Clerk Maxwell's electromagnetic theory

by H. A. Lorentz

Time does not permit me to dwell at length on the verifications of Maxwell's theory, but I should like to make an exception for two of them.

Allow me, in the first place, to say some words on the optical properties of metals.

"If the medium," so we read in Maxwell, "instead of being a perfect insulator, is a conductor, the disturbance" (viz. that which is produced by an incident beam of light) "will consist not only of electric displacements but of currents of conduction, in which electric energy is transformed into heat, so that the undulation is absorbed by the medium." After having stated in these words one of the most important consequences drawn from his theory, Maxwell goes on to calculate the coefficient of absorption as a function of the conductivity, and he proceeds: "Gold, silver and platinum are good conductors, and yet, when formed into very thin plates, they allow light to pass through them. From experiments which I have made on a piece of gold leaf, it appears that its transparency is very much greater than is consistent with our theory, unless we suppose that there is less loss of energy when the electromotive forces are reversed for every semi-vibration of light than when they act for sensible times, as in our ordinary experiments." Later researches have amply confirmed what Maxwell says here; obviously, bodies, both conductors and dielectrics, behave in general differently towards rapidly alternating electric forces and towards stationary ones. Yet, Hagen and Rubens have been able to show that when, instead of working with visible light, one uses infra-red rays of sufficiently great wave-length, the properties of metals will, in the limit, exactly conform to the theory, if we reckon with the ordinary conductivity.

Hagen and Rubens did not measure the amount of radiation that is transmitted through a thin plate but the coefficient of reflexion of a thick mirror. For the case of normal incidence, this coefficient and therefore also the loss of energy, i.e. the quantity that is absorbed by the mirror, can easily be calculated as a function of the conductivity. For the residual rays of sylvin, whose wavelength is 12 μ, and for silver, copper, gold and platinum, the absorbed energy was found to be respectively 1·15, 1·6, 2·1 and 3·5 per cent, of the incident energy, whereas it ought to have been 1·3, 1·4, 1·6, and 3·5 per cent, according to the theoretical formula.

The agreement became still better when the residual rays of fluorite with a wave-length of 25·5 μ were used. Since, however, for waves of this length the reflexion becomes nearly complete, it was not possible to determine the loss of energy with sufficient precision. Hagen and Rubens overcame this difficulty by measuring the emissivity of the different metals, or rather the ratio between this emissivity and that of a perfectly black body at the same temperature, a ratio which, by Kirchhoff's law, is equal to that between the absorbed and the incident energy for a beam falling on the metal from the outside, so that it can be calculated by the same formula as this latter ratio. For the four metals just mentioned (at a temperature of 170° C.) the ratio in question was found to be (after multiplication by 100) 1·13, 1·17, 1·56 and 2·82. The theoretical values were 1·15, 1·29, 1·39 and 2·96.

These numbers show conclusively that, however complicated things may be for shorter waves, we can calculate the optical properties of metals in the extreme infra-red by means of Maxwell's equations, simply substituting for the conductivity the value that has been deduced from experiments with constant or slowly alternating currents. This is certainly a most splendid confirmation, the counterpart to the verification, which for gaseous bodies at least has been very satisfactory, of Maxwell's relation of the dielectric constant to the index of refraction.

The phenomenon of the pressure of radiation may serve as a second example of verification. That a beam of light falling, say in the normal direction, on a mirror exerts on it a pressure proportional to the intensity of the beam was deduced by Maxwell from his formulae, and he calculated the force that may be expected in the case of sunlight. It lasted a quarter of a century before Lebedew succeeded in observing this small force, which, for sunlight, amounts to no more than about a ten millionth part of a gramme weight per cm.^2, and which it is therefore difficult to disentangle from other forces that are caused by the surrounding gas, even when this is highly rarefied. Some years later E. F. Nichols and Hull repeated the experiment with the utmost care and were able to measure the pressure and to prove that its intensity agrees with Maxwell's calculation.

We are now quite sure of this phenomenon which has come to play a great part in stellar physics. When we are concerned with very small particles near or in a star, the radiation pressure may very well become greater than the force of gravitation, and it is taken into account by many astronomers in their speculations about the state of heavenly bodies.

The forces exerted by rays of light or heat are a special case of what we call ponderomotive forces, i.e. of the forces with which the electromagnetic field acts on material bodies. Maxwell showed how, in general, these forces can be deduced from the values of the electromagnetic energy corresponding to different positions of a system of bodies, or from a consideration of certain stresses which exist in the electromagnetic field and of which he taught us to determine the direction and the intensity. Every student, even of rather elementary physics, now knows that the mutual attraction of two conducting plates between which there is a difference of potential, e.g. of the plates of an absolute electrometer, may be considered as due to stresses along the lines of force, that the same may be said of the attraction between a magnetic pole and a piece of iron, and that in the case of an electromagnetic motor we are concerned with the tangential stresses acting at the surface of the revolving system. Here again there has been a great deal of later development, but we continue to speak of "Maxwell's stresses."

The notion of the electromagnetic momentum, which Maxwell seems not to have had, though he was quite near it, has also proved very fruitful. A beam of light has a definite momentum, much like a moving ball, and when the beam is normally reflected by a mirror, so that the momentum is inverted, we can deduce the force acting on the mirror from the change of the momentum, exactly as we can do in the case of the ball or of a stream of material particles.