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Line 3:
Line 3: − + + + + + + + + + + + + + + + − <math>\boldsymbol{\nabla \cdot E} = 0 </math> + − + + + + + + + + + + + + + + + − <math>\boldsymbol{\nabla \cdot B} = 0</math> − Faradays's Law:+ − − − − Ampere's Law: − − <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 == − <font color="red">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.</font> − − Gauss' Law: − − <math>\boldsymbol{\nabla \cdot D} = \rho </math> − − Gauss' Law for Magnetism: − − − − Faradays's Law: − − <math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0</math> − − Ampere's Law: − − <math>\boldsymbol{\nabla \times H} - \frac{\partial \boldsymbol{D}}{\partial t}= \boldsymbol{j} </math> − − − Back to [[Mapping diamond surfaces using interference]]
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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:
|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>.
<math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0</math>
<math>\boldsymbol{\nabla \cdot B} = 0</math>