Editing Maxwell's Equations

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'''James Clerk Maxwell''' (b. 1831)
'''Joe Schmoe''' (b. xxxx)


'''''Maxwell's Equations''''' 1861
'''''Title''''' xxxx


In general, Maxwell's equations take the form:


: <math>\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)</math>
: <math>\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}</math>
: <math>\nabla \cdot \mathbf{B} = 0</math>
: <math>\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}</math>


where <math>\epsilon_0</math> is the permittivity of free space and <math>\mu_0</math> is the permeability of free space.
: $$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$
: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
: $$\nabla \cdot \mathbf{B} = 0$$
: $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$


In the example of an ideal vacuum with no charge or current, (i.e., <math>\rho=0</math> and <math>\mathbf{J}=0</math>), these equations reduce to:
In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$J=0$$), these equations reduce to:


: <math>\nabla \times \mathbf{B} = \mu_0 \epsilon_0Β  \frac{\partial \mathbf{E}}{\partial t}</math>
: $$\nabla \times \mathbf{B} = +\frac{1}{c^2} \frac{\partial \mathbf{E}}{\partial t}$$
: <math>\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}</math>
: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
: <math>\nabla \cdot \mathbf{B} = 0</math>
: $$\nabla \cdot \mathbf{B} = 0$$
: <math>\nabla \cdot \mathbf{E} = 0</math>
: $$\nabla \cdot \mathbf{E} = 0$$
Β 
Note that the speed of light is:
Β 
: <math>c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}</math>


== Resources: ==
== Resources: ==
*[https://en.wikipedia.org/wiki/Maxwell%27s_equations Maxwell's Equations]
*[https://en.wikipedia.org/wiki/Maxwell%27s_equations Maxwell's Equations]
== Discussion: ==
== Discussion: ==
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