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Cutnell & Johnson, Physics (Sixth Edition) Instructor’s Solutions Manual, Volume II (Wiley, 2004)

Answers to Even-Numbered Questions 1

CHAPTER 18 – ELECTRIC FORCES AND ELECTRIC FIELDS

2. -1.6 µC

4. 3.4×10!17 kg; object A has the larger mass

6. (a) 3.35×1026 electrons(b) -5.36×107 C

8. 26 N

10. 7.3×10!6 C; negative

12. 1.44×104 N; attractive

14. 17.3 N; 38.7E S of E

16. -2.60×10!6 C

18. +111 m/s2; the acceleration is along the +y axis

20. 9.0

22. -5.58 µC on left, +0.957 µC on right; -0.957 µC on left, +5.58 µC on right

24. 0.37 N

26.

28. 1.37

30. (a) x = 3.0 m(b) 0 N

32. (a) 7.5×10!2 N(b) 53.1E

34. 1.81×102 N/C; 3.11×102 N/C

36. 0.76

38. 1.0×107 m/s



40. 3.9×104 m/s

42. 2.09×103 N/C

44. (a) 4.2×10*9 C/m2

(b) 4.8×10!12 C

46. 35 N@m2/C

48. (a) 4.0×105 N@m2/C(b) -2.6×105 N@m2/C(c) 1.4×105 N@m2/C

50. 1.8×103 N@m2/C

52. (a) radially outward(b) radially inward(c) E = 0 N/C

54. E 'Q /L2πε0r

'λ

2πε0r

56. (a) 0.83 N(b) attractive

58. 54 N/C

60. x = +0.71 m

62. 0.16 N@m

64. 7.5×10!6 C

66. 2.5×104 N/C

68. 8.2×10!3 N

70. 6.5×104 N

72. (a) 2.0 N/C(b) 2.0 N/C

74. 1.4×1016 m/s2; 7.7×1012 m/s2

76. q2 = -6.0 µC

CHAPTER 19 – ELECTRIC POTENTIAL ENERGY AND THE ELECTRICALPOTENTIAL



2. (a) 5.80×10!3 J(b) 32.2 V(c) Point A

4. -2.1×10!11 J

6. 8.0×102 eV

8. 4.0 kg

10. 18.7 m/s

12. -4.05×104 V

14. -6.0×10!8 C

16. -9.4×103 V

18. ; dd3

20. 0.38 J

22. -4.8×10!6 C

24. x = 0.200 m to the right of the negative charge; x = 0.176 m to the left of the negative charge

