Electromagnetic wave equation

Lore & Background

Maxwell commented: 'The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.' The modern derivation uses the Heaviside form of Maxwell's equations, taking the curl of the curl equations in a vacuum- and charge-free space.

Reader's Guide

The electromagnetic wave equation is fundamental to understanding light as an electromagnetic wave. It shows that electric and magnetic fields propagate as waves at the speed of light, which is a fundamental physical constant in vacuum. The equation predicts that electromagnetic waves are transverse, with both electric and magnetic fields perpendicular to the direction of propagation. Maxwell's derivation unified electricity, magnetism, and optics, establishing that light is an electromagnetic disturbance. The modern method of deriving the equation from Maxwell's equations is less cumbersome than Maxwell's original approach. The equation remains central to physics and engineering, underpinning technologies from radio to optics.

Did You Know?

• The electromagnetic wave equation is a three-dimensional form of the wave equation.
• The equation predicts that electromagnetic waves are transverse, with E and B perpendicular to the direction of propagation.
• Maxwell's derivation combined displacement current with other equations to obtain a wave equation with speed equal to the speed of light.