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Line 3: − + + + + + + + + + + + + + + + − <math>\boldsymbol{\nabla \cdot E} = 0 </math> + − + − + − + + + + + + + + + + + + + − Faradays's Law: − + − − Ampere's Law: − − \begin{center} − − \end{center} − − {| class="wikitable" style="margin: 1em auto 1em auto" − |<math>\vec{\nabla}\times\vec{D}=\frac{\rho_{ext}}{\epsilon_0}</math> − |align="right" width="200"| (1) − |}
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These are the Maxwell's Equations we will be using to solve for regions "I" and "II" in our approximation of the Michelson interferometer.
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:
{|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 ==
Gauss' Law for Magnetism:
{|align=center
|Gauss' Law:
<math>\boldsymbol{\nabla \cdot B} = 0</math>
|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>
|}
<math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0</math>
Where <math>\boldsymbol{D} = \epsilon_0 \boldsymbol{E}</math> and <math>\boldsymbol{B} = \mu_0 \boldsymbol{H}</math>.
<math>\boldsymbol{\nabla \times B} - \mu_0\epsilon_0\frac{\partial \boldsymbol{E}}{\partial t}= 0 </math>