26. rA = 1.41×10!2 m

28. 1.1 m

30. 8.8×106 V/m

32. (a) 0 V(b) +290 V(c) -290 V

34. (a) 0 V/m(b) 1.0×101 V/m(c) 5.0 V/m

36. 12 V

38. 2×10!8 F

40. 7.0×1013

42. 5.66 V



44. 1.1×10!2 m

46. 7.7 V; decrease

48. 2.18×10!5 m

50. (a) 4.5×10!3 N; from A toward B(b) 3.0×103 N/C; from A toward B

52. (a) 1500 V(b) Point B

54. +7.8×106 V

56. 1.7×103 V/m; left

58. 6.8 m/s

60. (a) 0.187 m(b) 3.67

62. 1.15 m

64. 1.2 m

66. 6.3×10!5 F

68. 4.0×10!15 J



CHAPTER 20 – ELECTRIC CIRCUITS

2. (a) 3.6×10!2 C(b) 2.3×1017

4. 1.3×106 J

6. (a) 7.9×105 C(b) 350 A

8. 16 Ω

10. 0.58 Ω

12. 0.12 Ω

14. 0.0050 (CE)!1

16. 9.3%

18. 140 EC

20. 9.7×102 kg

22. (a) 4.4 Ω(b) 2.8 A

24. $5.0×106

26. 190 s

28. 50 m

30. 1.39×10!3 s

32. 21 V

34. 1.3×10!3 m

36. (a) 50.0 Hz(b) 2.40×102 Ω(c) 60.0 W

38. 32 A

40. 9.0 V

42. 4.0×101 Ω



44. three

46. 140 W

48. R2 = 446 Ω

50. 288 Ω

52. 19R

54. 2.00 Ω and 4.00 Ω

56. 5.24 Ω and 0.76 Ω

58. 4.67 Ω

60. 9.2 A

62. (a) 8.33×10!2 A(b) 0.833 W

64. 11.1 W; 2.78 W; 2.78 W

66. 600 Ω

68. 8.3 A

70. 10.9 V

72. 0.054

74. (a) 12 V(b) 24 V

76. 0.73 A; left

78. -1.82 A; the current in the 4.00-Ω resistor is directed downward

80. 0.0835 Ω

82. 30.0 V

84. 8.00×10!3 A; 820 Ω

86. 28.1 V

88. 25 V



90. 1.54

92. 10.0 V

94. 1.80 V

96. 4.0×103 Ω

98. 1.61

100. 228 W

102. 3.5×104 A

104. 5.00 A; 46.0 V

106. 7.2×10!5 C

108. (a) 1.6 A(b) 14 V; 8.0 V; 1.6 V(c) 23 W; 13 W; 2.6 W

110. 0.00116 Ω

112. (a) 8.99 V(b) 2.5 Ω

114. 1.8 V

116. 39.5EC

118. (a) 24.0 W; 12.0 W; 96.0 W; 48.0 W(b) 2.00 A; 1.00 A; 4.00 A; 2.00 A

120. 10.0 Ω; 5.00 Ω; 15.0 Ω

122. (a) 1.08×10!2 J(b) 2.39×10!3 J

124. Circuit A: 4.0 WCircuit B: 8.0 WCircuit C: 2.0 W



CHAPTER 21 – MAGNETIC FORCES AND MAGNETIC FIELDS

2. (a) 5.7×10!5 N; into the paper(b) 1.1×10!4 N; into the paper(c) 5.7×10!5 N; into the paper

4. 13

6. 5.9×1012 m/s2

8. 1.3×10!10 N; directed out of the page

10. 1.1×10!2 N

12. 2.7×10!3 kg

14. 4.3×102 m

16. E/B

18. 1.41

20. 6.8×105 C/kg

22. 0.71 m

24. (a) 4.4×10!3 N(b) 1.7×10!4 C

26. 5.1×10!5 T

28. 2.7 m

30. (a) 0 N; 24.2 N; perpendicularly out of the paper; 24.2 N, perpendicularly into the paper(b) 0 N

32. 3.00 A

34. 44E

36. 2.2 A

38. 3.3 cm

40. 1.27

42. 53.1E



44. 1.13

46. 0.12 m

48. 4.2×10!2 m

50. 1.21×10!4 N; perpendicular to the wire and is directed away from it

52. 3.8×10!5 T

54. 1.5×10!4 N

56. 0.50 m

58. 1.13×10!4 T, down (toward the bottom of the page)

60. the net current passing through the circular surface is zero

62. ; 0 TB 'µ0 I2πr

64. (a) 6.50×10!2 T(b) 9.10×103 m/s

66. 58E

68. 3.1×10!4 T

70. 0.19 N

72. (a) 4.3×10!5 T(b) 5.3×10!5 T

74. 0.030 m

76. 320 A

78. 0.12 T

80. 19 cm

82. Single-turn: 0.036 N@mTwo-turn: 0.018 N@m

84. Point A: 2.8×10!6 TPoint B: 2.8×10!6 T



CHAPTER 22 – ELECTROMAGNETIC INDUCTION

2. 1.0×10!3 V

4. 7800 V

6. 250 m

8. 25 m/s

10. 0.70

12. (a) 7.3×10!4 Wb(b) 0 Wb(c) 4.7×10!3 Wb

14. -9.4×10!2 Wb

16. 7.7×10!3 Wb

18. 276

20. 0.63 V; 2.5 A

22. 0.43 m2/s

24. 0.050 V

26. 2.4×10!3 A

28. counterclockwise induced current

30. the right end of the resistor must be the positive end

32. upward

34. (a) Location I: ; Location II: x 6 y 6 z z 6 y 6 x(b) Location II: ; Location II: z 6 y 6 x x 6 y 6 z

