Electromagnetic momentum and electron inertia in a current circuit

Abstract

In the second volume of his "Treatise on Electricity and Magnetism" Clerk Maxwell developed the theory of electric current-circuits from general dynamical principles, and discussed the experimental effects which should occur if an electric current is a true motion of some substance possessing inertia. Since none of these effects had at that time been observed, Maxwell developed his general electromagnetic theory on the assumption that they do not exist, or at least that they produce no sensible effect. It is now known, however, that an electric current in a conductor consists of moving electrons, and the inertia effects which were discussed by Maxwell have been observed experimentally. They are extremely small, and have not been brought within the scope of electromagnetic theory. A conduction current is usually assumed to be due to the drifting along the conductor, with a very small mean velocity, of all the available conduction electrons, so that the kinetic energy of the electrons due to this motion is negligible in comparison with the magnetic energy of the current. Electron-inertia effects in current circuits have therefore been accepted as something outside classical electromagnetic theory-a position which is illogical if, as is usual, we identify the kinetic and magnetic energies of a free electron. It is shown in the paper that it is possible to identify the kinetic energy of the conduction electrons in a current circuit with the magnetic energy of the current, so that electron-inertia effects can be included in the general electromagnetic scheme. In consequence, a current circuit can be said to possess an electromagnetic mass whose motion, when current flows, entails electromagnetic momentum. This momentum accounts for the known effects of electron inertia and also for the force on the end wire of a long rectangular circuit. The relativistic form of the theory indicates the possibility that electromagnetic laws may depart from the classical form, becoming non-linear in circuits where a high inductance per unit length of conductor is combined with a current greater than is usually found in practice. The inadequacy of classical theory also extends to the known electromagnetic properties of superconductors, and the present hypothesis suggests the possibility of a unified theory in which there would be no necessity to distinguish between a superconductor and a perfect conductor. LIST OF SYMBOLS

Magnetic energy and electron inertia in a superconducting sphere

“…The hypothesis that the magnetic energy of a current circuit is the kinetic energy of the effective conduction electrons, developed in a previous Monograph, 1 is applied to the case of a conducting sphere without resistivity in a uniform magnetic field. A surface current is induced which prevents the growth of a magnetic field within the sphere, and expressions are found for the number and velocity of effective conduction electrons which carry the current.…”

Action-reaction forces between current-carrying conductors

“…The author wishes to acknowledge a paper by Cullwick [30], and unpublished discussions with Thomas Phipps, as two of the most important of the many sources of stimulus. The dynamical model has been explored by Carver Mead [31], and shown to have a secure foundation in quantum mechanics.…”

Comparison of the practical advantages of alternative descriptions of electromagnetic momentum

“…Its application is limited to high-frequency devices such as waveguides, where it causes doubt when applied to different modes [l5], and it fails completely at sufficiently low frequencies, including DC, for reasons which are obscure even to those most familiar with it [16]. Page and Adams [17] have shown, for example, that the unbalance in the action/reaction forces between two current elements at right-angles to each other is due to the field momentum, but it seems that only Cullwick [18] has accounted for the failure of this explanation when applied to closed circuits, and his treatment depends on field concepts which many would reject (Sections 5 and 6).…”

“…This implies that the field around any one conductor is obtained by reversing the sign of the charges on some of the others. The quantity Dx B is not usually recognised in field theory, but, as Cullwick has pointed out [18], this is one reason for the limited scope of the field momentum concept. Substituting from eqns.…”