Complete Electromagnetism

Field View

Electromagnetism is most compactly written in terms of fields $\mathbf E$ and $\mathbf B$.

Maxwell Equations

The four equations organize sources, constraints, and dynamics:

$$\nabla\cdot\mathbf E=\frac{\rho}{\varepsilon_0}, \qquad \nabla\cdot\mathbf B=0,$$ $$\nabla\times\mathbf E=-\frac{\partial\mathbf B}{\partial t}, \qquad \nabla\times\mathbf B=\mu_0\mathbf J+\mu_0\varepsilon_0\frac{\partial\mathbf E}{\partial t}.$$

Waves

In vacuum these imply electromagnetic waves moving at $c$.