Electromagnetism

The life of James Clerk Maxwell

Timeline 1831Born on 13 June in Edinburgh, Scotland. Spends his childhood on the family estate, Glenlair. 1839His mother dies of cancer, when he is 8. 1846At 14, a paper of his on oval curves is read at the Royal Society of Edinburgh. 1850Enters the University of Cambridge. 1855Presents his theory of colour and the paper “On Faraday’s lines of force”. 1856Becomes a professor in Aberdeen, aged 25. 1859Publishes the essay on Saturn’s rings, which won the Adams Prize. Presents the distribution of molecular speeds. 1860Loses his job when two colleges merge. Moves to King’s College, London. 1861Shows the first colour photograph at the Royal Institution. 1862Calculates that electromagnetic waves travel at the speed of light. 1865Publishes “A dynamical theory of the electromagnetic field” and returns to Glenlair. 1871Becomes the first Cavendish Professor of Experimental Physics, in Cambridge. 1873Publishes the Treatise on Electricity and Magnetism. 1879Dies on 5 November in Cambridge, aged 48. ◀ Previous Follow the journey Next ▶ 1831 EdinburghBorn on 13 June. Later he studies at the Edinburgh Academy and University; at 14 a paper of his on ovals is read at the Royal Society of Edinburgh. 1831–1841 GlenlairHe spends his childhood on the family estate, asking “what’s the go of that?”. His mother dies when he is eight. 1850–1856 CambridgeHe studies at Trinity College. He presents his theory of colours and his paper on Faraday’s lines of force. 1856–1860 AberdeenA professor at 25. He wins the Adams Prize with his essay on Saturn’s rings and loses his job when the colleges merge. 1860–1865 LondonAt King’s College he shows the first colour photograph and discovers that light is an electromagnetic wave. 1865–1871 GlenlairHe returns to the country and writes the Treatise on Electricity and Magnetism. 1871–1879 CambridgeThe first Cavendish Professor, he founds the Cavendish Laboratory. He dies in 1879, aged 48. Enable JavaScript to see the map. The stages are listed below. Maxwell between Scotland and England, always returning to Glenlair. Map: © OpenStreetMap contributors

October 14, 2026 Read

Colour: the spinning top and the tartan ribbon

The science of colour must therefore be regarded as essentially a mental science. — James Clerk Maxwell, “Experiments on colour” (1855) Since Newton it had been known that white light is a mixture of all the colours of the rainbow. But the colour we see is something else: it depends on the eye and the brain. The English physician Thomas Young had proposed, in 1802, that the eye has only three kinds of sensor, and that every colour we perceive is a combination of the responses of those three. It was a bold hypothesis without proof. Maxwell, aged 24, turned it into mathematics.

October 14, 2026 Read

Saturn's rings cannot be solid

The only system of rings which can exist is one composed of an indefinite number of unconnected particles, revolving round the planet with different velocities according to their respective distances. — James Clerk Maxwell, On the Stability of the Motion of Saturn's Rings (1859) Galileo looked at Saturn through his telescope in 1610 and thought the planet had “ears”. In 1655 Huygens realised they were a thin, flat ring that does not touch the planet. Two hundred years later, nobody knew what the ring was made of. Was it a solid disc, like a vinyl record? A liquid? A cloud of stones?

October 14, 2026 Read

The speeds of molecules: the Maxwell distribution

I have been occupied lately with some questions about the motions and collisions of perfectly elastic spheres, as an exercise in mechanics. — James Clerk Maxwell, letter to George Stokes (30 May 1859) A litre of air contains about $2.5\times10^{22}$ molecules, all moving and colliding billions of times a second. Following each one is impossible. In 1859 Maxwell had an idea that changed physics: not to ask what each molecule does, but what fraction of them has each speed. It was the first time probabilities had been used in a law of physics. He presented the result at a meeting in Aberdeen in 1859 and published it in 1860.

October 14, 2026 Read

Maxwell's equations: from Faraday's lines of force to vectors

I was at first almost frightened when I saw such mathematical force made to bear upon the subject, and then wondered to see that the subject stood it so well. — Michael Faraday, letter to Maxwell (25 March 1857) Until 1820, electricity and magnetism were separate subjects. Electricity made sparks and raised the hair on your head; magnetism made compasses point north. That year, during a lecture at the University of Copenhagen, the Dane Hans Christian Oersted connected a battery to a wire and saw a nearby magnetic needle move. Electric current produced magnetism.

October 14, 2026 Read

The displacement current: the missing term

Of Maxwell’s four equations, three were already known in some form before him: Gauss’s law, the magnetic law and Faraday’s law. The fourth, Ampère’s, was known too, but it was incomplete. What Maxwell added to it was a single term, $\mu_0\varepsilon_0\frac{\partial\mathbf E}{\partial t}$. It looks like little. It was this term that turned electricity and magnetism into light. Ampère’s law In 1826 the Frenchman André-Marie Ampère found the rule linking a current to the magnetic field around it. In today’s language: if you go round a closed path around a wire and add up the component of the magnetic field along the path, the result is proportional to the current $I$ crossing any surface bounded by that path:

October 14, 2026 Read

Light is an electromagnetic wave

We can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena. — James Clerk Maxwell, “On physical lines of force” (1862), with the original italics In the summer of 1861, at Glenlair, far from his books, Maxwell did a calculation with his model of vortices and little wheels: if the medium that transmits electric and magnetic forces were shaken, the disturbance would travel as a wave. At what speed? The calculation gave a number that depended only on two constants measured in the laboratory with magnets and charges. He did not have the values to hand. When he returned to London in October, he looked them up. The number was the speed of light.

October 14, 2026 Read

The legacy of James Clerk Maxwell

This change in the conception of reality is the most profound and the most fruitful that physics has experienced since the time of Newton. — Albert Einstein, at Maxwell's centenary (1931) Maxwell died at 48, little known to the general public. In his lifetime, hardly anyone outside a small group of British physicists accepted his field theory. Today anyone using a mobile phone depends on it dozens of times a second.

October 14, 2026 Read

Image credits

Historical images and photographs All come from Wikimedia Commons. We use the thumbnails provided by Commons, unedited. Portrait of Maxwell, engraving by G. J. Stodart, 1890: source page · public domain. The tartan ribbon, the first colour photograph, by Maxwell and Thomas Sutton, 1861: source page · public domain. Saturn seen from above, by the Cassini spacecraft, 2013: NASA/JPL-Caltech/Space Science Institute, source page · public domain. Michael Faraday, photograph from the 1850s, unknown author: source page · public domain. Title page of the Treatise on Electricity and Magnetism, Oxford, 1873: source page · public domain. The statue of Maxwell with his dog Toby, in Edinburgh, photo by Зеленый кабинет: source page · CC BY-SA 2.0. Blog figures The cover, the wave profile and the graph of the Maxwell distribution for nitrogen are original illustrations, with versions in each of the site’s languages. The graph was calculated with the exact formula of the distribution. The discussion of quaternions and vectors, in the post on the equations, draws on passages from this site’s old course on vectors.

October 14, 2026 Read