Maxwell's equations
/ MAKS-welz /
Four short rules capture the whole of electricity and magnetism: how charges make electric fields, why there are no magnetic charges, how changing magnetism makes electricity, and how currents and changing electric fields make magnetism. Together they are the constitution of electromagnetism. They answer the biggest question of the subject: what are the complete laws of electric and magnetic fields?
Precisely, the four laws are Gauss's law (electric charge creates electric field: the electric flux out of a closed surface is proportional to the charge inside), Gauss's law for magnetism (there are no magnetic monopoles: the magnetic flux through any closed surface is zero), Faraday's law (a changing magnetic field creates an electric field: EMF = - dPhi_B/dt), and the Ampere-Maxwell law (currents and changing electric fields create magnetic fields, including the displacement current). Add the Lorentz force F = q(E + v cross B) and you can predict how any charge will move.
Solving them in empty space gives waves that travel at c = 1 / sqrt(mu_0 epsilon_0) — the speed of light — so Maxwell revealed that light itself IS an electromagnetic wave, uniting optics with electricity and magnetism. The honest caveat is that these classical equations, astonishingly accurate as they are, are not the last word: quantum electrodynamics extends them to describe individual photons and the fine details of atoms.
Feeding only the measured constants mu_0 and epsilon_0 into c = 1 / sqrt(mu_0 epsilon_0) gives about 3.0 * 10^8 m/s — the measured speed of light — which is how Maxwell first argued that light must be an electromagnetic wave.
The four laws force waves at c = 1 / sqrt(mu_0 epsilon_0), about 3.0 * 10^8 m/s — light itself.
The famous prediction is that the four equations force electromagnetic disturbances to travel at exactly the speed of light — the decisive clue that light is an electromagnetic wave.