Cause-effect relationships in Maxwell's equations and their implications in the teaching of electromagnetism in introductory physics courses

TL;DR

This paper clarifies the causal relationships in Maxwell's equations, emphasizing the importance of correct interpretation for teaching electromagnetism in introductory physics courses.

Contribution

It challenges common misconceptions about causality in Maxwell's equations and proposes classroom examples to improve physics teaching.

Findings

Charge and current densities generate electric and magnetic fields.

Misinterpretations can lead to contradictions in understanding electromagnetism.

Proposes teaching strategies to clarify cause-effect relationships.

Abstract

A thoughtless treatment of Maxwell's equations can lead to the interpretation of the existence of a causal relationship between their different terms and, therefore, that an electric field that varies in time generates a magnetic one and vice versa. In this article we address the problems associated with these interpretations and their consequences for the teaching of physics in introductory university physics courses. First, we develop the main arguments that support that charge and current densities, constant or variable in time, are the generators of electric and magnetic fields. Then, we propose a number of classroom examples at the level of introductory courses that allow us to discuss the reasons why considering the electric and magnetic fields as disjoint entities leads to contradictions. Finally, we analyze their implications in introductory physics teaching.