Editing Maxwell's Equations

'''James Clerk Maxwell''' (b. 1831)

'''''Maxwell's Equations''''' 1861

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.

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:

: <math>\nabla \times \mathbf{B} =  \mu_0 \epsilon_0  \frac{\partial \mathbf{E}}{\partial t}</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} = 0</math>

Note that the speed of light is:

: <math>c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}</math>

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