Numerical method for evaluating three-dimensional magnetic fields in the region of a current-carrying conductor

Abstract

A numerical method is developed for calculating the magnetic field within a rectangular conductor of finite cross section. The analysis begins with the equation of the law of Biot and Savart, which is a triple‐integral expression. Two of the integrations in this expression can be evaluated analytically, which will yield a single integration that must be evaluated numerically. The present method provides a numerically stable argument for the remaining integration that can be evaluated for arbitrary coil shapes and is computationally efficient. An accuracy of at least three significant figures is obtained by comparing the present method with the limited number of analytic solutions for three‐dimensional fields, resulting from a current‐carrying conductor at points external to and within the conductor.