Clerk Maxwell's electromagnetic theory

by H. A. Lorentz

Whereas Maxwell seems not to have tried the above experiment with the coil, he tried to observe another effect. A coil, through which a current could be passed and which could be provided with an iron core, was placed in a system rapidly revolving about a vertical axis, the arrangement being such that the coil was free to rotate in the revolving system, so that the axis of the coil could be inclined to different degrees with respect to the vertical axis of rotation. If in the formula for the kinetic energy there were terms of the kind which Maxwell wanted to detect, there would be a tendency for the coil to place itself with its axis parallel to the axis of rotation; it would behave as a gyroscope and might be called an electromagnetic gyroscope. No trace of a phenomenon of this kind could, however, be observed. I may insert the remark that, if the tendency of which I spoke existed to an appreciable extent, a magnetic needle would, even in the absence of the terrestrial magnetic field, still take a definite position that would be determined by the rotation of the earth; in fact, in virtue of its internal motions the magnetic needle would be comparable to a gyroscopic compass, such as has lately come into use in navigation.

Now that we know the intensity of the Einstein effect we can say with certainty that, if only his instrumental means had been more refined. Maxwell's experiment would have had a positive result. We can evaluate the magnitude of the effect and we can also calculate that the force which a magnetic needle experiences on account of its internal motions and of the rotation of the earth is thousands of millions of times smaller than the force due to the earth's magnetic field, so that you need not fear from this cause any error in measurements in terrestrial magnetism.

In the experiments just discussed we were concerned with forces acting on the material bodies. Maxwell next considers cases in which, always on account of the terms in question, not the material system but the electricity contained in it is set in motion. Here he reverts again to the suspended circular coil, and he points out that when a rotation is suddenly imparted to it there could be produced a transient electric current. Similarly, there would be a current, but now in the opposite direction, when the motion of the coil is stopped.

A very simple experiment may serve to give you an idea of these phenomena. We take a cylindrical tumbler, partly filled with water, and set it suddenly in rotation about its vertical axis. Then the friction between the glass and the water will make the fluid rotate likewise, but this will take some time; during a certain period the water will lag behind. Let us next suppose that the motion of the vessel has been kept constant for a sufficient length of time, so that the water has acquired the full angular velocity and then let the vessel be suddenly brought to rest. It is clear that the circulation of the water will continue for a certain time, until it is exhausted by the friction.

Similar phenomena could be observed with a closed circular tube capable of rotating about its axis, and there must be a corresponding electromagnetic phenomenon if a metallic wire contains something like movable electricity, as we are now in a position to assert, because we have good reasons for believing that an electric current consists in a motion of negative electrons. Though the experiment is much more delicate with electricity than with water, Tolman and Stewart have performed it with very satisfactory results. Using a coil with a great number of windings, rapidly rotating about its axis, they were able to observe with a sensitive galvanometer the transient electric current that was produced on stopping the motion by means of a brake. The electrons continued to move over some distance just as the water did in the experiment with the circular tube. The direction of the current showed that the movable particles really have negative charges and the observed deflections agreed with what can be inferred from the ratio between the charge and the mass of the electrons, a ratio that was found for the first time by Zeeman and Sir J. J. Thomson somewhat more than twenty-five years ago and has been repeatedly determined in later years.

No less remarkable than Tolman and Stewart's experiments are those made by Mr and Mrs Barnett. They found that a cylindrical rod of iron, rotating about its geometrical axis, becomes thereby magnetized in the direction of its length. Like the Einstein effect, to which it forms a counterpart, this new phenomenon can be predicated on the assumption that magnetization consists in a motion of electrons in the molecules of the metal. This allows us to assign the direction of the effects, but for the sake of truth I must add that both the rotation produced by the magnetization of rods and the magnetization caused by a rotation are, for some reason which we do not yet understand, only about half what the theory of electrons had led us to expect.

In Maxwell's time the electron was unknown and the mechanism of conduction was even more mysterious than it is now. It was precisely for this reason that he attached so much importance to the phenomena to which I have drawn your attention. He says in this connexion:

It appears to me that while we derive great advantage from the recognition of the many analogies between the electric current and a current of a material fluid, we must carefully avoid making any assumption not warranted by experimental evidence, and that there is, as yet, no experimental evidence to shew whether the electric current is really a current of a material substance, or a double current, or whether its velocity is great or small as measured in feet per second.

A knowledge of these things would amount to at least the beginning of a complete dynamical theory of electricity, in which we should regard electrical action, not, as in this treatise, as a phenomenon due to an unknown cause, subject only to the general laws of dynamics, but as the result of known motions of known portions of matter, in which not only the total effects and final results, but the whole intermediate mechanism and details of the motion, are taken as the object of study.

Maxwell did not always express himself so cautiously: at other times he did not shrink from imagining an elaborate mechanical model. All physicists know its principal features. The magnetic energy is considered as a true vis viva, the magnetic field being the seat of invisible motions, rotations of small particles about the lines of force. The system of these particles may be compared to a wheelwork, and Maxwell has to explain how it can be that all the wheels in an element of volume are rotating in the same direction. This shows that the motion is not transmitted directly from one wheel to the next. So Maxwell is led to assume that between these wheels of the magnetic field and in contact with them, there are smaller ones which transmit the motion in the manner of friction wheels.

What I called wheels might in reality be spheres capable of turning about axes in any direction and, as Maxwell showed, a system of this kind is amenable to mathematical analysis. In his image the friction wheels represent what we call electricity; in a conductor we must conceive them to be freely movable, whereas the centres of the larger wheels or balls have fixed positions. It is easily seen how a motion of translation imparted to the friction wheels can give rise to rotations of the larger balls; this is how a current produces a magnetic field. Other phenomena can be explained on the same lines; it is sufficient for this that Maxwell's equations can be deduced by means of the model.