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\centerline{\textbf{Calculating Total Charge}}
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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 $\rho (r) = \alpha r^{3}$

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\item A positively charged (dielectric) spherical shell of inner radius $a$ and outer radius $b$ with a spherically symmetric internal charge density $\rho (r) =3 \alpha e^{(kr)^{3}}$

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\item A positively charged (dielectric) spherical shell of inner radius $a$ and outer radius $b$ with a spherically symmetric internal charge density $\rho (r) = \alpha \frac{e^{(kr)}}{r^{2}}$

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\item A positively charged (dielectric) cylindrical shell of inner radius $a$ and outer radius $b$ with a cylindrically symmetric internal charge density $\rho (r) = \alpha r^{3}$

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\item A positively charged (dielectric) cylindrical shell of inner radius $a$ and outer radius $b$ with a cylindrically symmetric internal charge density $\rho (r) =3 \alpha e^{(kr)^{2}}$

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\item A positively charged (dielectric) cyilndrical shell of inner radius $a$ and outer radius $b$ with a cylindrically symmetric internal charge density $\rho (r) = \alpha \frac{e^{(kr)}}{r}$

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