The illuminating role of differential forms in electromagnetism (EM) 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 EM. The article is self-contained in that no previous knowledge of forms is needed to follow it. 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 physics teachers to bring the subject of differential forms to the classroom.
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