JAMES CLERK MAXWELL
A Treatise on Electricity and Magnetism
James Clerk Maxwell, the first professor of experimental physics at Cambridge, was born at Edinburgh on November 13, 1831, and before he was fifteen was already famous as a writer of scientific papers. In 1854 he graduated at Cambridge as second wrangler. Two years later he became professor of natural philosophy at Marischal College, Aberdeen. Vacating his chair in 1860 for one at King's College, London, Maxwell contributed largely to scientific literature. His great lifework, however, is his famous "Treatise on Electricity and Magnetism," which was published in 1873, and is, in the words of a critic, "one of the most splendid monuments ever raised by the genius of a single individual." It was in this work that he constructed his famous theory if electricity in which "action at a distance" should be replaced by "action through a medium," and first enunciated the principles of an electro-magnetic theory of light which has formed the basis of nearly all modern physical science. He died on November 5, 1879.
I.—The Nature of Electricity
Let a piece of glass and a piece of resin be rubbed together. They will be found to attract each other. If a second piece of glass be rubbed with a second piece of resin, it will be found that the two pieces of glass repel each other and that the two pieces of resin are also repelled from one another, while each piece of glass attracts each piece of resin. These phenomena of attraction and repulsion are called electrical phenomena, and the bodies which exhibit them are said to be "electrified," or to be "charged with electricity."
Bodies may be electrified in many other ways, as well as by friction. When bodies not previously electrified are observed to be acted on by an electrified body, it is because they have become "electrified by induction." If a metal vessel be electrified by induction, and a second metallic body be suspended by silk threads near it, and a metal wire be brought to touch simultaneously the electrified body and the second body, this latter body will be found to be electrified. Electricity has been transferred from one body to the other by means of the wire.
There are many other manifestations of electricity, all of which have been more or less studied, and they lead to the formation of theories of its nature, theories which fit in, to a greater or less extent, with the observed facts. The electrification of a body is a physical quantity capable of measurement, and two or more electrifications can be combined experimentally with a result of the same kind as when two quantities are added algebraically. We, therefore, are entitled to use language fitted to deal with electrification as a quantity as well as a quality, and to speak of any electrified body as "charged with a certain quantity of positive or negative electricity."
While admitting electricity to the rank of a physical quantity, we must not too hastily assume that it is, or is not, a substance, or that it is, or is not, a form of energy, or that it belongs to any known category of physical quantities. All that we have proved is that it cannot be created or annihilated, so that if the total quantity of electricity within a closed surface is increased or diminished, the increase or diminution must have passed in or out through the closed surface.
This is true of matter, but it is not true of heat, for heat may be increased or diminished within a closed surface, without passing in or out through the surface, by the transformation of some form of energy into heat, or of heat into some other form of energy. It is not true even of energy in general if we admit the immediate action of bodies at a distance.
There is, however, another reason which warrants us in asserting that electricity, as a physical quantity, synonymous with the total electrification of a body, is not, like heat, a form of energy. An electrified system has a certain amount of energy, and this energy can be calculated. The physical qualities, "electricity" and "potential," when multiplied together, produce the quantity, "energy." It is impossible, therefore, that electricity and energy should be quantities of the same category, for electricity is only one of the factors of energy, the other factor being "potential."
Electricity is treated as a substance in most theories of the subject, but as there are two kinds of electrification, which, being combined, annul each other, a distinction has to be drawn between free electricity and combined electricity, for we cannot conceive of two substances annulling each other. In the two-fluid theory, all bodies, in their unelectrified state, are supposed to be charged with equal quantities of positive and negative electricity. These quantities are supposed to be so great than no process of electrification has ever yet deprived a body of all the electricity of either kind. The two electricities are called "fluids" because they are capable of being transferred from one body to another, and are, within conducting bodies, extremely mobile.
