1 \begin{problem*}{24.11}
2 Four closed surfaces, $S_1$ through $S_4$, together with the charges
3 $-2Q$, $Q$, and $-Q$ are sketched in Figure~P24.11. (The colored
4 lines are the intersections of the surfaces with the page.) Find the
5 electric flux through each surface.
14 % S_3 contains -2Q, Q, -Q
15 % S_4 to the left, contains no charges
19 The flux through any surface is given by Gauss's law:
21 \Phi_E = \frac{q_\text{in}}{\varepsilon_0} \;,
25 \Phi_{E1} &= \frac{-2Q + Q}{\varepsilon_0}
26 = \ans{\frac{-Q}{\varepsilon_0}} \\
27 \Phi_{E2} &= \frac{Q - Q}{\varepsilon_0} = \ans{0} \\
28 \Phi_{E3} &= \frac{-2Q + Q - Q}{\varepsilon_0}
29 = \ans{\frac{-2Q}{\varepsilon_0}} \\
30 \Phi_{E4} &= \frac{0}{\varepsilon_0} = \ans{0} \;.