Superconductivity explained with the tools of the classical electromagnetism. Educational path for secondary school and its experimentation.

The work of this thesis describes an educational path for the presentation of superconductivity at the secondary school, together with the experimentation of some particular parts of the path with high school students. The educational path that we have developed is mainly centred on the phenomenological aspects of superconductivity and has been inspired by the two fluid theory of Gorter and Casimir (1934) where a superconductor is seen as a material in which two fluids are present, the normal fluid described by the Ohm's laws, and the superconductive fluid descibed by the London equation (1935). Both the Ohm's laws and the London equation give respectively the phenomenological descriptions of the conductive and the superconductive fluids. There is no reference to the microscopic structure of the conductor or of the superconductor. For this reason we have chosen these phenomenological models as the framework in which we contextualized our work and the reconstruction of the contents of superconductivity. In order to develop these phenomenological models in secondary school, we have reconstructed the contents of the electrical conduction and we have subsequently developed a formal analogy between conduction and superconduction from a mathematical point of view, by means of the introduction of the London equation. Therefore a very conspicuous part of this work pertains the presentation of the London equation, for whose writing it is necessary the introduction of the magnetic vector potential. Being the magnetic vector potential never treated in secondary schools, its introduction has required a lot of reconstruction work, mainly because the mathematics generally used in the literature for the vector potential is based on differential calculus, with operators as divergence and curl, that are really beyond the knowledge and the possibilities of most of the secondary school students. We have described the magnetic vector potential in analogy with the electric scalar potential, always present in the secondary school curriculum, we have used a mathematical formalism suitable for the level of the students, and we have realized how the introduction of this new, and somewhat complicated object at first glance, can be not only a suitable way for presenting superconductivity at secondary school level, but a stimulus for a deeper understanding of the electromagnetism as well. Once that the needed prerequisite are introduced and diffusely discussed, we could afford the actual description of the phenomenological characteristic of superconductivity. This has been developed in two steps. A first basic step, in which by the London equation a student may describe mathematically both, the resistivity of the superconductor that drops to zero at a certain temperature (called critical temperature) and also the expulsion of the magnetic field from the bulk of a superconductor (called Meissner effect). The second step is addressed to students that have a suitable back-ground in quantum physics, and has the goal of introducing some basic aspects of Ginzburg-Landau theory and move towards the BCS microscopic theory. The lines of this second step are hinted in the conclusive part of this work. Besides the educational reconstruction of the contents of conduction and superconduction, that have taken the large part of this thesis, we have experimented many parts of the path with high school students. As it has been refined three times in the framework of the design-based research method, in this Phd thesis we report the results of an analysis, both quantitative and qualitative, of the part of experimentations that regards electrical conduction and the considerations that yielded the conclusive proposal we made on electrical conduction. Moreover, it is reported also a first analysis of the experiemtation on the vector potential. This part is primarily focused on investigate how the introduction of the vector potential can be useful to better understanding of electromagnetism in secondary school. We briefly describe here the structure of the work. • A preliminary introduction to the Higgs mechanism in order to highlight its tight connections to superconductivity. A chapter that is almost off topic, but that is presented to suggest the immense power of superconductivity in putting together many different physics topics even those that are recently on everyone's lips, as the discovery of the Higgs boson. • A description of the superconductivity at secondary teachers level (or for everyone with a minimum physics back-ground). Here, the didactical problems are not considered, an the chapter contains a brief summary coming from the standard literature on the subject in order to summarize what a teacher could/should already know when deciding to treat superconductivity with students. • A schema of the educational path that will be subsequently discussed in the thesis: the essential topics and how they are related to each other. • The core of the thesis: two educational paths for secondary school, one on the electrical conduction (together with the experimentations and the obtained results that lead us to the actual path) and one on vector potential (together with a first analysis of the obtained results). In fact we retains that these topics are fundamental prerequisites for a meaningful introduction of superconductivity at secondary school . • Finally our main goal: an educational path for the description of superconductivity by means of the London equation and an its generalization, when the students' back-ground is suited.