\begin{problem*}{24.11}
Four closed surfaces, $S_1$ through $S_4$, together with the charges
$-2Q$, $Q$, and $-Q$ are sketched in Figure~P24.11.  (The colored
lines are the intersections of the surfaces with the page.)  Find the
electric flux through each surface.
% -2Q
%
%   Q
%
%  -Q

% S_1 contains -2Q, Q
% S_2 contains Q, -Q
% S_3 contains -2Q, Q, -Q
% S_4 to the left, contains no charges
\end{problem*}

\begin{solution}
The flux through any surface is given by Gauss's law:
\begin{equation}
  \Phi_E = \frac{q_\text{in}}{\varepsilon_0} \;,
\end{equation}
so
\begin{align}
  \Phi_{E1} &= \frac{-2Q + Q}{\varepsilon_0}
    = \ans{\frac{-Q}{\varepsilon_0}} \\
  \Phi_{E2} &= \frac{Q - Q}{\varepsilon_0} = \ans{0} \\
  \Phi_{E3} &= \frac{-2Q + Q - Q}{\varepsilon_0}
    = \ans{\frac{-2Q}{\varepsilon_0}} \\
  \Phi_{E4} &= \frac{0}{\varepsilon_0} = \ans{0} \;.
\end{align}
\end{solution}
