$$ \left\\\{\begin{aligned} \nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\\\ \nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\\\ \nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\\\ \nabla \cdot \vec{\mathbf{B}} & = 0 \end{aligned}\right. $$