Comparing students' understanding of Gauss's and Ampere's laws with field sources in square-like symmetries

The research in electricity and magnetism has commonly focused on problem-solving abilities and the application of physical principles. Several studies have found that some concepts represent a challenge for undergraduate students, such as Gauss's and Ampere's laws. The inability to identify and analyze the symmetry of field and field source distributions and focus on the surface features of these electricity and magnetism systems are two of the main difficulties associated with these laws. We present this study with a different perspective of observing 322 introductory electricity and magnetism students' understanding of these laws with unconventional shapes for the field sources' enclosing objects. We use a phenomenographic approach to detect difficulties and compare the two contexts. Our main findings suggest that some students make an incomplete or incorrect analysis of the situation when referring to its surface features. The confusions between flux and field in the electric context or between circulation and field in the magnetic context persist. Finally, we present recommendations for teachers to approach these difficulties.