# Maxwell's (D, H ) excitation fields: lessons from permanent magnets

## TL;DR

This paper critically examines the physical significance of excitation fields (D,H) in Maxwell's electrodynamics, especially in the context of permanent magnets, arguing they are mathematical constructs rather than physically real entities.

## Contribution

It challenges the conventional view of excitation fields as physically real, providing insights into their role in different constitutive models of permanent magnets.

## Key findings

- Excitation fields (D,H) may not have a physical existence.
- Different constitutive models can produce the same magnetic properties but differ in H behavior.
- The paper offers a new perspective on the interpretation of Maxwell's excitation fields.

## Abstract

Macroscopic Maxwellian electrodynamics consists of four field quantities along with electric charges and electric currents. The fields occur in pairs, the primary ones being the electric and magnetic fields (E,B), and the other the excitation fields (D,H). The link between the two pairs of field is provided by constitutive relations, which specify (D,H) in terms of (E,B); this last connection enabling Maxwell's (differential) equations to be combined in a way that supports waves. In this paper we examine the role played by the excitation fields (D,H), showing that they can be regarded as not having a physical existence, and are merely playing a mathematically convenient role. This point of view is made particularly relevant when we consider competing constitutive models of permanent magnets, which although having the same measurable magnetic properties, have startlingly different behaviours for the magnetic excitation field H.