Frequency dependence of induced currents

Abstract

Attempts to solve Maxwell's equations for regions inside electrical conductors generally meet with insuperable mathematical obstacles, unless a uniform magnetic field can be assumed to exist. In many practical instances the field will be non-uniform, since it is generated by currents flowing along wires. The lack of formulae for realistic geometrical arrangements is keenly felt in two cases. They are the prediction of eddy-current power losses and the development of electromagnetic methods for non-destructive testing. A metallic body can be considered to consist of an infinite number of closed filamentary circuits, coinciding with the streamlines of induced currents. It is then shown, for the most general case, how to express the current at any point in the metal by an infinite series of increasing powers of the frequency of a sinusoidal current flowing in an energizing filament. The coefficients of the series are functions of conductor geometry, electrical conductivity and magnetic permeability, but not of the current itself. This opens the way to measurements on scale models, the long numerical calculation of coefficients by digital computers and the tabulation of normalized coefficients for geometrically similar systems. Some possible causes of the `anomalous eddy-current loss' in magnetic laminations are briefly reviewd in order to illustrate the differing opinions that are still being held on this subject. It would, therefore, seem advisable to re-examine the methods of measuring eddy-current losses with reference to the theory of coupled circuits, and thereby determine whether the classical formulae are sufficiently good approximations. Experiments for this purpose are discussed.