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:

$$\boldsymbol{\nabla \times B} - \mu_0\epsilon_0\frac{\partial \boldsymbol{E}}{\partial t}= 0 $$