36. 16 Ω

38. (a) 115 V(b) 167 A(c) 7.28 Ω

40. 38 m

42. 2.0 V



44. 9.3×10!3 H

46. (a) -6.4 V(b) 0 V(c) +3.2 V

48. 1.6 A

50. 3.6×109 N/C

52. W '12(LIf ) If '

12LI 2

f

54. (a) step-up(b) 55:1

56. 9.2 V

58. 756

60. 1.1×104 W

62. 0.31 T

64. 0.43 V

66. 1/4

68. 0.86 A

70. (a) When the magnet is above the ring its magneticfield points down through the ring and isincreasing as the magnet falls. The inducedmagnetic field attempts to reduce the increasingfield and points up. The induced current in thering is as shown in the drawing at the right, andthen the ring looks like a magnet with its northpole at the top, repelling the north pole of thefalling magnet and retarding its motion. Whenthe magnet is below the ring, its magnetic field still points down through the ring butis decreasing as the magnet falls. The induced magnetic field attempts to bolster thedecreasing field and points down. The induced current in the ring is as shown in thedrawing, and the ring then looks like a magnet with its north pole at the bottom,attracting the south pole of the falling magnet and retarding its motion.

(b) The motion of the magnet is unaffected, since no induced current can flow in the cutring. No induced current means that no induced magnetic field can be produced torepel or attract the falling magnet.



72. 2.3×10!6 H

74. (a) 9.59 Ω(b) 95 V(c) 8.9 A

76. (a) 0-3.0 s: -1.0 V3.0-6.0 s: 0 V6.0-9.0 s: +0.50 V

(b) 0-3.0 s: -2.0 A6.0-9.0 s: +1.0 A

78. 0.16 T

80. (a) 1:13(b) 17×10!3 A(c) 2.0 W

82. First method: 140Second method: 140



CHAPTER 23 – ALTERNATING CURRENT CIRCUITS

2. 1.9 V

4. 2.7×10!6 F

6. (a) 6.4×10!6 F(b) 9.0×10!4 C

8. 75 V

10. 0.075 A

12. (a) 1.11×104 Hz(b) 6.83×10!9 F(c) 6.30×103 Ω(d) 7.00×102 Ω

14. 0.020 H

16. (a) 0.50(b) 0.34 A(c) 0.704 H

18. 3.0 W

20. 10.5 V; 19.0 V; 29.6 V

22. (a) 0.26 A(b) 0.11 A

24. 1.1×103 Hz

26. 2.7×10!5 H

28. 0.81 W

30. (a) 1.3×10!3 H(b) 8.7×10!6 F

32. 521 Hz

34. f1 = 3.11×103 Hz; f2 = 7.50×103 Hz

36. (a) 10.7 V(b) -29.8E

38. 4



40. 310 Hz

42. 123 W

44.R2

R1

' 3

46. 1.1 A

48. 49.7 Ω; 185 Ω

50. 1.8 µF

52. (a) 1.17×10!6 J(b) 5.58×10!3 A



CHAPTER 24 – ELECTROMAGNETIC WAVES

2. (a) 1.28 s(b) t = 1.9×102 s

4. 3.62×10!12 ! 5.45×10!12 F

6. 8.5×10!5 V

8. 8.37

10. 1.93×1012

12. 4.500×107 Hz

14. 8.8 y

16. 0.24 s

18. 42.3 m/s

20. 1.6×106 m

22. 990 N/C

24. 1.8×10!5 J

26. 602 W/m2

28. (a) 2.1×104 W/m2

(b) 1.1×102 W(c) 18 s

30. (a) 2.7×10!5 N(b) 3.3×10!9 N

32. (a) 640 Hz(b) the wave that returns to the police car has the greater frequency

34. (a) 0.55 W/m2

(b) 3.7×10!2 W/m2

36. 206 W/m2

38. 104E

40. 68 N/C



42. (a) 6.81×105 N/C(b) 2.27×10!3 T

44. 4.8×10!5 J

46. (a) 1.09×106 Hz(b) AM radio wave

48. 32 m/s

50. 720 W/m2

52. 75.3 W

54.100 SP

Sp % SU

'

