Electricity and magnetism are fundamentally interconnected, as represented by the symmetry in Maxwell's equations. Much of the research on Gauss's and Ampere's laws has focused on their application in calculating electric or magnetic fields. However, there remains a significant gap in the literature in exploring these laws in a broader context--particularly in understanding electric flux and magnetic circulation as distinct yet related concepts through the lens of the superposition principle. This study will fill this gap by examining students' comprehension of electric flux and magnetic circulation. It focuses on their role in Gauss's and Ampere's laws beyond their typical use for computing other physical quantities. The study involved 322 engineering students completing a course on electricity and magnetism. The students were given two open-ended questionnaires of parallel problems: half answered questions addressing the electricity context, and the other half responded to questions addressing magnetism. Our phenomenographic analysis revealed significant conceptual confusion between electric field and electric flux, as well as between magnetic field and magnetic circulation, which affected their ability to apply the superposition principle. Additionally, some students incorrectly assigned physical reality to Gaussian surfaces and Amperian loops, further hindering their understanding of the superposition principle due to a blocking effect. We identify several factors that may contribute to these difficulties and suggest implications for teaching to address the conceptual difficulties identified in this study.