Understanding student challenges with circulation and Amp\`ere-Maxwell law

TL;DR

This study explores how students understand and apply the circulation concept in the context of the Ampere-Maxwell law, revealing common misconceptions and reasoning patterns through qualitative analysis.

Contribution

It provides insights into student difficulties with circulation and Ampere-Maxwell law, highlighting specific misconceptions and reasoning strategies.

Findings

Students believe symmetry is necessary for applying circulation.

Students overlook the shape of magnetic field lines in calculations.

Some think the electric field must cross the entire loop.

Abstract

We investigated how students apply the concept of circulation when faced with problems related to the Ampere-Maxwell law. For this purpose, we designed a metacognitive pencil-and-paper question, presented it to 65 students, and analysed their responses using phenomenography. We complemented our research by conducting interviews with 12 students. The results show that students tend to think that they can only use the magnetic field circulation to calculate magnetic fields if the curve used is symmetric, and that they do not take into account the shape of the magnetic field lines when applying it. We also find that some students believe that a variable electric field must cross the entire Amperian curve in order to apply Amp\'ere-Maxwell's law and find the magnetic field.