100 Smax & Smin

cos2θSmax & Smin % 2 Smin

cos2θ

'100 Smax & Smin

Smax % Smin

56. (a) 263 W/m2; 2370 W/m2

(b) 1.05×10!6 T; 3.15×10!6 T(c) 263 W/m2; 2370 W/m2

58. (a) 2.5×10!5 N(b) 0 N(c) 2.5×10!5 N(d) 3.1×10!9 N

60. (a) 24 W/m2

(b) 0 W/m2

(c) 18 W/m2

62 A is removed; B, C, and D remain – 3.8 W/m2

D is removed; A, B, and C remain – 5.1 W/m2



CHAPTER 25 – THE REFLECTION OF LIGHT

2. (a) 0.91 m(b) 0.85 m

4. Image 1: x = !2.0 m, y = +1.0 mImage 2: x = +2.0 m, y = !1.0 mImage 3: x = +2.0 m, y = +1.0 m

6. 7.2 m

8. (a) 30E(b) βN = 30E

10. (a) image distance is 7.5 cm(b) image height is 1.0 cm

12. (a) 24 cm(b) The ray diagram is similar to that shown in Figure 25.16.

14. (a) smaller(b) larger(c) 3

16. +32 cm

18. di = +31 cm

20. 14 cm

22. (a) 180 cm(b) 6.0×101 cm

24. f = -17 cm

26. 0.67

28. -1/2

30. (a) the image is 20.0 cm behind the mirror, or di = -20.0 cm(b) the image height is 6.0 cm

32. sees the arrow at A in its entirety; does not see the arrow at B in its entirety

34. (a) di = -1.8 m(b) virtual(c) 0.19 cm



36. (a) 70.6E(b) 62.1E

38. 56 cm

40. (a) +9.0×101 cm; +45 cm(b) +15 cm; -3.0×101 cm

42. 2.00 h

44. f = 9.1 cm

46. -x direction and has a magnitude of 1.2 m/s



CHAPTER 26 – THE REFRACTION OF LIGHT: LENSES AND OPTICALINSTRUMENTS

2. 1.66×108 m/s

4. 0.800

6. carbon disulfide

8. 4.3 cm

10. 0.87

12. 1.47

14. 32E

16. 2.1 cm

18. 2.7 m

20. 51.9E

22. 21.4 cm

24. 37.79E

26. 2.5 m

28. 0.813

30. 1.35

32. 67.5E

34. 32E

36. (a) 60.1E(b) 1.74

38. 0.86E

40. 30.39E

42. 20.4E



44. (a) -12 cm(b) +0.63(c) virtual(d) upright(e) reduced

46. -8.1 cm

48. (a) 204 cm(b) real(c) -17.1 cm

50. (a) 3.78 m(b) Width: -8.40×102 mm; Height: 1.26×103 mm

52. (a) -85.1 cm(b) 134.1 cm

54. (a) away from the lens(b) 0.15 m

56. 12 m

58. xx ) ' f 2

60. -5.6 cm

62. (a) -150 cm(b) 9.0 cm

64. 160.0 cm

66. (a) 4.50 cm to the right of the second lens(b) -0.75(c) real(d) inverted(e) smaller

