Force and eddy currents in a solid conducting cylinder due to aneccentric circular current loop

Abstract

A solution of the eddy currents problem in a solid conducting cylinderplaced in the field of an eccentric circular current loop is presented. Theconventional potential theory can only deal with the simple case of rotationalsymmetry and axially directed exciting wires. If, however, the exciting currentloop is placed such that the conventional vector potential has all threecomponents, the vector field equation in cylindrical coordinates cannot beseparated, hence no solution can be obtained. An advanced vector potential istherefore introduced to solve the present three-dimensional boundary valueproblem for the steady-state skin effect, which consists of two vectorpotentials that give transverse electric and transverse magnetic fieldcomponents. Formulae for the eddy current distribution in the cylinder due to aneccentric circular current loop are developed and the results are then given inthe form of a Fourier integral series. The analysis is then extended to cover anarbitrary current loop in a general position. In addition, the force acting onthe conducting cylinder is evaluated and the results are given in the form of aFourier integral series, which is then presented in a graphical form.