Reanalyzing the Ampère-Maxwell Law

Abstract

In a recent TPT article,1 I addressed a common miscommunication about Faraday's law, namely, that introductory texts often say the law expresses a causal relationship between the magnetic fields time variation and the electric fields circulation. In that article, I demonstrated that these field behaviors share a common cause in a time-varying current density. From that, many readers may have rightly guessed at a symmetric conclusion: while the Ampère-Maxwell law is commonly said to express a causal relation between the electric fields time variation and the magnetic fields circulation, these field behaviors share a distinct, common cause. Together, Faraday's law and the Ampère-Maxwell law constitute half of Maxwell's laws that form a foundation for almost all of electricity and magnetism. By misrepresenting these two laws, introductory texts not only present students with unnecessary conceptual hurdles early in their physics educations but also leave them with enduring misunderstandings about the very foundation of electricity and magnetism. Fortunately, compared to what is commonly taught, the actual cause of these field variations is conceptually simpler and more consistent with what the students will have already learned in the introductory texts' own earlier chapters.