Maxwell's equations allow electric and magnetic fields to sustain one another as travelling disturbances. These disturbances are electromagnetic waves.

Coupled fields

A changing electric field contributes to magnetic circulation, while a changing magnetic field produces circulating electric field. In free space, these coupled changes can propagate without charges, currents or a material medium.

For a plane electromagnetic wave, the electric field $\mathbf E$, magnetic field $\mathbf B$ and propagation direction are mutually perpendicular.

Speed in vacuum

Maxwell's equations give the vacuum wave speed

$$c=\frac1{\sqrt{\mu_0\varepsilon_0}}.$$

Its numerical value is approximately

$$c\approx3.00\times10^8,\mathrm{m/s}.$$

The agreement with the measured speed of light identifies light as electromagnetic radiation.

Field relationship

For a plane wave in vacuum,

$$E=cB$$

for the field magnitudes.

The electric and magnetic fields oscillate in phase and together transport energy and momentum.

Transverse character

Because both fields are perpendicular to the propagation direction, electromagnetic waves are transverse. This makes polarization a natural property of electromagnetic radiation.