Closed-form expressions for the magnetic field of permanent magnets in three dimensions

TL;DR

This paper derives a closed-form expression for the magnetic field of finite-sized permanent magnets using surface current densities, enabling precise calculations of multipoles and fringe effects.

Contribution

It introduces a novel closed-form formula for the magnetic field of finite-size permanent magnets modeled as surface current densities.

Findings

Derived a closed-form magnetic field expression for finite magnets.

Applied the method to analyze multipoles and fringe fields.

Demonstrated the approach on a finite-length dipole of magnetic cubes.

Abstract

We derive a closed-form expression of the magnetic field of a finite-size current sheet and use it to calculate the field of permanent magnets, which are modeled through their surface current densities. We illustrate the method by determining the multipoles and the effective length due to fringe fields of a finite-length dipole constructed of magnetic cubes.