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Line 4: − + + − + − + − + + + + − + − <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 for Magnetism:+ − + − + − + − + − + − + − + − Ampere's Law:+ − + − + − Back to [[Mapping diamond surfaces using interference]]+
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{|align=center
{|align=center
|Gauss' Law:|Gauss' Law for Magnetism:
|Gauss' Law:
|Gauss' Law for Magnetism:
|-
|-
|<math>\boldsymbol{\nabla \cdot E} = 0 </math>
|<math>\boldsymbol{\nabla \cdot E} = 0 </math>
|<math>\boldsymbol{\nabla \cdot B} = 0</math>
|<math>\boldsymbol{\nabla \cdot B} = 0</math>
|-
|-
|Faradays's Law:|Ampere's Law:
|height="20"| ||
|-
|-
|<math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0</math>
|Faradays's Law:
|<math>\boldsymbol{\nabla \times B} - \mu_0\epsilon_0\frac{\partial \boldsymbol{E}}{\partial t}= 0 </math>
|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 ==
== In the Presence of Charges and Dielectric Media ==
Gauss' Law:
{|align=center
|Gauss' Law:
<math>\boldsymbol{\nabla \cdot D} = \rho </math>
|Gauss' Law for Magnetism:
|-
|<math>\boldsymbol{\nabla \cdot D} = \rho </math>
|<math>\boldsymbol{\nabla \cdot B} = 0</math>
<math>\boldsymbol{\nabla \cdot B} = 0</math>
|-
|height="20"| ||
Faradays's Law:
|-
|Faradays's Law:
<math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0</math>
|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 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>.