Current loop and point dipole configurations for magnetic multipoles

Abstract

Multipoles are a widely used tool in magnetostatics, but very little is known about the possible current distributions that may generate them. Here we propose constructions for the currents corresponding to the multipole fields. We begin with a small current loop which creates a dipolar field, and then investigate how to construct current configurations for multipoles of all degrees and orders, by using differentiation and considering ideas of symmetry and nesting loops. We also investigate using point dipoles instead of loops. Many equivalent configurations are found, most of which are not presented elsewhere in the literature.