Understanding student challenges with circulation and Ampère–Maxwell law

Abstract We investigated how students apply the concept of circulation when faced with problems related to the Ampère–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 Ampère–Maxwell's law and find the magnetic field.