68. -0.14 mm

70. (a) 2.8 m(b) -3.1×10!2 cm

72. 121 cm from the eyes

74. (a) 31.3 cm(b) 2.43 m



76. 18

78. 13.7 cm

80. 0.15 rad

82. 15.4

84. 9×10!3 rad

86. 0.86 cm

88. (a) 30.0(b) 4.27 cm(c) -4.57

90. 198 diopters

92. (a) 0.775 m(b) 0.780 m

94. (a) -194(b) -7.8×10!5 m(c) 1.94×106 m

96. -31

98. 4.8×10!3 rad

100. 12.1 m

102. 3.9 cm

104. 0.011 m

106. (a) 0.025 rad(b) 0.040 rad(c) the player looks larger on television

108. 21.7E

110. (a) -10.0 cm(b) +0.500

112. (a) 2.0×101 diopters(b) 5.6

114. 0.333 m



116. 8.0 cm

118. (a) 46E(b) 50E(c) 69E(d) 0E

120. a-b interface: 1.30; b-c interface: 1.10

122. (a) 60.0 cm(b) 20.0 cm

124. (a) 15.0 cm(b) 45.0 cm



CHAPTER 27 – INTERFERENCE AND THE WAVE NATURE OF LIGHT

2. 4.9×10!7 M

4. destructive interference is occurring

6. 4.3×10!3 m

8. toward the slits; 0.115 m

10. 1.30×102 nm; 3.90×102 nm

12. (a) 150 nm(b) 210 nm

14. 1.18

16. (a) 1.0×10!7 m(b) 2.1×10!7 m

18. R = 0.0256 m

20. 0.0390 m

22. 0.576 m

24. 8

26. 0.012 m

28. (a) 3.53 m(b) 2.15 m

30. 5.6×1017 m

32. (a) 5.6 m(b) 56 m

34. 5.1 s

36. (a) 550 m(b) 370 m

38. 5.90×10!7 m

40. 644 nm

42. 640 nm; 480 nm



44. 6540 lines/cm

46. (a) 0.68E(b) 1.4E(c) 2.0E

48. 6.12×10!7 m

50. 403 nm

52. 0.0254 m

54. 2.0×10!5 m

56. 50 bright fringes

58. (a) 487 nm(b) 518 nm

60. 4

62. 3.3×10!6 m

64. 2400 m!1

66. (a) 0.29 m(b) 0.22 m



CHAPTER 28 – SPECIAL RELATIVITY

2. 72 H

4. 1.8 breaths per min

6. 4.4×10!4 s

8. 8.1 km

10. 1.0×103 yr

12. 3400 m × 1500 m

14. θ) ' 40.2E

16. 8.59

18. (a) 1.7×107 kg@m/s(b) 3.0×107 kg@m/s

20. 1.0 m

22. 1.7×10!13 J

24. 5.3×109 mi

26. (a) 6.7×105 J(b) 7.4×10!12 kg

28. 1.3×107 kg@m/s

30. 0.36c

32. 0.920c

34. (a) at the speed of light, c(b) +0.994c(c) 0.200c(d) 0.194c

36. 8.7×10!30 kg

38. 0.999 95c

40. 0.94c

42. (a) 3.8×10!12 J



(b) 0.9998c

44. (a) 0.72×1011 m(b) 3.0×102 s

46. (a) 7.44×10!12 kg(b) 5.02×10!11 kg

48. 0.866c; 0.943c; 0.745c



CHAPTER 29 – PARTICLES AND WAVES

2. (a) 1.63×10!7 m(b) 1.84×1015 Hz; 1.84×1015 Hz(c) ultraviolet region

4. 2.56 eV

6. 2.5×1021 photons/(s@m2)

8. 1.9×10!7 m

10. 9.56×10!12 m

12. (a) 7760 N/C(b) 2.59×10!5 T

14. 1.0×1013 Hz

16. 75E

18. (a) 0.1819 nm(b) 1.092×10!15 J(c) 1.064×10!15 J(d) 2.8×10!17 J

20. (a) 1.0×10!8 N(b) 5.0×10!9 N

22. 1.41×103 m/s

24. 2.45×103 m/s

26. 1.73×10!6 rad

28. 6.01×10!11 m

30. 4.0×101

32. 8.8×10!21 kg@m/s

34. 37 J@s

36. 3.6×104 m/s

38. x-ray; infrared

40. (a) 2.5×10!7 m



(b) 5.6×10!10 m

42. 1.26 eV

44. 9.32×105 m/s

46. 2.75×10!7 m; 3.35×10!7 m

48. 5.82×10!23 kg@m/s

50. λ = 2.0×10!34 m



CHAPTER 30 – THE NATURE OF THE ATOM

2. 2 mi

4. 1.7×10!13 J

6. 7.3×10!14 m

8. 5

10. 2.38×10!10 m

12. -0.213 eV

14. 6.56×10!7 m; 1.22×10!7 m

16. 22.8 nm

18. 2

20. (a) vn '2πke 2Znh

(b) 2.19×106 m/s(c) 1.09×106 m/s(d) are consistent with ignoring relativistic effects

