Intrinsic symmetry of Ampère’s circuital law and other educational issues
This paper explores Ampère’s circuital law (ACL) from an educational perspective. The interchangeability of the ampèrian loop with the current loop, an intrinsic symmetry of ACL that is seldom addressed in the literature or textbooks, is illustrated here. It is verified that the symmetry axis of a circular current is an ampèrian loop. The attempt to apply ACL to a finite wire, a common source of student misunderstanding, is used to highlight the limitations of ACL. The generalisation of ACL is illustrated using an instructive example where the displacement current is unconfined and not spatially uniform. This work is primarily intended for teachers and more advanced undergraduate students, who may benefit from the ideas that are presented here.