1. c. From symmetry, the fields of the positive charges cancel. The net field is that of the negative charge, which is toward the charge.

2. $\eta {}_C={\eta }_B={\eta }_A$. All pieces of a uniformly charged surface have the same surface charge density.

3. b, e, and h. b and e both increase the linear charge density $\lambda$.

4. $E{}_1=E{}_2=E{}_3=E{}_4=E{}_5$. The field strength of a charged plane is the same at all distances from the plane. An electric field diagram shows the electric field vectors at only a few points; the field exists at all points.

5. $E{}_1=E{}_2=E{}_3=E{}_4=E{}_5$. The electric field strength between the plates of a capacitor is the same at all points.

6. c. Parabolic trajectories require constant acceleration and thus a uniform electric field. The proton has an initial velocity component to the left, but it’s being pushed back to the right.

1. $7.6\times {10}^3\text{N}\text{/}\text{C}$ vertical, $0\text{°}$ from vertical

3. $5.4\times {10}^2\text{N}\text{/}\text{C}$, $90\text{°}$ cw from horizontal

5.

1. 28 nC mm

2. 28 nC

3. 3.8 nC

7. $2.9\times {10}^{-3}\text{N}$

9. 4000 N/C

11. $2.3\times {10}^5\text{N}\text{/}\text{C}\text{,}1.67\times {10}^5\text{N}\text{/}\text{C}\text{,}2.3\times {10}^5\text{N}\text{/}\text{C}$

13. 15 nC

15.

1. $(2.6\times {10}^4\text{N}\text{/}\text{C}\text{,}\text{left})$

2. $(2.6\times {10}^{-5}\text{N,}\text{right})$

17. 27 nC

19. $-{\displaystyle \frac{{\eta }_0}{{ϵ}_0}}î$, $-(2{\eta }_0\text{/}{ϵ}_0)î$, $+({\eta }_0\text{/}{ϵ}_0)î$

21. $-0.35\text{pC}$

23. 1.9 cm

25. 6.7 nC

27.

1. $3.6\times {10}^6\text{N}\text{/}\text{C}$

2. $8.3\times {10}^5\text{m}\text{/}\text{s}$

29. 0.18 m

31.

1. 0.040 s

2. $1.6\times {10}^4\text{N}\text{/}\text{C}$

33.

1. ${\displaystyle \frac{1}{4\pi {ϵ}_0}}{\displaystyle \frac{qQs}{r^3}}$

2. ${\displaystyle \frac{1}{4\pi {ϵ}_0}}{\displaystyle \frac{qQs}{r^2}}$

35. $1.8\times {10}^{-21}\text{N m}$

37.

1. $1.2\times {10}^4\text{N/C}î+2.4\times {10}^5\text{N/C}ĵ$

2. $2.5\times {10}^5\text{N}\text{/}\text{C}$, $87\text{°}\text{ccw from }+x\text{-axis}$

39. ${\displaystyle \frac{1}{4\pi {ϵ}_0}}{\displaystyle \frac{Q}{L^2}}(\sqrt{2}-1)(î+ĵ)$

41. ${\displaystyle \frac{1}{4\pi {ϵ}_0}}{\displaystyle \frac{16\text{λ}y}{4y^2+d^2}}$

45. $E_z={\displaystyle \frac{zQ}{4\pi {ϵ}_0(z^2+R^2{)}^{3\text{/}2}}}$

47.

1. $\pm {\displaystyle \frac{R}{\sqrt{2}}}$

2. ${\displaystyle \frac{2}{3\sqrt{3}}}{\displaystyle \frac{}{}}{\displaystyle \frac{Q}{4\pi {ϵ}_{0R}{}^2}}$

49.

1. $(E_i){}_x={\displaystyle \frac{1}{4\pi {ϵ}_0}}\left({\displaystyle \frac{2Q}{\pi R^2}}\right)\text{Δ}\theta \text{cos}{\theta }_i\text{,}(E_i){}_y={\displaystyle \frac{1}{4\pi {ϵ}_0}}\left({\displaystyle \frac{2Q}{\pi R^2}}\right)\text{Δ}\theta \text{sin}{\theta }_i$

2. $E_x={\displaystyle \frac{1}{4\pi {ϵ}_0}}\left({\displaystyle \frac{2Q}{\pi R^2}}\right){\displaystyle {\int }_0^{\pi \text{/}2}}\text{cos}\theta d\theta \text{,}{E}_y={\displaystyle \frac{1}{4\pi {ϵ}_0}}\left({\displaystyle \frac{2Q}{\pi R^2}}\right){\displaystyle {\int }_0^{\pi \text{/}2}}\text{sin}\theta d\theta$

3. $\vec{E}{}_{\text{net}}={\displaystyle \frac{1}{4\pi {ϵ}_0}}{\displaystyle \frac{2Q}{\pi R^2}}(î+ĵ)$

51. $3.8\times {10}^6\text{m}\text{/}\text{s}$

53. $1.19\times {10}^7\text{m}\text{/}\text{s}$

55.

1. Negative

2. $3.8\times {10}^4\text{N}\text{/}\text{C}$

3. 2.5 mm

57. $4.2\times {10}^{-4}\text{N}$

59. $6.56\times {10}^{15}\text{Hz}$

61.

1. ${\displaystyle \frac{{\text{C}}^2{\text{s}}^2}{\text{kg}}}$

2. ${\vec{F}}_{\text{ion on dipole}}=\left({\left({\displaystyle \frac{1}{4\pi {ϵ}_0}}\right)}^2{\displaystyle \frac{2q^2\alpha }{r^5}},\text{ toward ion}\right)$

63. 0.74 GHz

65.

2. 14 cm

67.

2. $7.4\times {10}^{-11}\text{C}$

69.

• c.

  

  Full Alternative Text

71. ${\displaystyle \frac{\eta }{2{ϵ}_0}}[1-{\displaystyle \frac{R}{\sqrt{L^2+R^2}}}]$

73. $-2.3\text{nC}\text{/}\text{m}$