The explicative power of the vector potential for superconductivity: a path for high school

In the classroom practice the notion of the magnetic vector potential is never introduced, both because it is not contained in secondary school textbooks and because teachers usually associate this concept with complex topics they dealt with in their university courses. In our experience instead, we have found that the introduction of the vector potential can be of great help in students’ understanding of electromagnetism and modern physics topics. In this paper we will show how the use of the vector potential allows a phenomenological and consistent explanation of superconductivity at a level suitable for high school students. We will deal with the two main aspects of superconductivity: the resistivity of the superconductor that drops to zero at the critical temperature and the expulsion of the magnetic field from the bulk of a superconductor (Meissner effect). By the use of the vector potential, students can build a phenomenological interpretation of superconductivity, always remaining in the frame of electromagnetism and thus avoiding the use of too complicated mathematical tools that the explanation of the microscopic mechanism would require.