# Homopolar Induction

## Homopolar Induction

(in Russian, unipoliarnaia induk-tsiia), the generation of an electromotive force (emf) in a magnetized body moving in a direction that is not parallel to the axis of magnetization. The direction of the emf is perpendicular to the plane in which the magnetic induction vector B and the magnet’s velocity vector v lie.

If the magnetized body is a conductor, homopolar induction may be explained in the framework of classical electrodynamics. Under the action of the Lorentz force, free electrons drift within the body in a direction perpendicular to the directions of v and B until an electric field that impedes the drift is generated in the body.

The theory of relativity provides a consistent explanation of homopolar induction. In the reference frame associated with the magnet, or the proper frame of reference, there is no electric field E. Suppose the magnet moves with a velocity v in the laboratory reference frame and the motion is uniform, translational, and rectilinear. Then, according to the relativistic field-strength equations, the electric field E in the laboratory frame is E = – [vB]/c, where c is the speed of light; the value of E is accurate to within the factor , which is practically equal to 1 for small values of v. The equation for the electric field is applicable both within and outside the magnetized body, regardless of whether the body is a conductor. Thus, homopolar induction is a relativistic effect in which the relative nature of the partition of an electromagnetic field into an electric field and a magnetic field is explicitly revealed.

The presence of an electric field gives rise to a constant potential difference. This phenomenon is used to generate a direct current in homopolar generators.

The term “unipolar induction,” of which the Russian term is a cognate, is deprecated in English. The term came into use because, in a homopolar generator, all the magnetic poles presented to the circuit in which the emf is induced are of the same polarity.

### REFERENCE

Tamm, I. E. Osnovy teorii elektrichestva, 8th ed. Moscow, 1966.
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