Maxwell's Equations

In Free Space

Gauss' Law:

${\boldsymbol {\nabla \cdot E}}=0$

Gauss' Law for Magnetism:

${\boldsymbol {\nabla \cdot B}}=0$

Faradays's Law:

${\boldsymbol {\nabla \times E}}+{\frac {\partial {\boldsymbol {B}}}{\partial t}}=0$

Ampere's Law:

${\boldsymbol {\nabla \times B}}-\mu _{0}\epsilon _{0}{\frac {\partial {\boldsymbol {E}}}{\partial t}}=0$