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:	Gauss' Law for Magnetism:
${\boldsymbol {\nabla \cdot E}}=0$	${\boldsymbol {\nabla \cdot B}}=0$
Faradays's Law:	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:	Gauss' Law for Magnetism:
${\boldsymbol {\nabla \cdot D}}=\rho$	${\boldsymbol {\nabla \cdot B}}=0$
Faradays's Law:	Ampere's Law:
${\boldsymbol {\nabla \times E}}+{\frac {\partial {\boldsymbol {B}}}{\partial t}}=0$	${\boldsymbol {\nabla \times H}}-{\frac {\partial {\boldsymbol {D}}}{\partial t}}={\boldsymbol {j}}$

Where ${\boldsymbol {D}}=\epsilon _{0}{\boldsymbol {E}}$ and ${\boldsymbol {B}}=\mu _{0}{\boldsymbol {H}}$.

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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