1. b. Charged objects are attracted to neutral objects, so an attractive force is inconclusive. Repulsion is the only sure test.

2. $q{}_{\text{E}}(+3e)>q_A(+1e)>q_D\left(0\right)>q{}_B(-1e)>q_C(-2e)$.

3. a. The negative plastic rod will polarize the electroscope by pushing electrons down toward the leaves. This will partially neutralize the positive charge the leaves had acquired from the glass rod.

4. b. The two forces are an action/reaction pair, opposite in direction but equal in magnitude.

5. c. There’s an electric field at all points, whether an $\overrightarrow{E}$ vector is shown or not. The electric field at the dot is to the right. But an electron is a negative charge, so the force of the electric field on the electron is to the left.

6. $E{}_2>E{}_1>E{}_4>E{}_3$.

1. $-5.6\text{nC}$

3.

1. Electrons transferred to the sphere

2. $3.1\times {10}^{10}$

5. $-9.6\times {10}^7\text{C}$

7. $9.0\times {10}^{13}$

13.

1. 0.90 N

2. $0.90\text{m}\text{/}{\text{s}}^2$

15.

1. 58 N

2. $4.7\times {10}^{-35}\text{N}$

3. ${\displaystyle \frac{F_{\text{E}}}{F_{\text{G}}}}=1.2\times {10}^{36}$

17. 0 N

19. $1.8\times {10}^{-4}\text{N }(-î)$, downward

21.

1. $(1.3\times {10}^{14}{\text{m/s}}^2\text{,}\text{t}\text{o}\text{w}\text{a}\text{r}\text{d}\text{b}\text{e}\text{a}\text{d})$

2. $(2.4\times {10}^{17}{\text{m/s}}^2\text{,}\text{a}\text{w}\text{a}\text{y}\text{f}\text{r}\text{o}\text{m}\text{b}\text{e}\text{a}\text{d})$

23. $\frac{4}{9}q$, negative, $x={\displaystyle \frac{L}{3}}$

25. −440 nC

27.

1. $(1.4\times {10}^{-3}\text{N/C, away from proton})$

2. $(1.4\times {10}^{-3}\text{N/C, toward electron})$

29.

1. $\left(6.4î+1.6\widehat{j}\right)\times {10}^{-17}\text{ N}$

2. $\left(6.4î+1.6\widehat{j}\right)\times {10}^{-17}\text{ N}$

3. $4.0\times {10}^{10}\text{ m}\text{/}{\text{s}}^2$

4. $7.3\times {10}^{13}\text{ m}\text{/}{\text{s}}^2$

31. $(-2.5\text{cm, }-2.5\text{cm})$

33. $4.3\times {10}^4î\text{ N/C, }\left(-1.5\times {10}^4î+1.5\times {10}^4\widehat{j}\right)\text{N/C, }\left(-1.5\times {10}^4î-1.5\times {10}^4\widehat{j}\right)\text{\hspace{0.17em}N/C}$

35. $-1.0\times {10}^5\widehat{j}\text{ N/C, }\left(-2.9\times {10}^4î-2.2\times {10}^4î\right)\text{ N/C, }-5.6\times {10}^4î\text{ N/C}$

37. 82 nC

39. 0.92 N/m

41. $8.4\times {10}^{21}$

43. $\text{4}\text{.6}\times {\text{10}}^{\text{−3}}\text{ N, 81}°\text{ccw}\text{from}-x\text{-axis}$

45. $1.0\times {10}^{-3}î\text{N}$

47. $1.1\times {10}^{-5}î\text{N}$

49.

1. $-2.4\text{cm}$

2. Yes

51. 0.68 nC

53. $(2-\sqrt{2}){\displaystyle \frac{KQq}{L^2}}$

55. $6.6\times {10}^{15}\text{rev}\text{/}\text{s}$

57. 8.1 nC

59. $7.2\times {10}^{-4}\text{N}\text{/}\text{s}$

61. $\tau =Eqs=pE$

63. $4.4\text{°}$

65.

1. $(-1.0\text{cm,}2.0\text{cm})$

2. $(3.0\text{cm, }3.0\text{cm})$

3. $(4.0\text{cm}\text{,}-2.0\text{cm})$

67. $0.18\mu C$

69. 19 mm

71. 0.32 N

73.

2. $\pm 22\text{nC}$

75.

2. 5.1 nC

77. 7.3 m/s

79. $1.7\times {10}^{-4}\text{N}$