The physical meaning of the magnetic scalar potential, and how to use it to design an electromagnet

TL;DR

This paper explains the physical interpretation of the magnetic scalar potential and presents a practical method for designing electromagnets by specifying fields and constructing coils along equipotential surfaces.

Contribution

It introduces a construction algorithm that uses the magnetic scalar potential to design electromagnets with precise field control, based on boundary conditions and physical principles.

Findings

The method allows accurate electromagnet design within physical limits.

Coil elements are aligned along equipotential surfaces for optimal field shaping.

Examples demonstrate the effectiveness and limitations of the approach.

Abstract

The magnetic scalar potential can be used to design electromagnets accurately and efficiently. I will describe a practical construction algorithm: the prescribed field in a "Target" region (constrained only by Maxwell's equations) specifies boundary conditions which uniquely determine the potential in the surrounding field "Return" region. As required by the physical representation of the magnetic scalar potential, the conducting elements of the resulting coil are directed along equipotentials on the surface of each region, at equal increments of the potential. I give some examples and comments on the limits of precision of the constructed field.