Improving student understanding of electrodynamics: the case for differential forms

TL;DR

This paper advocates for teaching differential forms in electromagnetism to enhance student understanding, illustrating their power through examples like gravitational effects on vacuum polarization and the Casimir effect.

Contribution

It introduces a self-contained approach to differential forms in electromagnetism, emphasizing its pedagogical value and practical interpretative advantages.

Findings

Differential forms simplify complex electromagnetic phenomena.

Examples include vacuum polarization in gravitational fields and the Casimir effect.

The approach is accessible without prior knowledge of differential forms.

Abstract

The illuminating role of differential forms in electromagnetism is seldom discussed in the classroom. It is the aim of this article to bring forth some of the relevant insights that can be learnt from a differential forms approach to E\&M. The article is self-contained in that no previous knowledge of forms is needed to follow it through. The effective polarization of the classical vacuum due to a uniform gravitational field and of the quantum vacuum in the Casimir effect are used to illustrate the power and easiness of interpretation of differential forms in dealing with electromagnetism in nontrivial situations. We hope that this article motivates the physics teacher to bring the subject of differential forms to the classroom.