Analytical and numerical solution of the eddy-current problem in spherical coordinates based on the second-order vector potential formulation

The three-dimensional (3-D) eddy-current problem, described in spherical coordinates, is studied both analytically and numerically. Since the vector field equation is not separable in the spherical coordinate system, the second-order vector potential (SOVP) formulation is used to treat the problem by reducing it to the solution of the scalar field equation. While the analytical solution is expressed in terms of known orthogonal expansions, the numerical solution utilizes the finite difference method. Examples of engineering applications are provided, concerning computation of eddy-current distribution in a conducting sphere by a filamentary excitation of arbitrary shape.