Why is Ampère’s law so hard? A look at middle-division physics

Because mathematicians and physicists think differently about mathematics, they have different goals for their courses and teach different ways of thinking about the material. As a consequence, there are a number of capabilities that physics majors need in order to be successful that might not be addressed by any traditional course. The result is that the total cognitive load is too high for many students at the transition from the calculus and introductory physics sequences to upper-division courses for physics majors. We illustrate typical student difficulties in the context of an Ampère’s law problem.