An educational path for the magnetic vector potential and its physical implications

We present an educational path for the magnetic vector potential A aimed at undergraduate students and pre-service physics teachers. Starting from the generalized Ampère–Laplace law, in the framework of a slowly varying timedependent field approximation, themagnetic vector potential is written in terms of its empirical references, i.e. the conduction currents. Therefore, once the currents are known, our approach allows for a clear and univocal physical determination of A, overcoming the mathematical indeterminacy due to the gauge transformations.We have no need to fix a gauge, since for slowly varying time-dependent electric and magnetic fields, the ‘natural’ gauge for A is the Coulomb one. We stress the difference between our approach and those usually presented in the literature. Finally, a physical interpretation of the magnetic vector potential is discussed and some examples of the calculation of A are analysed.