E & M Equation Sheet
(1)
\begin{align} \LARGE \vec{\nabla} \times \vec{E} = \left| \begin{array}{ccc} \frac{\hat{r}}{r} & \hat{\theta} & \frac{\hat{z}}{r} \\ \frac{\partial}{\partial r} & \frac{\partial}{\partial \theta} & \frac{\partial}{\partial z} \\ E_{r} & r E_{\theta} & E_{z} \end{array}\right| \end{align}
(2)
\begin{align} \phi (r, \theta) = \sum^\infty_{l=0} \left ( A_l r^l + \frac{C_l}{r^{l+1}} \right ) P_l (\cos{\theta}) \end{align}
(3)
\begin{align} \nabla \cdot \mathbf{D} = 4\pi\rho \end{align}
(4)
\begin{align} \nabla \cdot \mathbf{B} = 0 \end{align}
(5)
\begin{align} \nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}} {\partial t} \; \end{align}
(6)
\begin{align} \nabla \times \mathbf{H} = \frac{1}{c} \frac{\partial \mathbf{D}} {\partial t} + \frac{4\pi}{c} \mathbf{J} \end{align}
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