Analysis and comparison of students’ conceptual understanding of symmetry arguments in Gauss’s and Ampere’s laws

Identifying students’ difficulties in understanding Gauss’s and Ampere’s laws is important for developing educational strategies that promote an expertlike understanding of the field concept and Maxwell’s equations of electromagnetic phenomena. This study aims to analyze and compare students’ understanding of symmetry when applying Gauss’s and Ampere’s laws to calculate the electric or magnetic field. We conducted a study to analyze how students reason regarding the symmetry conditions necessary to apply Gauss’s or Ampere’s laws to calculate the electric or magnetic field in three inverse problems. We applied two open-ended questionnaires with parallel surface features, one for Gauss’s law and the other for Ampere’s law, to 322 engineering students. The three inverse problems present different scenarios with the common characteristic that there is no sufficient symmetry to solve the electric or magnetic field from its corresponding equation. We analyzed students’ answers with a phenomenographic approach, focusing on students’ answers to a yes or no question and their reasoning. The main findings of the study are the descriptive categories of understanding and the comparison of the categories between contexts (outcome space). The correct reasoning is identifying the necessary symmetry to apply Gauss’s or Ampere’s law. The other categories refer to the surface features of each scenario to explain students’ answers, applying Gauss’s or Ampere’s law in an oversimplified way and thinking that it would be possible but more complicated in these scenarios. The descriptive categories are related to some of the difficulties previously reported in the literature with standard problems involving Gauss’s and Ampere’s laws. However, inverse problems elicited variations in the types of reasoning related to the surface features of the scenarios and their parallel representations. The comparative analysis between the electricity and magnetism contexts allowed for identifying that analyzing currents can be more challenging for students than analyzing point charges. This study’s findings can guide introductory and intermediate electricity and magnetism instructors to redirect their approach to Gauss’s and Ampere’s laws by introducing the analysis of inverse problems.

Figure 1

Comparison of the most relevant findings in the literature of students’ difficulties when understanding and applying symmetry in Gauss’s and Ampere’s laws. The bubbles on the left side of the figure represent the difficulties of Gauss’s law, and on the right side for Ampere’s law. The bubbles in the middle are difficulties found in both contexts.

Figure 2

Three different inverse problems where the field cannot be solved from Gauss’s or Ampere’s laws. The scenarios use parallel representations for the two contexts.