22. (a) -1.51 eV(b) 2.58×10!34 J@s(c) 2.11×10!34 J@s

24. R = 4; n = 5

26. 0 J@s; ; 2h2π

6h2π

28. (a) ; n ' 2, R ' 0, mR ' 0, ms ' %12n ' 2, R ' 0, mR ' 0, ms ' &

12

(b) , n ' 2, R ' 1, mR ' %1, ms ' %12n ' 2, R ' 1, mR ' %1, ms ' &

12

, n ' 2, R ' 1, ms ' %12n ' 2, R ' 1, mR ' 0, ms ' &

12

, n ' 2, R ' 1, mR ' &1, ms ' %12n ' 2, R ' 1, mR ' &1, ms ' &

12

30. 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10

32. strontium, Sr

34. 1.07×10!14 J



36. (a) 1.08×10!14 J(b) 6.75×104 eV

38. 6.03×107 m/s

40. 2.2×1016

42. 19

44. 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 3

46. carbon

48. 10 700 V

50. 4.41×10!10 m

52. KE 'n 2h 2

8mL 2where n ' 1,2,3, ...

54. λ = 30.39 nm

56. (a) The quantum number R must be less than n.(b) The quantum number mR must be less than or equal to R.(c) The quantum number R cannot be negative.

58. (a) 3.55×10!11 m(b) Molybdenum: 7.23×10!11 m; Silver: 5.74×10!11 m

60. (a) 1.8(b) Z = 11: 4.3×10!11 m; Z = 1.8: 2.6×10!10 m



CHAPTER 31 – NUCLEAR PHYSICS AND RADIOACTIVITY

2. (a) 92(b) 122(c) 41

4. 4.4×10!15 m

6. 1.14

8. (a) 2.3×1017 kg/m3

(b) 1.2×1010 kg(c) 80

10. 7.90 MeV per nucleon

12. (a) 1.741 670 u(b) 1622 MeV(c) 7.87 MeV

14. 39.25 MeV

16. (a) 10.55 MeV(b) 7.55 MeV(c) neutron

18. (a) X represents a β! particle (electron)(b) X represents a β+ particle (positron)(c) X represents a γ ray(d) X represents an α particle (helium nucleus)

20. 0.313 MeV

22. 1.38 MeV

24. 0.072 MeV; 4.2 MeV

26. AZX '

21284 Po

28. 2.60×10!12 m

30. 3.66 days

32. 7.53%

34. 379 yr

36. 2.1×10!11 kg



38. 1.2×10!7 g

40. 2.2×103 yr

42. (a) 0.999(b) 1.36×10!9

(c) 0.755

44. 3.29×109 yr

46. (a) 25 000 yr(b) 22 000 yr

48. (a) +1.31×10!17 C(b) 126(c) 208(d) 7.1×10!15 m(e) 2.3×1017 kg/m3

50. 4.87 MeV

52. 13 000 yr

54. 1.29×10!3 g

56. 9.37 days

58. 0.81 MeV

60. 3720 kg

62. 1.56×1025 MeV



CHAPTER 31 – IONIZING RADIATION, NUCLEAR ENERGY, AND ELEMENTARYPARTICLES

2. 12

4. 3.7×10!6 J

6. 2.4×104 m

8. 9.2×108

10. 2010 Ne

12. (a) 147 N(n,p) 14

6 C

(b) 23892 U(n,γ) 239

92 U

(c) 2412 Mg(n,d) 23

11 Na

14. (a) A = 233; Z = 90; Thorium ( 23390 Th)

(b) 23392 U

16. zinc, 6430 Zn

18. 3

20. 173 MeV

22. 6.4×108 W

24. 160 MeV

26. (a) 3.1×1024

(b) 1.2×103 g(c) 1.1 g

28. 2.0 MeV

30. (a) A = 2; Z = 0; neutron; deuterium nucleus(b) 6.2 MeV

32. (a) 1.0×1022

(b) 8.1×109 kg

34. 33.9 MeV

36. 140.9 MeV



38. (a) The K! particle does not contain u, c, or t quarks.

(b) The K! particle does not contain , , or antiquarksd s b

40. 0.18 MeV

42. (a) 460 rem(b) a 50% chance of dying

44. 232.7851 u

46. 2.26×108 rd

48. 1.1×106 kg

50. γ rays: 3electrons: 2protons: 1slow neutrons: 4

52. (a) AZX '42 He

(b) AZX '11 H

(c) AZX '2714 Si

(d) AZX '24 He

54. 14.1 MeV; 3.5 MeV