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

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