Weber's Diamagnetism

After the publication of his memoir on the law of force between electrons, Weber turned to the question of diamagnetism.

He developed Faraday’s idea regarding the explanation of diamagnetic phenomena by the effects of electric currents induced in the diamagnetic bodies.[19]

Weber remarked that if, with Ampère, we assume the existence of molecular circuits in which there is no ohmic resistance, so that currents can flow without dissipation of energy, it is quite natural to suppose that currents would be induced in these molecular circuits if they were situated in a varying magnetic field.

He pointed out that such induced molecular currents would confer upon the substance the properties characteristic of diamagnetism.

The difficulty with this hypothesis is to avoid explaining too much.

If it were accepted, the inference seems to be that all bodies, without exception, should be diamagnetic.

Weber escaped from this conclusion by supposing that in iron and other magnetic substances there exist permanent molecular currents, which do not owe their origin to induction, and which, under the influence of the impressed magnetic force, set themselves in definite orientations.

Since a magnetic field tends to give such a direction to a pre-existing current that its course becomes opposed to that of the current which would be induced by the increase of the magnetic force, it follows that a substance stored with such pre-existing currents would display the phenomena of paramagnetism:

The bodies ordinarily called paramagnetic are, according to this hypothesis, those bodies in which the paramagnetism is strong enough to mask the diamagnetism.

The radical distinction which Weber postulated between the natures of paramagnetism and diamagnetism accords with many facts which have been discovered subsequently.

Thus in 1895, P. Curie showed that the magnetic susceptibility per gramme-molecule is connected with the temperature by laws which are different for paramagnetic and diamagnetic bodies. For the former it varies in inverse proportion to the absolute temperature, whereas for diamagnetic bodies it is independent of the temperature.

The conclusions which followed from the work of Faraday and Weber were adverse to the hypothesis of magnetic fluids; for according to that hypothesis the induced polarity would be in the same direction whether due to a change of orientation of pre-existing molecular magnets, or to a fresh separation of magnetic fluids in the molecules.[20]

Weber[21] wrote in 1852:

The latter hypothesis is, moreover, unable to account for the phenomena shown by bodies which are strongly magnetic, like iron: for it is found that when the magnetizing force is gradually increased to a very large value, the magnetization induced in such bodies does not increase in proportion, but tends to a saturation value.

This effect cannot be explained on the assumptions of Poisson, but is easily deducible from those of Weber; for, according to Weber’s theory, the magnetizing force merely orients existing magnets, and when it has attained such a value that all of them are oriented in the same direction, there is nothing further to be done.

Weber’s theory in its original form is, however, open to some objection. If the elementary magnets are supposed to be free to orient themselves without encountering any resistance, it is evident that a very small magnetizing force would suffice to turn them all parallel to each other, and thus would produce immediately the greatest possible intensity of induced magnetism.

To overcome this difficulty, Weber assumed that every displacement of a molecular circuit is resisted by a couple, which tends to restore the circuit to its original orientation. This assumption fails, however, to account for the fact that iron which has been placed in a strong magnetic field does not return to its original condition when it is removed from the field, but retains a certain amount of residual magnetization.

Another alternative was to assume a frictional resistance to the rotation of the magnetic molecules; but if such a resistance existed, it could be overcome only by a finite magnetizing force; and this inference is inconsistent with the observation that some degree of magnetization is induced by every force, however feeble.

The hypothesis which has ultimately gained acceptance is that the orientation is resisted by couples which arise from the mutual action of the molecular magnets themselves.

In the unmagnetized condition the molecules “arrange themselves so as to satisfy their mutual attraction by the shortest path, and thus form a complete closed circuit of attraction,” as D. E. Hughes wrote[22] in 1883; when an external magnetizing force is applied, these small circuits are broken up; and at any stage of the process a molecular magnet is in equilibrium under the joint influence of the external force and the forces due to the other molecules.

This hypothesis was suggested by Maxwell,[23] and has been since developed by J. A. Ewing:[24] its consequences may be illustrated by the following simple examples[25]:

Consider 2 magnetic molecules, each of magnetic moment m, whose centres are fixed at a distance c apart.

When undisturbed, they dispose themselves in the position of stable equilibrium, in which they point in the same direction along the line c.

Now let an increasing magnetic force H be made to act on them in a direction at right angles to the line c. The magnets tum towards the direction of H; and when H attains the value 3m/c3, they become perpendicular to the line c, after which they remain in this position, when H is increased further.

Thus they display the phenomena of induction initially proportional to the magnetizing force, and of saturation. If the magnetizing force H be supposed to act parallel to the line c, in the direction in which the axes originally pointed, the magnets will remain at rest.

But if H acts in the opposite direction, the equilibrium will be stable only so long as H is less than mics; when H increases beyond this limit, the equilibrium becomes unstable, and the magnets turn over so as to point in the direction of H; when H is gradually decreased to zero, they remain in their new positions, thus illustrating the phenomenon of residual magnetism.

By taking a large number of such pairs of magnetic molecules, originally oriented in all directions, and at such distances that the pairs do not sensibly influence each other, we may construct a model whose behaviour under the influence of an external magnetic field will closely resemble the actual behaviour of ferromagnetic bodies.

In order that the magnets in the model may come to rest in their new positions after reversal, it will be necessary to suppose that they experience some kind of dissipative force which damps the oscillations; to this would correspond in actual magnetic substances the electric currents which would be set up in the neighbouring mass when the molecular magnets are suddenly reversed; in either case, the sudden reversals are attended by a transformation of magnetic energy into heat.