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Basic Stuff\\
\begin{equation}\vec{E}=\sum\frac{q_1q_2}{r^2}\hspace{1in} \Phi = \oint_S\vec{E}\cdot\vec{n}dS = 4\pi Q \end{equation}\\
\begin{equation}U = W = \sum\frac{q_1q_2}{r} \hspace{1in}div \vec{E} = \frac{d\phi}{dV} = 4\pi\rho \end{equation}\\
\begin{equation}U = \frac{1}{8\pi}\int E^2dV = \frac{1}{2}\int\rho\phi dV \hspace{1in}curl\vec{E} = \vec{\nabla}\times\vec{E} = 0 \end{equation}\\
Conductor Stuff\\
\begin{equation}\vec{E}_{out} = 4\pi\sigma   \vec{E}_{in} = 0 \hspace{1in}\phi = C \end{equation}\\
Conversions between $\vec{E}, \rho, and \phi$\\
\begin{equation}\vec{E} = \int\frac{\rho}{r^2}\vec{r}dv  \hspace{1in}\rho = \frac{1}{4\pi}\vec{\nabla}\cdot\vec{E}\end{equation}\\
\begin{equation}\phi = \int\frac{\rho}{r}dv  \hspace{1in}\rho = \frac{-1}{4\pi}\nabla^2\phi\end{equation}\\
\begin{equation}\phi = -\int\vec{E}ds  \hspace{1in}\vec{E} = - \vec{\nabla}\phi\end{equation}\\
Work Stuff\\
\begin{equation}U = \frac{1}{8\pi}\int E^2dV = \frac{1}{2}\int\rho\phi dv = \frac{N}{2}\sum\frac{q_iq_j}{r_{ij}}\end{equation}\\
Uniform distribution of charge in a sphere\\
\begin{equation}U_{sphere} = \frac{3}{5}\frac{Q^2}{R}\end{equation}\\
Some Units stuff, not real equations\\
\begin{equation}\vec{E} = \frac{q}{r^2} = \frac{\phi}{r}  \hspace{1in}\phi = \frac{q}{r}\end{equation}\\

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