**Law 0.0.1 **  **Maxwell's Equations** are a set of coupled differential equations that form the foundations of classical electromagnetism.
\[\nabla\cdot \vec{E} = \frac{\rho}{\varepsilon_0}\]
\[\nabla\cdot \vec{B} = 0\]
\[\nabla\times\vec{E} = -\frac{\partial \vec{B}}{\partial t}\]
\[\nabla\times \vec{B} = \mu_0\left( \vec{J} + \varepsilon_0\frac{\partial \vec{E}}{\partial t} \right)\]