Maxwell's Equations

Differential Form

Equation	Expression
Gauss (electric)	$\nabla \cdot \mathbf{E} = \rho/\varepsilon_0$
Gauss (magnetic)	$\nabla \cdot \mathbf{B} = 0$
Faraday	$\nabla \times \mathbf{E} = -\partial\mathbf{B}/\partial t$
Ampere-Maxwell	$\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0\varepsilon_0\,\partial\mathbf{E}/\partial t$

Electromagnetic Waves

In vacuum ($\rho=0$, $\mathbf{J}=0$) the equations reduce to the wave equation:

$$\nabla^2\mathbf{E} - \mu_0\varepsilon_0 \frac{\partial^2 \mathbf{E}}{\partial t^2} = 0$$

with wave speed $c = 1/\sqrt{\mu_0\varepsilon_0} \approx 3\times 10^8\,\text{m/s}$.

Related curriculum: book-classical-physics.