Analytical Evaluation of 2-D Flux Integral for Magnetostatic Galerkin Method of Moments

This paper presents a closed-form analytical solution of the integral of the tangent component of magnetic field along a line in 2-D space. The magnetic field considered herein originates from a sheet current. Handling of adjacent and coincident singularities encountered in practice is detailed. The intended application of the result is to simplify the evaluation of integrals within Galerkin method of moments and boundary element method-based solutions of 2-D magnetostatic problems. This work is extended to general potential problems by relating the magnetostatic case to a traditional Green's function formulation. A comparison with numerical methods is provided.