Superphysics
Chapter 8g

# Leroux's Phenomenon

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This opinion that conductors are the media of propagation of electric disturbance was entertained also by Ludwig Lorenz (b. 1829, d. 1891), of Copenhagen, who independently developed an electromagnetic theory of light[60] a few years after the publication of Maxwell’s memoirs.

The procedure which Lorenz followed was that which Riemann had suggested[61] in 1858—namely, to modify the accepted formulae of electrodynamics by introducing terms which, though too small to be appreciable in ordinary laboratory experiments, would be capable of accounting for the propagation of electrical effects through space with a finite velocity. We have seen that in Neumann’s theory the electric force E was determined by the equation

(1)

where φ denotes the electrostatic potential defined by the equation

ρ′ being the density of electric charge at the point (x′, y′, z′), and where a denotes the vector-potential, defined by the equation

ι′ being the conduction-current at (x′, y′, z′). We suppose the specific inductive capacity and the magnetic permeability to be everywhere unity.

Lorenz proposed to replace these by the equations

the change consists in replacing the values which ρ′ and ι′ have at the instant t by those which they have at the instant (t - r/c), which is the instant at which a disturbance travelling with velocity c must leave the place (x′, y′, z′) in order to arrive at the place (x, y, z) at the instant t. Thus the values of the potentials at (x, y, z) at any instant t would, according to Lorenz’s theory, depend on the electric state at the point (x′, y′, z′) at the previous instant (t - r/c): as if the potentials were propagated outwards from the charges and currents with velocity c. The functions φ and a formed in this way are generally known as the retarded potentials.

The equations by which φ and a have been defined are equivalent to the equations

(2)

(3)

while the equation of conservation of electricity,

gives

(4)

From equations (1), (2), (4), we may readily derive the equation

(I)

and from (1), (3), (4), we have

(II)

where H or curl a denotes the magnetic force: while from (1) we have

(III)

The equations (I), (II), (III) are, however, the fundamental equations of Maxwell’s theory; and therefore the theory of L. Lorenz is practically equivalent to that of Maxwell, so far as concerns the propagation of electromagnetic disturbances through free aether.

Lorenz himself, however, does not appear to have clearly perceived this; for in his memoir he postulated the presence of conducting matter throughout space, and was consequently led to equations resembling those which Maxwell had given for the propagation of light in metals.

Observing that his equations represented periodic electric currents at right angles to the direction of propagation of the disturbance, he suggested that all luminous vibrations might be constituted by electric currents, and hence that there was “no longer any reason for maintaining the hypothesis of an aether, since we can admit that space contains sufficient ponderable matter to enable the disturbance to be propagated.”

Lorenz was unable to derive from his equations any explanation of the existence of refractive indiecs, and his theory lacks the rich physical suggestiveness of Maxwell’s.

The value of his memoir lies chiefly in the introduction of the retarded potentials. It may be remarked in passing that Lorenz’s retarded potentials are not identical with Maxwell’s scalar and vector potentials; for Lorenz’s a is not a circuital vector, and Lorenz’s φ is not, like Maxwell’s, the electrostatic potential, but depends on the positions occupied by the charges at certain previous instants.

For some years no progress was made either with Maxwell’s theory or with Lorenz’s. Meanwhile, Maxwell had in 1865 resigned his chair at King’s College, and had retired to his estate in Dumfricsshire, where he occupied himself in writing a connected account of electrical theory.

In 1871, he returned to Cambridge as Professor of Experimental Physics; and two years later published his Treatise on Electricity and Magnetism.

In this celebrated work is comprehended almost every branch of electric and magnetic theory; but the intention of the writer was to discuss the whole as far as possible from a single point of view, namely, that of Faraday; so that little or no account was given of the hypotheses which had been propounded in the two preceding decades by the great German electricians.

So far as Maxwell’s purpose was to disseminate the ideas of Faraday, it was undoubtedly fulfilled; but the Treatise was less successful when considered as the exposition of its author’s own views.