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.

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提高学生对电动力学的理解：微分形式的案例

课堂上很少讨论微分形式在电磁学中的启发作用。本文的目的是提出一些相关的见解，这些见解可以从 E\&M 的差异形式方法中学到。这篇文章是自包含的，因为不需要任何形式的先前知识来完成它。由均匀引力场引起的经典真空和卡西米尔效应中的量子真空的有效极化被用来说明微分形式在处理非平凡情况下的电磁时的能力和解释的容易性。我们希望这篇文章能够激励物理老师将微分形式的主题带入课堂。