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+'''James Clerk Maxwell''' (b. 1831)
+'''''Maxwell's Equations''''' 1861
 In general, Maxwell's equations take the form:
-: $$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)$$
+: <math>\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)</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>
-: $$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$
+: <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:
-where $$\epsilon_0$$ is the permittivity of free space and $$\mu_0$$ is the permeability of free space. \\
+: <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>
-In the example of an ideal vacuum with no charge or current, (i.e., $$\rho=0$$ and $$\mathbf{J}=0$$), these equations reduce to:
+Note that the speed of light is:
-: $$\nabla \times \mathbf{B} =  \mu_0 \epsilon_0  \frac{\partial \mathbf{E}}{\partial t}$$
+: <math>c = \frac{1}{\sqrt{\epsilon_0 \mu_0}}</math>
-: $$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$
-: $$\nabla \cdot \mathbf{B} = 0$$
-: $$\nabla \cdot \mathbf{E} = 0$$
 == Resources: ==
 *[https://en.wikipedia.org/wiki/Maxwell%27s_equations Maxwell's Equations]
 == Discussion: ==