Electromagnetic induction in accelerated conductors

Abstract

Boundary conditions are derived for the interfaces of a conductor moving across an external magnetic field in an ambient medium (vacuum or nonconductor), which consider the emission of electromagnetic waves from the conductor surface as a result of electromagnetic induction. These boundary conditions are applied to the initial-boundary-value problem for the electromagnetic induction in a conducting slab, which is accelerated across a homogeneous magnetic field to a nonrelativistic velocity. Fourier-series solutions are presented for the transient electromagnetic fields in the moving conductor and the discontinuous electromagnetic waves in the ambient space. It is shown that the transient electromagnetic fields inside and outside the conductor are due to two mechanisms, i.e., "velocity induction" (ordinary induction) and "acceleration induction" [$\frac{d\stackrel{\ensuremath{\rightarrow}}{\mathrm{v}}(t)}{\mathrm{dt}}\ensuremath{\ne}\stackrel{\ensuremath{\rightarrow}}{0}$]. The latter result cannot be explained by means of the Lorentz transformation, which is valid only for constant conductor velocities (inertial frames).