch
14 Givens 61. +y Because each charge is the sae size and all are the sae distance fro the center, q E 1 E E 3 E 4 E 5 k Cq r q E E 3 E 1,y 0 N/C q E 5,y E,y E(sin 7 ) 36 7 E 1 +x 7 E 4,y E 3,y E(sin 36 ) E 4 q E 5 E y E 1,y + E,y + E 3,y + E 4,y + E 5,y E y 0 N/C + E(sin 7 ) + E(sin 36 ) E(sin 36 ) E(sin 7 ) 0 N/C q E 1,x E E,x E 5,x E(cos 7 ) E 3,x E 4,x E(cos 36 ) E x E 1,x + E,x + E 3,x + E 4,x + E 5,x E x E + E(cos 7 ) E(cos 36 ) E(cos 36 ) + E(cos 7 ) E x E + E(cos 7 ) E(cos 36 ) E( ) E x 0 N/C E (E x ) + ( E y ) (0 N /C ) + ( 0 N /C ) 0 N/C 6. E N/C e kg v i 0 /s v f (0.100)( /s) p kg F qe ( C)( N/C) a. a /s e e kg b. v f a x x v f [(0.100)( /s)] a ()( /s ) F qe ( C)( N/C) c. a /s p p kg 63. r 1.17 q C q C r (0.0100)(.17 ) 64. E N/C t 1.00 s e kg p kg F electric F elastic k Cq1q r kr 1 k k Cq1q ( N /C )( C) r 1 r ( ) 3 (0.0100) k N/ F qe ( C)(370.0 N/C) a e /s e e kg x e 1 a e t (0.5)( /s )( s) 3.5 F qe ( C)(370.0 N/C) a p /s p p kg x p 1 a p t (0.5)( /s )( s) x p x tot x e + x p ( ) 3.5 Ch Holt Physics Solution Manual
15 65. E N/C e kg t s F qe ( C)(300.0 N/C) a. a /s e e kg b. v f a t ( /s )( s) /s 66. E N/C along the positive x-axis a. F qe ( C)( N/C) N F N, along the positive x-axis p kg 16 F N b. a p kg /s v f /s 67. v f,1 (0.010)( /s) x 1.0 e kg c. t v f /s s a /s vf,1 a. a x1 E ea evf,1 q x1q E ( kg)[(0.010)( /s)] ()( )( C) E N/C x 4.0 vf,1 [(0.010)( /s)] b. a /s x1 ()( ) 68. KE J x 1.5 v f 0 /s p kg v f, a x v f, KE 1 p v i v i K E p a v f v i x a x F qe p a E pa ( p ( vf v q () i ) q) ( x) E ( )( /s (4.0 ) ) /s p v f p K p E (q)( x) ( kg)(0 /s) ()( J) ( C)()(1.5 ) E N/C opposite the proton s velocity pvf KE (q)( x) N/C Section One Pupil s Edition Ch
( N m 2 /C 2 )( C)( C) J
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