Marco Giliberti

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 Ampere–Laplace law, in the framework of a slowly varying time-dependent field approximation, the magnetic 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.

Theatre to motivate the study of physics

A survey we carried out in upper secondary schools showed that the majority of the students consider physics as an important resource, yet as essentially connected to technology in strict terms, and not contributing “culture”, being too difficult a subject. Its appreciation tends to fade as their education progresses through the grades. The search for physics communication methods to increase interest and motivation among students prompted the Department of Physics at the University of Milan to establish the Laboratory of ScienzATeatro (SAT) in 2004. Up to May 2010, SAT staged three shows and one lesson-show having physics as a main theme, for students attending any grades at school. Good indicators of the efficacy of those shows are: the number of repeats (256 of them up to May 2010), the reputation of the theatres in which they were performed, and the results of two surveys on the achievement of the goals, which saw the participation of over 50 classes each.

Detecting anharmonicity at a glance

Harmonic motion is generally presented in such a way that most of the students believe that the small oscillations of a body are all harmonic. Since the situation is not actually so simple, and since the comprehension of harmonic motion is essential in many physical contexts, we present here some suggestions, addressed to undergraduate students and pre-service teachers, that allow one to find out at a glance the anharmonicity of a motion. Starting from a didactically motivated definition of harmonic motion, and stressing the importance of the interplay between mathematics and experiments, we give a four-point criterion for anharmonicity together with some emblematic examples. The role of linear damping is also analysed in relation to the gradual changing of harmonicity into anharmonicity when the ratio between the damping coefficient and the zero-friction angular frequency increases.

Motion of a superconducting loop in an inhomogeneous magnetic field: a didactic experiment

We present an experiment conductive to an understanding of both Faradays law and the properties of the superconducting state. It consists in the analysis of the motion of a superconducting loop moving under the influence of gravity in an inhomogeneous horizontal magnetic field. Gravity, conservation of magnetic flux, and friction combine to give damped harmonic oscillations. The measured frequency of oscillation and the damping constant as a function of the magnetic field strength (the only free parameter) are in good agreement with the theoretical model.

Theories as Crucial Aspects in Quantum Physics Education

A lot of difficulties aroused in interpreting quantum physics from its very beginnings up today are still at the core of most educational presentations. In fact, usually people try to grasp theoretical concepts by referring to a blend of ideas taken from scientific, pre-scientific and common sense schemes. In this paper a pre-condition for every educational approach will be proposed: to rigorously keep to quantum mathematical formalism in order to understand the meaning and the “reality” of quantum physics. It will be argued that the addition to quantum theories of most extraneous concept or common sense scheme comes from an ambiguous idea of nature, scope and aims of science itself.

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

We present an educational path on the magnetic vector potential A addressed to undergraduate students and to pre-service physics teachers. Starting from the generalized Ampere-Laplace law, in the framework of a slowly varying time-dependent field approximation, the magnetic vector potential is written in terms of its empirical referent, i. e. the conduction current. Therefore, once the currents are known, our approach allows 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 calculation of A are analysed.