Difference between revisions of "Maxwell's Equations"
| Line 3: | Line 3: | ||
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: | |
| − | <math>\boldsymbol{\nabla \cdot E} = 0 </math> | + | |<math>\boldsymbol{\nabla \cdot E} = 0 </math> |
| − | + | |Gauss' Law for Magnetism: | |
| − | Gauss' Law for Magnetism: | + | |<math>\boldsymbol{\nabla \cdot B} = 0</math> |
| − | + | |- | |
| − | <math>\boldsymbol{\nabla \cdot B} = 0</math> | + | |Faradays's Law: |
| − | + | |<math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 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> | |
| − | <math>\boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0</math> | + | |} |
| − | |||
| − | 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 == | == In the presence of charges and dielectric media == | ||
Revision as of 15:42, 21 March 2007
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: | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \boldsymbol{\nabla \cdot E} = 0 } | Gauss' Law for Magnetism: | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \boldsymbol{\nabla \cdot B} = 0} |
| Faradays's Law: | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0} | Ampere's Law: | Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \boldsymbol{\nabla \times B} - \mu_0\epsilon_0\frac{\partial \boldsymbol{E}}{\partial t}= 0 } |
In the presence of charges and dielectric media
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.
Gauss' Law:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \boldsymbol{\nabla \cdot D} = \rho }
Gauss' Law for Magnetism:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \boldsymbol{\nabla \cdot B} = 0}
Faradays's Law:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \boldsymbol{\nabla \times E} + \frac{\partial \boldsymbol{B}}{\partial t}= 0}
Ampere's Law:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \boldsymbol{\nabla \times H} - \frac{\partial \boldsymbol{D}}{\partial t}= \boldsymbol{j} }