! . 1 . ( , ) Problem 1. Gauss and Graphs! ???? 0. (E): : N/C = E_s = 1.0 \times 10^8\ \mathrm{N/C} 1 = 1.0 \times 10^7\ \mathrm{N/C} (r): : cm m 2 = 1.0 cm 1 = 0.5 cm = 0.005 m = 0 cm ~ 5 cm = 0.05 m ???? 1. : E vs r : r a 2. (Given) E_s = 1.0 \times 10^8\ \mathrm{N/C}, \quad k = \frac{1}{4\pi\epsilon_0} = 8.99 \times 10^9\ \mathrm{N \cdot m^2/C^2} E_{\text{in}} = E(2.0\ \mathrm{cm}) = 5 \ \text{} = 5.0 \times 10^7\ \mathrm{N/C} r_{\text{in}} = 2.0\ \mathrm{cm} = 0.020\ \mathrm{m} E_{\text{out}} = E(4.0\ \mathrm{cm}) = 3 \ \text{} = 3.0 \times 10^7\ \mathrm{N/C} r_{\text{out}} = 4.0\ \mathrm{cm} = 0.040\ \mathrm{m} ???? 3. (A) q (B) Q_{\text{shell}} ???? 4. (A) q 1. E = \frac{k |q|}{r^2} \Rightarrow q = \frac{E \cdot r^2}{k} 2. q = \frac{(5.0 \times 10^7\ \mathrm{N/C}) \cdot (0.020\ \mathrm{m})^2}{8.99 \times 10^9\ \mathrm{N \cdot m^2/C^2}} 3. q = \frac{(5.0 \times 10^7)(0.0004)}{8.99 \times 10^9} = \frac{2.0 \times 10^4}{8.99 \times 10^9} = 2.2247 \times 10^{-6}\ \mathrm{C} 4. \boxed{q = +2.22\ \mu\mathrm{C}} (B) Q_{\text{shell}} 1. E_{\text{out}} = \frac{k (q + Q_{\text{shell}})}{r^2} \Rightarrow Q_{\text{shell}} = \frac{E_{\text{out}} \cdot r^2}{k} - q 2. Q_{\text{shell}} = \frac{(3.0 \times 1