1. Zero. The motion is always perpendicular to the electric force.

2. $U{}_{\text{B}}=U{}_{\text{D}}>U{}_{\text{A}}=U{}_{\text{C}}$. The potential energy depends inversely on $r$. The effects of doubling the charge and doubling the distance cancel each other.

3. The proton gains speed by losing potential energy. It loses potential energy by moving in the direction of decreasing electric potential.

4. $V{}_1=V{}_2>V{}_3>V{}_4=V{}_5$.

5. $\text{Δ}V{}_{13}=\text{Δ}V{}_{23}>\text{Δ}V{}_{12}$. The potential depends only on the distance from the charge, not the direction. $\text{Δ}{V}_{12}=0$ because these points are at the same distance.

1. $1.4\times {10}^5\text{m}\text{/}\text{s}$

3. $2.1\times {10}^6\text{m}\text{/}\text{s}$

5. 0 J

7. $1.4\times {10}^{-3}\text{N}$

9. $1.61\times {10}^{-3}\text{ N/C}$

11. $1.87\times {10}^7\text{m/s}$

13. $-8.4\times {10}^4\text{V}$

15.

1. Higher

2. 3340 V

17. 10 nC

19. $1.5\times {10}^5\text{m}\text{/}\text{s}$

23.

1. 200 V

2. 400 V

25. $1.4\times {10}^3\text{V}$

27.

1. 1800 V, 1800 V, 900 V

2. 0 V, 900 V

29.

1. 27 V

2. $-4.3\times {10}^{-18}\text{J}$

31. $8.7\times {10}^2\text{V}$

33. $1.1\times {10}^6\text{m}\text{/}\text{s}$

35. 0 V

37. $-10\text{ nC, }40\text{ nC}$

39. 3.0 cm, 6.0 cm

41. $y=\pm 12\text{cm}$

43. $1.0\times {10}^5\text{m}\text{/}\text{s}$

45. 2.5 cm/s

47.

1. $9.8\times {10}^5\text{m}\text{/}\text{s}$

2. $1.4\times {10}^6\text{m}\text{/}\text{s}$

49. $1.5\text{kV}$

51. $8.0\times {10}^7\text{m}\text{/}\text{s}$

53. $-5.1\times {10}^{-19}\text{J}$

55. $4.2\times {10}^{-10}\text{C}$

57. $4.1\times {10}^7\text{m}\text{/}\text{s}$

59. $3.3\times {10}^5\text{m}\text{/}\text{s}$

61.

1. 15 V, $3.0\text{kV/m,}2.1\times {10}^{-10}\text{C}$

2. 15 V, $1.5\text{kV/m,}1.0\times {10}^{-10}\text{C}$

3. 15 V, $3.0\text{ kV/m}\text{,}8.3\times {10}^{-10}\text{ C}$

63. $1.8\times {10}^2\text{ N/C}$

65. 0.47 kV

67. 5447 V, point 2

69. $V_{\text{net}}={\displaystyle \frac{1}{4\pi {ϵ}_0}}{\displaystyle \frac{(2q{s}^2)}{y^3}}={\displaystyle \frac{1}{4\pi {ϵ}_0}}{\displaystyle \frac{Q}{y^3}}$

71. $V={\displaystyle \frac{Q}{2\pi {ϵ}_{0}L}}\text{ ln}\left[\left({\displaystyle \frac{L}{2z}}\right)+\sqrt{1+{\left({\displaystyle \frac{L}{2z}}\right)}^2}\right]$

73. $V={\displaystyle \frac{Q}{2\pi {ϵ}_{0}R{}_{\text{out}}2}}[\sqrt{R{}_{\text{out}}2+z^2}-z]$

75.

2. 10 nC, 30 nC

77.

2. 6.0 cm

79. $1.9\times {10}^{-14}\text{m}$

81. $-9.8\text{ cm/s,}\text{4}\text{.9 cm/s}$

83. ${\displaystyle \frac{2Q\text{/}L}{4\pi {ϵ}_0}}{\left[\text{ln}\left(z+\sqrt{R^2+z^2}\right)\right]}_0^{L\text{/}2}$