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Line 3:
Line 3: − + + + + + + + + + + + + + + + − <math>\boldsymbol{\nabla \cdot E} = 0 </math> + − + − + − + − + − + − + − + − + − Ampere's Law:+ − + − {| class="wikitable" style="margin: 1em auto 1em auto"|<math>\boldsymbol{\nabla \times B} - \mu_0\epsilon_0\frac{\partial \boldsymbol{E}}{\partial t}= 0 </math>|align="right" width="200"| (4) |} + + + + + − Need to add possibly derivation of wave equation and definitely Maxwell's equation in prescence − {| 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:
|-
Faradays's Law:
|<math>\boldsymbol{\nabla \cdot D} = \rho </math>
|<math>\boldsymbol{\nabla \cdot B} = 0</math>
<math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 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>.