Upper-division students’ difficulties with Ampère’s law

Abstract

This study presents and interprets some conceptual difficulties junior-level physics students experience with Ampère’s law. We present both quantitative data, based on students’ written responses to conceptual questions, and qualitative data, based on interviews of students solving Ampère’s law problems. We find that some students struggle to connect the current enclosed by an Ampèrian loop to the properties of the magnetic field while some students do not use information about the magnetic field to help them solve Ampère’s law problems. In this paper, we show how these observations may be interpreted as evidence that some students do not see the integral in Ampère’s law as representing a sum and that some students do not use accessible information about the magnetic field as they attempt to solve Ampère’s law problems. This work extends previous studies into students’ difficulties with Ampère’s law and provides possible guidance for instruction

Students’ difficulties with integration in electricity

“…Most recently, Wallace and Chasteen [10] found that part of students' difficulties with Ampère's law was due to students not viewing the integral in Ampère's law as representing a sum, which aligned with the work of Manogue et al [11] on the same topic.…”

Students’ understanding of continuous charge distributions

“…This issue persists as students progress with their studies. A recent study has shown that students taking upper division courses in electrodynamics have difficulty visualizing the integrals as a sum [9], hence they are challenged in solving problems with continuous charge distributions [10]. Our Physics Education Research (PER) literature review resulted in very few focused studies describing how introductory physics students fare with the concepts of continuous charge, and thus more research needs to be done on this topic.…”

Students’ use of symbolic forms when constructing differential length elements

“…While previous work has addressed student use and understanding of integration [2][3][4], applications of Gauss's and Ampère's Laws [1,[6][7][8], and vector differential equations in mathematics and physics settings [9][10], little work has been done to address student understanding of differential elements and how they are constructed or determined in the non-Cartesian coordinate systems typically employed in E&M. Pepper and colleagues identified an instance in a homework help session where students neglected to include the necessary scaling factors when writing spherical differential areas, using rather than [1]. Another group of students attempted a line integral in three dimensions using as a length element [1].…”