Maxwell Unifies Electricity, Magnetism, and Light
Four equations show that light itself is an electromagnetic wave
Quick facts
- Key paper
- A Dynamical Theory of the Electromagnetic Field, 1865
- Final form
- Electricity and Magnetism, 1873
- Core result
- Light is an electromagnetic wave
- Built on
- Michael Faraday's lines of force
What happened
James Clerk Maxwell took Michael Faraday's qualitative picture of electric and magnetic lines of force and translated it into rigorous mathematics. In his 1865 paper A Dynamical Theory of the Electromagnetic Field, and in final form in his 1873 book Electricity and Magnetism, Maxwell set out four partial differential equations, now called Maxwell's equations, describing how electric and magnetic fields interact and propagate. Around 1862 he calculated that the speed of propagation of an electromagnetic field matched the known speed of light and concluded, in his own words preserved by MacTutor, that we can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena. Maxwell had shown that light, electricity, and magnetism were the same underlying phenomenon.
Why it matters
Maxwell's equations are one of the great achievements of 19th-century mathematics and remain, unmodified except by relativity's reformulation, the working theory of classical electromagnetism used in every radio, motor, and antenna built since. The prediction that light is an electromagnetic wave, confirmed experimentally by Heinrich Hertz in the 1880s, also planted the conceptual seed, a fixed speed of light in the equations, that Einstein would use forty years later to build special relativity.
How we know
Maxwell's own papers and his 1873 Treatise on Electricity and Magnetism survive as the primary published record of his equations; MacTutor's biography draws directly on Maxwell's published statements about the electromagnetic nature of light.
Sources
- MacTutor History of Mathematics, University of St Andrews. James Clerk Maxwell (1831 - 1879) · Primary source (author-declared)mathshistory.st-andrews.ac.uk · Cited as a "primary" source (no stronger domain match). · Link is live and its text matches the event's key terms (Jul 2026)
- MacTutor History of Mathematics, University of St Andrews. Michael Faraday (1791 - 1867) · Primary source (author-declared)mathshistory.st-andrews.ac.uk · Cited as a "primary" source (no stronger domain match). · Link is live and its text matches the event's key terms (Jul 2026)
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