Science › Classical physics
Electromagnetism (Maxwell's equations)
1865· Theory
ProvenTested many times; part of working physics.
The theory that electricity, magnetism and light are one phenomenon, summed up in Maxwell's equations (1865).
See it on the Science map →How it works
Electric charges create electric fields; moving charges (currents) create magnetic fields; a changing magnetic field creates an electric field, and vice versa. Maxwell's four equations capture all of this. Together they mean a disturbance in one field regenerates the other, sending a self-sustaining wave through space at about 300,000 km per second. Radio, visible light and X-rays are all such waves at different frequencies.
Why it matters
It is the physics of nearly all technology: motors, generators, electronics, communications. Its fixed speed of light triggered relativity.
How we know
Hertz's radio waves (1887–1888), Marconi's transatlantic radio (1901), and every working circuit since. Its quantum version, quantum electrodynamics, matches experiment to better than one part in a billion.
Still a mystery
Why electric charge comes in exact multiples of a basic unit, and whether magnetic monopoles (lone north or south poles) exist, are unanswered.
Connections (7)
▸Michael Faraday discovered induction for Electromagnetism (Maxwell's equations)Proven
The relationship
Faraday showed that a changing magnetic field drives an electric current, the reverse of Ørsted's 1820 finding that current produces magnetism. This two-way link meant electricity and magnetism form one interacting system. His picture of fields filling space gave Maxwell something to turn into equations, and induction became one of the four.
How the link was found
Faraday, at the Royal Institution in London, in August 1831, using an iron ring wound with two coils, then a magnet pushed into a coil.
Why it's proven
Induction is directly measurable and powers every generator and transformer. Maxwell's equations, built on it, predict experiments precisely.
Open questions and mysteries
Faraday's 'lines of force' raised the question of whether fields are real things or just bookkeeping. Modern physics treats them as real, but the debate shaped physics for decades.
▸James Clerk Maxwell unified into four equations Electromagnetism (Maxwell's equations)Proven
The relationship
Maxwell gathered the known laws of electricity and magnetism, from Coulomb, Ampère, Gauss and Faraday, into one mathematical system. He found them inconsistent when currents change, and added a term (the 'displacement current'). With it the system closed into a complete theory in which a change in each field creates the other.
How the link was found
Maxwell, in papers of 1861–1862 and his 1865 'A Dynamical Theory of the Electromagnetic Field'. Oliver Heaviside rewrote them as today's compact four equations in the 1880s.
Why it's proven
Hertz's radio waves (1887–1888) confirmed the predicted waves. The equations still design every antenna, motor and circuit.
Open questions and mysteries
The equations survive Einstein's relativity unchanged, but at atomic scales they give way to quantum electrodynamics. Why electric charge comes in fixed units remains unexplained.
▸Electromagnetism (Maxwell's equations) was the first complete theory of Fields: what everything is made ofProven
The relationship
Maxwell's equations describe electric and magnetic fields as continuous quantities filling space, each changing the other. They were the first complete, mathematical theory of a field. They showed fields can carry waves on their own, detached from any charge, moving at the speed of light. That made fields physical things with energy, not just a way to describe forces.
How the link was found
James Clerk Maxwell, in his 1865 paper 'A Dynamical Theory of the Electromagnetic Field', building on Faraday's lines of force.
Why it's proven
Heinrich Hertz generated and detected radio waves in 1887-88, exactly as Maxwell predicted. Every radio, phone and microwave oven since depends on it.
Open questions and mysteries
Maxwell's theory is not quantum; light also comes in lumps (photons). Reconciling the two took until the late 1940s.
▸Electromagnetism (Maxwell's equations) predicted Light is an electromagnetic waveProven
The relationship
Maxwell's equations let a changing electric field create a magnetic field, which creates an electric field, and so on, travelling outward as a wave. The equations fix that wave's speed from two lab-measured constants describing electric and magnetic strength. The speed matched light's, implying light is this wave.
How the link was found
Maxwell noticed the match in 1862 and stated the conclusion in his 1865 paper.
Why it's proven
Hertz made electromagnetic waves with electric sparks in 1887–1888 and showed they reflect, refract and travel at light speed, as predicted.
Open questions and mysteries
A wave seemed to need a medium, and the search for that 'ether' failed. Quantum theory later showed light also comes in particle-like packets.
▸Electromagnetism (Maxwell's equations) clashed with Newton, leading to Special relativityProven
The relationship
Maxwell's equations predict one fixed speed of light. Newton's mechanics says speeds add, so light should look faster or slower to moving observers. The two theories could not both be right. Einstein kept Maxwell's equations and changed the rules of space and time instead. His 1905 paper was titled "On the Electrodynamics of Moving Bodies."
How the link was found
Lorentz (1904) and Poincaré (1905) found the needed math; Einstein, in June 1905, gave the clean physical explanation.
Why it's proven
Maxwell's equations need no change in special relativity, and the combined theory matches all experiments on fast-moving charges and light.
Open questions and mysteries
Settled. Quantum electrodynamics, its quantum version, is one of the most precisely tested theories ever.
▸Electromagnetism (Maxwell's equations) was made quantum in QED: the theory of light and electronsProven
The relationship
Maxwell's smooth electromagnetic field was rewritten under quantum rules: its energy comes only in lumps, which are photons. Charged particles interact by emitting and absorbing photons. In everyday conditions, with huge numbers of photons, QED reproduces Maxwell's equations exactly, the way a crowd's average behavior hides individual people.
How the link was found
Dirac began quantizing the electromagnetic field in 1927. The working theory came in 1947-49 from Feynman, Schwinger, Tomonaga and Dyson.
Why it's proven
QED reproduces all of Maxwell's classical results and adds quantum corrections, like the Lamb shift (1947), measured to extreme precision.
Open questions and mysteries
Why electric charge comes in exactly the units it does, and why the strength of electromagnetism (about 1/137) has its value, are unexplained.
▸Calculus: the math of change is the language of Electromagnetism (Maxwell's equations)Proven
The relationship
Fields vary from point to point and moment to moment, and Maxwell's equations describe how they change across space and time. That takes calculus in several variables: rates of change in each direction, and sums over surfaces and volumes. Combining the equations this way yields a wave equation, which is how the light-speed prediction appeared.
How the link was found
Maxwell used calculus methods from Gauss, Green and Stokes in the 1860s. Heaviside and Josiah Willard Gibbs developed vector calculus in the 1880s to write the equations compactly.
Why it's proven
The calculus predictions match measurements in every circuit, antenna and optical device. The math itself is rigorous.
Open questions and mysteries
Calculus treats fields as perfectly smooth. At quantum scales fields fluctuate, and taming the resulting infinities needed new methods (renormalisation) in the 1940s.