In the one-fluid theory everything is the same as in the theory of two fluids, except that, instead of supposing the two substances equal and opposite in all respects, one of them, generally the negative one, has been endowed with the properties and name of ordinary matter, while the other retains the name of the electric fluid. The particles of the fluid are supposed to repel each other according to the law of the inverse square of the distance, and to attract those of matter according to the same law. Those of matter are supposed to repel each other and attract those of electricity. This theory requires us, however, to suppose the mass of the electric fluid so small that no attainable positive or negative electrification has yet perceptibly increased or diminished the mass or the weight of a body, and it has not yet been able to assign sufficient reasons why the positive rather than the negative electrification should be supposed due to an excess quantity of electricity.
For my own part, I look for additional light on the nature of electricity from a study of what takes place in the space intervening between the electrified bodies. Some of the phenomena are explained equally by all the theories, while others merely indicate the peculiar difficulties of each theory. We may conceive the relation into which the electrified bodies are thrown, either as the result of the state of the intervening medium, or as the result of a direct action between the electrified bodies at a distance. If we adopt the latter conception, we may determine the law of the action, but we can go no further in speculating on its cause.
If, on the other hand, we adopt the conception of action through a medium, we are led to inquire into the nature of that action in each part of the medium. If we calculate on this hypothesis the total energy residing in the medium, we shall find it equal to the energy due to the electrification of the conductors on the hypothesis of direct action at a distance. Hence, the two hypotheses are mathematically equivalent.
On the hypothesis that the mechanical action observed between electrified bodies is exerted through and by means of the medium, as the action of one body on another by means of the tension of a rope or the pressure of a rod, we find that the medium must be in a state of mechanical stress. The nature of the stress is, as Faraday pointed out, a tension along the lines of force combined with an equal pressure in all directions at right angles to these lines. This distribution of stress is the only one consistent with the observed mechanical action on the electrified bodies, and also with the observed equilibrium of the fluid dielectric which surrounds them. I have, therefore, assumed the actual existence of this state of stress.
Every case of electrification or discharge may be considered as a motion in a closed circuit, such that at every section of the circuit the same quantity of electricity crosses in the same time; and this is the case, not only in the voltaic current, where it has always been recognised, but in those cases in which electricity has been generally supposed to be accumulated in certain places. We are thus led to a very remarkable consequence of the theory which we are examining, namely, that the motions of electricity are like those of an incompressible fluid, so that the total quantity within an imaginary fixed closed surface remains always the same.
The peculiar features of the theory as developed in this book are as follows.
That the energy of electrification resides in the dielectric medium, whether that medium be solid or gaseous, dense or rare, or even deprived of ordinary gross matter, provided that it be still capable of transmitting electrical action.
That the energy in any part of the medium is stored up in the form of a constraint called polarisation, dependent on the resultant electromotive force (the difference of potentials between two conductors) at the place.
That electromotive force acting on a dielectric produces what we call electric displacement.
That in fluid dielectrics the electric polarisation is accompanied by a tension in the direction of the lines of force combined with an equal pressure in all directions at right angles to the lines of force.
That the surfaces of any elementary portion into which we may conceive the volume of the dielectric divided must be conceived to be electrified, so that the surface density at any point of the surface is equal in magnitude to the displacement through that point of the surface reckoned inwards.
That, whatever electricity may be, the phenomena which we have called electric displacement is a movement of electricity in the same sense as the transference of a definite quantity of electricity through a wire.
II.—Theories of Magnetism
Certain bodies—as, for instance, the iron ore called loadstone, the earth itself, and pieces of steel which have been subjected to certain treatment—are found to possess the following properties, and are called magnets.
If a magnet be suspended so as to turn freely about a vertical axis, it will in general tend to set itself in a certain azimuth, and, if disturbed from this position, it will oscillate about it.
It is found that the force which acts on the body tends to cause a certain line in the body—called the axis of the magnet—to become parallel to a certain line in space, called the "direction of the magnetic force."
