History of Maxwell's equations

In 1831, Michael Faraday discovered electromagnetic induction through his experiments, and proposed lines of forces to describe it.

In 1834, Emil Lenz solved the problem of the direction of the induction, and Franz Ernst Neumann wrote down the equation to calculate the induced force by change of magnetic flux.

In the 1850s, Maxwell was working at the University of Cambridge where he was impressed by Faraday's lines of forces concept.

Faraday created this concept by impression of Roger Boscovich, a physicist that impacted Maxwell's work as well.

Later, Maxwell moved to King's College London where he actually came into regular contact with Faraday, and became life-long friends.

He also modeled the vacuum as a kind of insulating elastic medium to account for the stress of the magnetic lines of force given by Faraday.

Moreover, the 1862 paper already derived the speed of light c from the expression of the velocity of the electromagnetic wave in relation to the vacuum constants.

In summary, Maxwell's equations successfully unified theories of light and electromagnetism, which is one of the great unifications in physics.

The relationships amongst electricity, magnetism, and the speed of light can be summarized by the modern equation: The left-hand side is the speed of light and the right-hand side is a quantity related to the constants that appear in the equations governing electricity and magnetism.

The discovery of this relationship started in 1855, when Wilhelm Eduard Weber and Rudolf Kohlrausch determined that there was a quantity related to electricity and magnetism, "the ratio of the absolute electromagnetic unit of charge to the absolute electrostatic unit of charge" (in modern language, the value

[15] Towards the end of 1861 while working on Part III of his paper On Physical Lines of Force, Maxwell travelled from Scotland to London and looked up Weber and Kohlrausch's results.

[16] The four modern Maxwell's equations can be found individually throughout his 1861 paper, derived theoretically using a molecular vortex model of Michael Faraday's "lines of force" and in conjunction with the experimental result of Weber and Kohlrausch.

But it was not until 1884 that Oliver Heaviside, concurrently with similar work by Josiah Willard Gibbs and Heinrich Hertz, grouped the twenty equations together into a set of only four, via vector notation.

is clearly visible in a glass case in the Wren Library of Trinity College, Cambridge, where Newton's manuscript is open to the relevant page.

Maxwell's contribution to science in producing these equations lies in the correction he made to Ampère's circuital law in his 1861 paper On Physical Lines of Force.

The physicist Richard Feynman predicted that, "From a long view of the history of mankind, seen from, say, ten thousand years from now, there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics.

The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade.

Imagine his feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarized waves, and at the speed of light!

To few men in the world has such an experience been vouchsafed ... it took physicists some decades to grasp the full significance of Maxwell's discovery, so bold was the leap that his genius forced upon the conceptions of his fellow workers.

[23] The four equations we use today appeared separately in Maxwell's 1861 paper, On Physical Lines of Force: The difference between the B and the H vectors can be traced back to Maxwell's 1855 paper entitled On Faraday's Lines of Force which was read to the Cambridge Philosophical Society.

It is later clarified in his concept of a sea of molecular vortices that appears in his 1861 paper On Physical Lines of Force.

The extension of the above considerations confirms that where B is to H, and where J is to ρ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that E is to D i.e. B parallels with E, whereas H parallels with D. In 1865 Maxwell published "A dynamical theory of the electromagnetic field" in which he showed that light was an electromagnetic phenomenon.

All the principal equations concerning Maxwell's electromagnetic theory are recapitulated in Chapter IX of Part IV.

Presciently, Maxwell also mentions that although some of the equations could be combined to eliminate some quantities, the objective of his list was to express every relation of which there was any knowledge of, rather than to obtain compactness of mathematical formulae.

[c] A more theoretical approach was suggested by Hendrik Lorentz along with George FitzGerald and Joseph Larmor.

Albert Einstein also dismissed the notion of the aether, and relied on Lorentz's conclusion about the fixed speed of light, independent of the velocity of the observer.

Maxwell's equations played a key role in Einstein's groundbreaking 1905 scientific paper on special relativity.

For example, in the opening paragraph of his paper, he began his theory by noting that a description of an electric conductor moving with respect to a magnet must generate a consistent set of fields regardless of whether the force is calculated in the rest frame of the magnet or that of the conductor.

For example, Theodor Kaluza and Oskar Klein in the 1920s showed that Maxwell's equations could be derived by extending general relativity into five physical dimensions.

This strategy of using additional dimensions to unify different forces remains an active area of research in physics.