Vector potential at high school: a proposal for its introduction

We describe the motivations and purposes, together with an educational reconstruction, for the effective introduction of magnetic vector potential in high schools. Although addressed to high schools, most of the content of this paper can be usefully used in undergraduate teaching, especially in what concerns the physical meaning and the importance of the concept of vector potential. In fact, magnetic vector potential can highlight unifying ideas, clarify many aspects of electromagnetism and provide a natural link to the history of physics, so often useful in physics education. In our framework, it can also help students with poor mathematical ability to visualize electromagnetic phenomena and improve their understanding of the standard concepts of circulation and flux. Moreover, it is fundamental in treating-even just at a phenomenological level-several important aspects of modern physics and superconductivity, thus avoiding the presentation of modern physics in a discursive way only. We therefore strongly recommend dealing with the vector potential in the modern high school curriculum. Furthermore, we discuss the physical meaning of the vector potential and the gauge invariance and the necessity for an educational reconstruction of topics suitable for high schools. We then present a detailed approach, well embodied in a high school presentation of classical electromagnetism, which, starting from its empirical reference (the currents), introduces the vector potential in analogy with the scalar potential using examples, hints and physical motivations.