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This study presents and interprets some conceptual difficulties junior-level physics students experience with Amp\`ere's law. We present both quantitative data, based on students' written responses to conceptual questions, and qualitative data, based on interviews of students solving Amp\`ere's law problems. We find that some students struggle to connect the current enclosed by an Amp\`erian loop to the properties of the magnetic field while some students do not use information about the magnetic field to help them solve Amp\`ere'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 Amp\`ere's law as representing a sum and that some students do not use accessible information about the magnetic field as they attempt to solve Amp\`ere's law problems. This work extends previous studies into students' difficulties with Amp\`ere's law and provides possible guidance for instruction.
Wallace et al. (Mon,) studied this question.
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