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 for Magnetism:
${\boldsymbol {\nabla \cdot E}}=0$	${\boldsymbol {\nabla \cdot B}}=0$
Ampere's Law:
${\boldsymbol {\nabla \times E}}+{\frac {\partial {\boldsymbol {B}}}{\partial t}}=0$	${\boldsymbol {\nabla \times B}}-\mu _{0}\epsilon _{0}{\frac {\partial {\boldsymbol {E}}}{\partial t}}=0$

In the presence of charges and dielectric media

Need to add possibly derivation of wave equation and definitely Maxwell's equation in presence. Need also to introduce D and H and relate them to E and B.

Gauss' Law:

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

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:

${\boldsymbol {\nabla \times H}}-{\frac {\partial {\boldsymbol {D}}}{\partial t}}={\boldsymbol {j}}$

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