The ends of a long thin magnet are commonly called its poles, and like poles repel each other; while unlike poles attract each other. The repulsion between the two magnetic poles is in the straight line joining them, and is numerically equal to the products of the strength of the poles divided by the square of the distance between them; that is, it varies as the inverse square of the distance. Since the form of the law of magnetic action is identical with that of electric action, the same reasons which can be given for attributing electric phenomena to the action of one "fluid," or two "fluids" can also be used in favour of the existence of a magnetic matter, fluid or otherwise, provided new laws are introduced to account for the actual facts.
At all parts of the earth's surface, except some parts of the polar regions, one end of a magnet points in a northerly direction and the other in a southerly one. Now a bar of iron held parallel to the direction of the earth's magnetic force is found to become magnetic. Any piece of soft iron placed in a magnetic field is found to exhibit magnetic properties. These are phenomena of induced magnetism. Poisson supposes the magnetism of iron to consist in a separation of the magnetic fluids within each magnetic molecule. Weber's theory differs from this in assuming that the molecules of the iron are always magnets, even before the application of the magnetising force, but that in ordinary iron the magnetic axes of the molecules are turned indifferently in every direction, so that the iron as a whole exhibits no magnetic properties; and this theory agrees very well with what is observed.
The theories establish the fact that magnetisation is a phenomenon, not of large masses of iron, but of molecules; that is to say, of portions of the substance so small that we cannot by any mechanical method cut them in two, so as to obtain a north pole separate from the south pole. We have arrived at no explanation, however, of the nature of a magnetic molecule, and we have therefore to consider the hypothesis of Ampère—that the magnetism of the molecule is due to an electric current constantly circulating in some closed path within it.
Ampère concluded that if magnetism is to be explained by means of electric currents, these currents must circulate within the molecules of the magnet, and cannot flow from one molecule to another. As we cannot experimentally measure the magnetic action at a point within the molecule, this hypothesis cannot be disproved in the same way that we can disprove the hypothesis of sensible currents within the magnet. In spite of its apparent complexity, Ampère's theory greatly extends our mathematical vision into the interior of the molecules.
III.—The Electro-Magnetic Theory of Light
We explain electro-magnetic phenomena by means of mechanical action transmitted from one body to another by means of a medium occupying the space between them. The undulatory theory of light also assumes the existence of a medium. We have to show that the properties of the electro-magnetic medium are identical with those of the luminiferous medium.
To fill all space with a new medium whenever any new phenomena are to be explained is by no means philosophical, but if the study of two different branches of science has independently suggested the idea of a medium; and if the properties which must be attributed to the medium in order to account for electro-magnetic phenomena are of the same kind as those which we attribute to the luminiferous medium in order to account for the phenomena of light, the evidence for the physical existence of the medium is considerably strengthened.
According to the theory of emission, the transmission of light energy is effected by the actual transference of light-corpuscles from the luminous to the illuminated body. According to the theory of undulation there is a material medium which fills the space between the two bodies, and it is by the action of contiguous parts of this medium that the energy is passed on, from one portion to the next, till it reaches the illuminated body. The luminiferous medium is therefore, during the passage of light through it, a receptacle of energy. This energy is supposed to be partly potential and partly kinetic, and our theory agrees with the undulatory theory in assuming the existence of a medium capable of becoming a receptacle for two forms of energy.
Now, the properties of bodies are capable of quantitative measurement. We therefore obtain the numerical value of some property of the medium—such as the velocity with which a disturbance is propagated in it, which can be calculated from experiments, and also observed directly in the case of light. If it be found that the velocity of propagation of electro-magnetic disturbance is the same as the velocity of light, we have strong reasons for believing that light is an electro-magnetic phenomenon.
It is, in fact, found that the velocity of light and the velocity of propagation of electro-magnetic disturbance are quantities of the same order of magnitude. Neither of them can be said to have been determined accurately enough to say that one is greater than the other. In the meantime, our theory asserts that the quantities are equal, and assigns a physical reason for this equality, and it is not contradicted by the comparison of the results, such as they are.
