We discuss common difficulties in upper-division electricity and magnetism (E&M) in the areas of Gauss's law, vector calculus, and electric potential using both quantitative and qualitative evidence. We also show that many of these topical difficulties may be tied to student difficulties with mathematics. At the junior level, some students…

Over the course of four years, we have researched and transformed a key course in the career of an undergraduate physics major--junior-level electricity and magnetism. With the aim of educating our majors based on a more complete understanding of the cognitive and conceptual challenges of upper-division courses, we used principles of active…

As part of an effort to systematically improve our junior-level E&M I course, we have developed a tool to assess student conceptual learning of electrostatics at the upper division. Together with a group of physics faculty, we established a list of learning goals for the course that, with results from student observations and interviews, served as…

This study presents and interprets some conceptual difficulties junior-level physics students experience with Ampere's law. We present both quantitative data, based on students' written responses to conceptual questions, and qualitative data, based on interviews of students solving Ampere's law problems. We find that some students struggle to…