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Line 1: − Gauss' Law: − <math>\boldsymbol{\nabla \cdot E} = 0 </math>+ − + + + + + + + + + + + + + + + − <math>\boldsymbol{\nabla \cdot B} = 0</math>+ − + − + + + + + + + + + + + + + + + + +
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== In Free Space ==
== 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:
{|align=center
|Gauss' Law:
|Gauss' Law for Magnetism:
|-
|<math>\boldsymbol{\nabla \cdot E} = 0 </math>
|<math>\boldsymbol{\nabla \cdot B} = 0</math>
|-
|height="20"| ||
|-
|Faradays's Law:
|Ampere's Law:
|-
|width="400"|<math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0</math>
|width="400"|<math>\boldsymbol{\nabla \times B} - \mu_0\epsilon_0\frac{\partial \boldsymbol{E}}{\partial t}= 0 </math>
|}
== In the Presence of Charges and Dielectric Media ==
Faradays's Law:
{|align=center
<math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}} {\partial t}= #0</math>
|Gauss' Law:
|Gauss' Law for Magnetism:
|-
|<math>\boldsymbol{\nabla \cdot D} = \rho </math>
|<math>\boldsymbol{\nabla \cdot B} = 0</math>
|-
|height="20"| ||
|-
|Faradays's Law:
|Ampere's Law:
|-
|width="400"|<math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0</math>
|width="400"|<math>\boldsymbol{\nabla \times H} - \frac{\partial \boldsymbol{D}}{\partial t}= \boldsymbol{j} </math>
|}
Where <math>\boldsymbol{D} = \epsilon_0 \boldsymbol{E}</math> and <math>\boldsymbol{B} = \mu_0 \boldsymbol{H}</math>.