Lorenz has deduced from Kirchoff's equations of electric currents a new set of equations, indicating that the distribution of force in the electro-magnetic field may be considered as arising from the mutual action of contiguous elements, and that waves, consisting of transverse electric currents, may be propagated, with a velocity comparable with that of light, in non-conducting media. These conclusions are similar to my own, though obtained by an entirely different method.
The most important step in establishing a relation between electric and magnetic phenomena and those of light must be the discovery of some instance in which one set of phenomena is affected by the other. Faraday succeeded in establishing such a relation, and the experiments by which he did so are described in the nineteen series of his "Experimental Researches." Suffice it to state here that he showed that in the case of aray of plane-polarised light the effect of the magnetic force is to turn the plane of polarisation round the direction of the ray as an axis, through a certain angle.
The action of magnetism on polarised light leads to the conclusion that in a medium under the action of a magnetic force, something belonging to the same mathematical class as an angular velocity, whose axis is in the direction of the magnetic force, forms part of the phenomenon. This angular velocity cannot be any portion of the medium of sensible dimensions rotating as a whole. We must, therefore, conceive the rotation to be that of very small portions of the medium, each rotating on its own axis.
This is the hypothesis of molecular vortices. The displacements of the medium during the propagation of light will produce a disturbance of the vortices, and the vortices, when so disturbed, may react on the medium so as to affect the propagation of the ray. The theory proposed is of a provisional kind, resting as it does on unproved hypotheses relating to the nature of molecular vortices, and the mode in which they are affected by the displacement of the medium.
IV.—Action at a Distance
There appears to be some prejudice, or a priori objection, against the hypothesis of a medium in which the phenomena of radiation of light and heat, and the electric actions at a distance, take place. It is true that at one time those who speculated as to the cause of physical phenomena were in the habit of accounting for each kind of action at a distance by means of a special æthereal fluid, whose function and property it was to produce these actions. They filled all space three and four times over with æthers of different kinds, the properties of which consisted merely to "save appearances," so that more rational inquirers were willing to accept not only Newton's definite law of attraction at a distance, but even the dogma of Cotes that action at a distance is one of the primary properties of matter, and that no explanation can be more intelligible than this fact. Hence the undulatory theory of light has met with much opposition, directed not against its failure to explain the phenomena, but against its assumption of the existence of a medium in which light is propagated.
The mathematical expression for electro-dynamic action led, in the mind of Gauss, to the conviction that a theory of the propagation of electric action would in time be found to be the very keystone of electro-dynamics. Now, we are unable to conceive of propagation in time, except either as the flight of a material substance through space or as the propagation of a condition of motion or stress in a medium already existing in space.
In the theory of Neumann, the mathematical conception called potential, which we are unable to conceive as a material substance, is supposed to be projected from one particle to another, in a manner which is quite independent of a medium, and which, as Neumann has himself pointed out, is extremely different from that of the propagation of light. In other theories it would appear that the action is supposed to be propagated in a manner somewhat more similar to that of light.
But in all these theories the question naturally occurs: "If something is transmitted from one particle to another at a distance, what is its condition after it had left the one particle, and before it reached the other?" If this something is the potential energy of the two particles, as in Neumann's theory, how are we to conceive this energy as existing in a point of space coinciding neither with the one particle nor with the other? In fact, whenever energy is transmitted from one body to another in time, there must be a medium or substance in which the energy exists after it leaves one body, and before it reaches the other, for energy, as Torricelli remarked, "is a quintessence of so subtile a nature that it cannot be contained in any vessel except the inmost substance of material things."
Hence all these theories lead to the conception of a medium in which the propagation takes place, and if we admit this medium as an hypothesis, I think we ought to endeavour to construct a mental representation of all the details of its action, and this has been my constant aim in this treatise.