Result

Electromagnetic wave speed

(E12.3.1) E12.3 · Plane Electromagnetic Waves →

c = \frac{1}{μ _{0} ε _{0}}, E = c B

Statement

The speed of a plane electromagnetic wave in vacuum, and the fixed ratio between its electric and magnetic field amplitudes.

Symbols and units

$c$	speed of light	2.998×10⁸ m/s
$μ_{0}$	permeability of free space	4π×10⁻⁷ T·m/A
$ε_{0}$	permittivity of free space	8.85×10⁻¹² C²/(N·m²)
$E, B$	electric, magnetic field magnitude	V/m, T

When it applies

Plane waves in vacuum, far from any source charges or currents.

Don't use when

Specific to plane waves in vacuum far from source charges or currents — inside a medium the speed is reduced by the medium's permittivity and permeability.

Derivation

Combining Faraday's and the Ampère-Maxwell law for oscillating E and B fields with no charges or currents present gives a wave equation whose speed depends only on the two field constants:

c = \frac{1}{μ _{0} ε _{0}}

Watch out for

That this predicted speed matched the already-measured speed of light was the discovery that light itself IS an electromagnetic wave — not a coincidence Maxwell went looking for, but one his own equations forced on him.