A Dynamical Theory of the Electromagnetic Field
Electricity and magnetism are one field — and light is a ripple travelling through it.
Maxwell discovered that electricity and magnetism are two faces of one thing — and that light itself is a wave rippling through it.
The big idea
By Maxwell's day, experiments had shown that electricity and magnetism are entangled: a moving magnet pushes electricity along a wire, and an electric current deflects a compass needle. Maxwell's first move was to stop picturing these as forces reaching between objects and instead imagine invisible “fields” — patterns of influence spread through all of space — and to write down a compact set of equations for how the electric and magnetic fields create and bend each other.
Then came the astonishing part. His equations said a wiggle in these fields doesn't stay put: it travels outward as a wave, and he could calculate its speed from numbers already measured in the laboratory. The answer was the speed of light. That could not be coincidence. Light, Maxwell concluded, simply is an electromagnetic wave — and if visible light is one such wave, there must be others, of longer and shorter wavelength, that our eyes cannot see.
How it came about
Maxwell built on Michael Faraday, a largely self-taught experimenter who had filled the space around magnets and charges with imaginary “lines of force” but lacked the mathematics to make them precise. Maxwell admired Faraday's physical pictures and set out to give them equations. In an earlier 1862 paper he had even imagined the field as a lattice of spinning cells and idle wheels — a mechanical model — and noticed that its elasticity implied waves travelling at the speed of light.
In this 1865 paper he dropped the elaborate machinery and presented the theory in its mature form: a “dynamical theory of the electromagnetic field,” resting on the equations themselves rather than on any particular mechanical picture. It was read to the Royal Society in December 1864. Full vindication came in 1887, eight years after Maxwell's early death at 48, when Heinrich Hertz produced and caught these waves on a laboratory bench.
Why it mattered
Maxwell achieved the second great unification in physics, after Newton: he showed that electricity, magnetism, and light are one phenomenon, governed by a single set of laws. That insight is the foundation of the entire electrical and wireless age — every radio, phone, and Wi-Fi signal is one of his waves. And his equations carried a hidden clue, the fixed speed of light built into them, that would lead Einstein to relativity a generation later.
A way to picture it
Picture two dancers, electricity and magnetism, who can only move by cueing each other. When the electric field rises and falls, its change conjures a magnetic field beside it; when that magnetic field rises and falls, its change conjures an electric field a step further on — and so the pair leapfrogs through empty space, each one's change giving birth to the other. That self-renewing relay, racing forward at the speed of light, is a light wave. Change how fast the dancers shake — the frequency — and you change the colour, from radio to visible to X-ray; but the relay always advances at exactly the same speed, c.
What came next
Maxwell's fixed speed of light, the same for everyone, was a riddle classical physics could not answer — until Einstein made it the cornerstone of special relativity in 1905, abolishing absolute space and time. Maxwell's equations needed no revision; they had been relativistic all along.
On the other front, light's wave description met its limits with hot, glowing bodies and the photoelectric effect, which forced physics to accept that light also comes in discrete packets — photons. The reconciliation of Maxwell's fields with the quantum became quantum electrodynamics, the most precisely tested theory in all of science. Maxwell's four equations remain its exact classical limit — and still the working tool of every electrical engineer.
Introductory — a theory of the field
The energy lives in the medium
We may therefore receive, as a datum derived from a branch of science independent of that with which we have to deal, the existence of a pervading medium of small but real density, capable of being set in motion, and of transmitting motion from one part to another with great, but not infinite, velocity.
Waves transverse, like light
The agreement, and the conclusion
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.