Electromagnetic Waves and the Speed of Light

Propagation equation

In vacuum, with no charge or current (rho = 0, J = 0), combining Maxwell-Faraday and Maxwell-Ampère — taking the curl of curl(E) = -dB/dt and substituting curl(B) via Maxwell-Ampère — yields a propagation equation:

laplacian(E) = mu0 * epsilon0 * d^2E/dt^2

An identical equation holds for B. This is the classical wave equation, whose propagation speed is:

c = 1 / sqrt(mu0 * epsilon0)

Numerical example

With epsilon0 = 8.85e-12 F/m and mu0 = 4pi1e-7 H/m, we calculate:

c = 1 / sqrt(8.85e-12 * 4pi1e-7) ~ 3.00e8 m/s

This value matches the experimentally measured speed of light, which led Maxwell to conclude that light is an electromagnetic wave.

Structure of the plane wave

In a plane progressive electromagnetic wave, E and B are perpendicular to each other and perpendicular to the direction of propagation. Their amplitudes satisfy |E| = c * |B|, and the cross product E x B gives the direction of propagation (the Poynting vector).

Common pitfall

Believing that E and B have the same numerical amplitude in SI units: in reality |E| = c * |B|, with c ~ 3e8, so E is numerically much larger than B for the same wave.