Maxwell's Equations

In Free Space

These are the Maxwell's Equations we will be using to solve for regions "I" and "II" in our approximation of the Michelson interferometer.

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:

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

Need to add possibly derivation of wave equation and definitely Maxwell's equation in presence

Gauss' Law:

${\boldsymbol {\nabla \cdot D}}=\rho$

Gauss' Law for Magnetism:

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

Faradays's Law:

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

Ampere's Law:

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

${\vec {\nabla }}\times {\vec {D}}={\frac {\rho _{ext}}{\epsilon _{0}}}$

(1)