Maxwell’s Equations

The development of the idea that light is an electromagnetic radiation is one of the most dramatic in the history of physics. We quote below from the introduction to the paper¹⁾ in which Maxwell announced the-electromagnetic theory of light. In the introduction, Maxwell summarizes the results of his mathematical investigations, describing eight relationships, which he calls the general equations of the electromagnetic field. These are essentially equivalent to the four relationships now called Maxwell's equations. Maxwell then goes on to discuss some of the implications of his results in the following paragraphs:

The general equations are next applied to the case of a magnetic disturbance propagated through a nonconducting field, and it is shown that the only disturbances which can be so propagated are those which are transverse to the direction of propagation, and that the velocity of propagation is the velocity v, found from experiments such as those of Weber, which expresses the number of electrostatic units of electricity which are contained in one electromagnetic unit.*

This velocity is so nearly that of light, that it seems we have strong reason to conclude that light itself (including radiant heat, and other radiations if any) is an electromagnetic disturbance in the form of waves propagated through the electromagnetic field according W electromagnetic laws. If so, the agreement between the elasticity of the medium as calculated from the rapid alternations of luminous vibrations, and as found by the slow processes of electrical experiments, shows how perfect and regular the elastic properties of the medium must be when not encumbered with any matter denser than air. If the same character of the elasticity is retained in dense transparent bodies, it appears that the square of the index of refraction is equal to the product of the specific dielectric capacity and the specific magnetic capacity. Conducting media are shown to absorb such radiations rapidly, and therefore to be generally opaque.

The conception of the propagation of transverse magnetic disturbances to the exclusion of normal ones is distinctly set forth by Professor Faraday in his "Thoughts on Ray Vibrations." The electromagnetic theory of light, as proposed by him, is the same in substance as that which 1 have begun to develop in this paper, except that in 1846 there were no data to calculate the velocity of propagation.

1) James Clerk Maxwell, A Dynamical Theory of the Electromagnetic Field, Phil. Trans. Roy. Soc. London, 155:459 (1865).