A physical approach to computing magnetic fields1

Abstract

AbstractThe superposition integral expressing the field due to a magnetic source body is relatively simple to evaluate in the case of a homogeneous magnetization. In practice this generally requires that any remnant component is uniform and the susceptibility of the body is sufficiently low to permit the assumption of a uniform induced magnetization. Under these conditions the anomalous magnetic field due to a polyhedral body can be represented in an intuitive and physically appealing manner. It is demonstrated that the components of the magnetic field H can be expressed as a simple combination of the potentials due to two elementary source distributions. These are, firstly, a uniform double layer (normally directed dipole moment density) located on the planar polygonal faces of the body and, secondly, a uniform line source located along its edges. In practice both of these potentials (and thus the required magnetic field components) are easily computed. The technique is applicable to polyhedra with arbitrarily shaped faces and the relevant expressions for the magnetic field components are suitable for numerical evaluation everywhere except along the edges of the body where they display a logarithmic singularity.