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.

An educational path for the magnetic vector potential and its physical implications / S. Barbieri, M. Cavinato, M. Giliberti. - In: EUROPEAN JOURNAL OF PHYSICS. - ISSN 0143-0807. - 34:5(2013 Jul 18), pp. 1209-1219. [10.1088/0143-0807/34/5/1209]

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

#### Abstract

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.
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vector potential ; electromagnetic field ; education
Settore FIS/08 - Didattica e Storia della Fisica
18-lug-2013
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/230507`