Physics!

\begin{equation}m\mathbf{a} = q\mathbf{E} + \frac{q}{c}\mathbf{v} \times \mathbf{B} \\ \end{equation} \begin{equation}\frac{\partial \rho}{\partial t} = -\nabla \cdot (\rho \mathbf{v}) \\ \end{equation} \begin{equation}\rho \frac{\partial \mathbf{v}}{\partial t} = -\rho \mathbf{v} \cdot \nabla \mathbf{v} - \nabla p + \mathbf{J}\times\mathbf{B} \\ \end{equation} \begin{equation}\frac{\partial p}{\partial t} = -\mathbf{v}\cdot\nabla p - \gamma p \nabla \cdot \mathbf{v}\\ \end{equation} \begin{equation}\frac{\partial \mathbf{B}}{\partial t} = -c\nabla \times \mathbf{E} \\ \end{equation} \begin{equation}\mathbf{E} + \frac{1}{c}(\mathbf{v} \times \mathbf{B}) = 0 \\ \end{equation} (5) & (6) are usually combined to give: \begin{equation}\frac{\partial \mathbf{B}}{\partial t} = \nabla \times (\mathbf{v}\times \mathbf{B}) \\ \end{equation}