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\begin{document}
\centerline{\textbf{Calculating Total Charge}}
\bigskip
For each case below, find the total charge. What are the dimensions of the
constants $\alpha$ and $k$?
(If the total charge is infinite, what should you calculate instead to provide
meaningful information?)
\begin{enumerate}
\item A positively charged (dielectric) spherical shell of inner radius $a$
and outer radius $b$ with a spherically symmetric internal charge density
$\rho (r) = \alpha r^{3}$
\vfill
\item A positively charged (dielectric) spherical shell of inner radius $a$
and outer radius $b$ with a spherically symmetric internal charge density
$\rho (r) =3 \alpha e^{(kr)^{3}}$
\vfill
\item A positively charged (dielectric) spherical shell of inner radius $a$
and outer radius $b$ with a spherically symmetric internal charge density
$\rho (r) = \alpha \frac{e^{(kr)}}{r^{2}}$
\vfill
\item A positively charged (dielectric) cylindrical shell of inner radius $a$
and outer radius $b$ with a spherically symmetric internal charge density
$\rho (s) = \alpha s^{3}$
\vfill
\item A positively charged (dielectric) cylindrical shell of inner radius $a$
and outer radius $b$ with a spherically symmetric internal charge density
$\rho (s) =3 \alpha e^{(ks)^{2}}$
\vfill
\item A positively charged (dielectric) cylindrical shell of inner radius $a$
and outer radius $b$ with a spherically symmetric internal charge density
$\rho (s) = \alpha \frac{e^{(ks)}}{s}$
\end{enumerate}
\vfill
\end{document}