In differential form:

\[
\begin{aligned}
\nabla\cdot\textbf{E} &= {\rho \over \varepsilon_0}\\
\nabla\cdot\textbf{B} &= 0\\
\nabla\times\textbf{E} &= -\frac{\partial\textbf{B}}{\partial t}\\
\nabla\times\textbf{B}&=\mu_0\left(\textbf{J} + \varepsilon_0\frac{\partial\textbf{E}}{\partial t}\right)
\end{aligned}
\]