Alternating Current Distribution Between Planar Conductors

The general theory for the vector potential produced by a sinusoidal current of finite cross section has been developed in a preceding paper.1 In the present work, this theory is applied to a coil between a number of plates of finite electrical conductivities and permeabilities. Linear, isotropic, and homogeneous media are assumed throughout. The Green's function solution is first obtained, and the principle of superposition is then 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 electromagnetic induction problems, while each of the expressions obtained for the physically observable phenomena is in terms of an infinite integral that may readily be evaluated on a computer. In all cases for which experimental measurements have been made, the agreement between calculated and observed values is within the limits of experimental error. Preliminary investigations of other cases tend to support the validity of the corresponding theoretical expressions.