Clerk Maxwell's Electromagnetic Theory

Part 1

CLERK MAXWELL'S ELECTROMAGNETIC THEORY

The Rede Lecture for 1923

H. A. LORENTZ

CAMBRIDGE AT THE UNIVERSITY PRESS

1923

CLERK MAXWELL'S ELECTROMAGNETIC THEORY

WHEN I had the honour to be invited to deliver a lecture in the Rede Foundation, I thought I might perhaps present to you a brief review of the electromagnetic theory of your great physicist James Clerk Maxwell. The choice seemed the more appropriate as it is now exactly fifty years ago that the work which raised him at once to the very first rank of investigators of all ages, the Treatise on Electricity and Magnetism, was published. In this work it was proved beyond all doubt that electric and magnetic actions can be conceived as being transmitted through a medium and the theory was crowned by the wonderful revelation that light is an electromagnetic phenomenon.

Maxwell's theory was also a great simplification. Indeed, before his time there was much uncertainty and confusion in this part of physics and many contending theories were in the field. In electrodynamics, for instance, we had the laws of Ampère and Grassmann for the actions between elements of current, and, when we went further, we found the speculations of Weber, Riemann and Clausius about the mutual actions of particles of electricity. In connexion with these theories there was a good deal of discussion on the phenomena that were to be expected in the case of closed and in that of open circuits. It was thought in those days that the current in a wire by means of which a metallic conductor is charged, ends on that conductor, and even the discharge current of a condenser was considered not to be closed; there was a gap in the circuit, because we had no idea that something is going on in the insulating layer between the coatings.

In optics we had no less trouble. It is true that the general principles of the undulatory theory of light had been firmly established and physicists were justly proud of the success that had been achieved in the explanation of interference and diffraction, double refraction and polarization. Yet, when we tried to penetrate somewhat deeper, we were confronted with serious difficulties. When we wanted to account for the different optical properties of various substances, of air and water for instance, we had the choice between two assumptions. Fresnel had sought the cause of the difference in an inequality of the density of the ether in the two substances, the elasticity being the same in both. F. E. Neumann, on the other hand, had supposed the densities to be the same, but the elasticities to be different. On either of these suppositions, and in no other way, it had been found possible to deduce the right value for the ratio between the amplitude of the reflected and that of the incident light. You know that in this problem two principal cases must be distinguished, the vibrations being normal to the plane of incidence in the one case and parallel to that plane in the other. The two values for the ratio in question are

sin (i — r) / sin (i + r)

and

tg (i - r) / tg (i + r),

if i is the angle of incidence and r the angle of refraction; and it is remarkable that, of the two rival theories, one led to the expression with the sines when the other required that with the tangents, and conversely. In connexion with this Fresnel supposed the vibrations of plane polarized light to be at right angles to the plane of polarization, whereas Neumann wanted them to be parallel to that plane.

Here was a problem that long baffled the efforts of physicists, and many attempts were made to determine experimentally the direction of the vibrations. One cannot say that the result has been very satisfactory and the question remained open until Maxwell's theory settled it once for all.

I have enumerated some only of the difficulties with which we had to struggle. I could have mentioned similar problems that arose in the theory of double refraction and I may add that in some cases longitudinal vibrations intruded themselves and complicated the theory.

Maxwell relieved us of all these doubts and uncertainties. By his bold assumption that in a non-conducting body, in a dielectric as he called it, there can exist what is truly a motion of electricity, and that, if this motion, the dielectric displacement, is taken into account, electricity can always be said to move as an incompressible fluid, the open currents and the longitudinal vibrations that were closely allied to them were made to vanish from the scene. Further, the optical behaviour of non-conducting substances was shown to depend on two properties, each characterized by a physical constant, the dielectric constant, or Faraday's specific inductive capacity, and the magnetic permeability. It is true that the way in which these constants are determined by the constitution of matter, by the structure of molecules and atoms, was not considered and that, so far, they were no less inaccessible than the ethereal density and elasticity of the old theories, but there was this important difference that, whereas these latter constants had no connexion with any other phenomena, the dielectric constant and the magnetic permeability can be measured by means of statical experiments, so that, at least in certain simple cases, we can deduce the optical properties of a substance from wholly different data. It was found that in the new theory the treatment of the reflexion problem was much like that in the old one; one is led to the two formulae which I recalled to you, if one supposes either the dielectric constant or the magnetic permeability to be the same in the two substances. The choice between these alternative suppositions again entailed a decision concerning the direction of the vibrations with respect to the plane of polarization, but the choice was not doubtful now, as it had been ascertained experimentally that the ratios between the magnetic permeabilities of transparent substances are little different from unity, whereas the dielectric constants diverge to a much greater extent. It was therefore at once established that the electric vibrations are normal to the plane of polarization. This implies that the magnetic vibrations are in that plane, so that, in a sense, the contending parties both had their will.

In the case of crystals it became certain that their double refraction is due to an inequality of the dielectric properties in different directions.

So, many difficulties and outstanding problems melted away as snow before the sun. Indeed, a reviewer in Nature actually compared Maxwell's work to the sun, his only criticism being that there are spots on the sun itself, which, however, "are not visible save to those whose eyes can bear the full glare of the glowing orb." My eyes certainly were not as strong as that. I could not see the spots, but what I could see was that the sun was not entirely unclouded; what sun always was? It was not always easy to grasp Maxwell's ideas, and one feels a want of unity in his book, due to the fact that it faithfully reproduces his gradual transition from old to new ideas. When we read what Maxwell says of Ampère and Faraday, of the former having removed all traces of the scaffolding by which he had built up a perfect demonstration of his law, whereas Faraday "shews us his unsuccessful as well as his successful experiments, and his crude ideas as well as his developed ones," we feel that, great though the difference may be between the Experimental Researches and Maxwell's largely mathematical Treatise, yet the two works were written in the same spirit. In fact, Maxwell repeatedly expresses his indebtedness to Faraday, from whom he had borrowed part of his fundamental ideas, so that, when there is question of Maxwell's theory, we must often think of Faraday also.

Maxwell's followers, of whom there were many, in this country and elsewhere, have perfected the theory in its form and extended it by the introduction of new ideas. Think, for instance, of Poynting's beautiful and important theorem on the flow of energy, determined at every point by the electric and the magnetic force existing in the field, a theorem that has produced more clearness perhaps than any other and which is now so essential that we can hardly recall the state in which physics was when we did not know it. Yet, notwithstanding all innovations of this kind, we always speak, and with full justice, of "Maxwell's Theory." We continue to do so now that we have been led to introduce electric charges supposed to exist in the interior of molecules and atoms, by which we have come to the theory of electrons. And when we refer to those wonderfully simple equations in which the fundamental laws of electromagnetism are embodied with a conciseness that could never have been dreamed of before, we call them "Maxwell's Equations." Surely, though Maxwell did not use them in their modern form, no name could be more appropriate, for the general relations which they express are those that were constantly in his mind.

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