Axially Symmetric Eddy Currents in a Spherical Conductor

The general theory for the vector potential produced by a sinusoidal current of finite cross section is developed and applied to a coil encircling two concentric, spherical shells of finite electrical conductivities and permeabilities. Linear, isotropic, and homogeneous media are assumed throughout the analysis. First, the Green's function solution is obtained, and then the principle of superposition is used to effect the desired result. A number of physically observable phenomena—such as the impedance, the power loss due to the presence of the conductors, and the time-averaged electromagnetic force on the conductors—are subsequently calculated from the vector potential. The treatment is sufficiently general to allow the solution of a number of difficult problems of electromagnetic induction, while each of the expressions obtained for the physically observable phenomena is in terms of an infinite sum that may be readily evaluated on a computer.