The behavior of electric and magnetic fields is governed by Maxwell’s equations. In differential form, Gauss’s law states

where is the electric field, the charge density, and the vacuum permittivity.

Faraday’s law of induction relates time-varying magnetic fields to induced electric fields:

The Ampère-Maxwell law includes the displacement current term:

Combining these yields the electromagnetic wave equation in vacuum:

The propagation speed is .

The Lorentz force on a charged particle with charge and velocity is

The energy density stored in electromagnetic fields is