Maxwell’s Equations: The Mathematics of Electromagnetism

Maxwell’s equations are four elegant laws that unify electricity and magnetism.
Gauss’s law says electric charges create electric fields.
Gauss’s law for magnetism shows magnetic poles always come in north–south pairs.
Faraday’s law explains how changing magnetic fields create electric currents.
Ampère–Maxwell’s law shows electric currents and changing electric fields create magnetism.
Together, they predict the existence of electromagnetic waves, like light.
Maxwell’s equations showed light is an electromagnetic wave traveling at a finite speed.
They underpin technologies like motors, radios, and wireless communication.
These equations are written in both vector calculus and differential form.
At their heart, Maxwell’s equations reveal electricity, magnetism, and light as one phenomenon.