\begin{problem*}{19.36}
An $m = 10.0\U{g}$ piece of Styrofoam carries a net charge of $q =
-0.700\U{$\mu$C}$ and floats above the center of a large horizontal
sheet of plastic that has a uniform charge density $\sigma$ on it's
surface.  Find $\sigma$.
\end{problem*} % problem 19.36

\begin{solution}
Because the Styrofoam is floating in equilibrium, the sum of forces in
the vertical direction must be zero.  So
\begin{align}
 F_g = mg &= F_E = q E = q \frac{\sigma}{2 \epsilon_0} \\
 \sigma &= \frac{2\epsilon_0 mg}{q}
         = \frac{2 \cdot 8.54\E{-12}\U{C$^2$/N$\cdot$m$^2$} \cdot 0.0100\U{kg} \cdot 9.80\U{m/s$^2$}}{-0.700\E{-6}\U{C}}
         = \ans{2.39\E{-6}\U{C/m$^2$}}
\end{align}
\end{solution}
