Beyond the magnetic field of a finite wire: a teaching approach using the superposition principle

Abstract

The traditional lecture-based scheme of teaching physics have shown to be ineffective in several aspects [1][2][3][4][5][6][7]. It results in a lack of motivation, with low impact on students, to address more complex physical systems than the ones presented in textbooks. A clear example in university-level education is the electromagnetics course, in particular when the magnetic field concept is introduced [8-10].Empirical laws of magnetism are usually discussed after a phenomenological description of the magnetic interaction and its relation with electric currents as magnetic sources. The textbooks show in that section how to apply the Biot-Savart law to evaluate the magnetic field in any point in space due to a little element of a current-carrying wire of arbitrary shape. Then, it is exemplified considering a straight finite wire and evaluating the magnetic field B at a specific point, however, it involves several assumptions, which make the problem easy to solve, but which are not discussed in detail, such as: i) choosing a symmetry point to evaluate B; ii) applying the superposition principle to simplify vector operations; and iii) reducing the number of dimensions of the system, from 3D to 2D or 1D. Even if it can be justified, it makes difficult for students to solve some of the exercises proposed at the end of the textbook section, that aim to explore the magnetic field of more complex systems like an