Electromagnetism as a world view: implications for the teaching of energy

Abstract

There are considerable differences in the ways mechanics and electromagnetism conceptualize energy. In the former, energy is defined in terms of force and work in a process-like reasoning that remits us to the "past" of a given body or system. Moreover, in the mechanical framework energy is ascribed to matter, i.e., one speaks of the energy of a system of bodies. The electromagnetic picture is quite different. There, energy assumes a form localized directly in the fields, i.e., if a region in space contains E and/or B fields, then there is energy. Furthermore, in electromagnetism energy is no longer a property of an object, but some kind of extensive quantity in space. We argue that traditional physics instruction in introductory courses fails to highlight these differences and thus students do not become aware of important traits of the electromagnetic "world view". Analyzing the case of electrostatic energy, we both review critically the standard mechanical discourse and introduce a didactical approach to motivate the electromagnetic way of thinking of energy without the need of an advanced mathematical formalism. The latter is more akin to the practice of present day physics, which relies on lagrangians based on field energy densities.

Quantum Hall effect: from the drude conductivity model to the Chern-Simons field description

“…There is also a guide for an undergraduate Hall effect experiment in copper [11] and a correlated idea associated to magnetic polarity and Hall sensors [12]. In [13], the Hall effect is applied as a tool to describe the microscopic structure of a wire as well as its charge density from a set of macroscopic measurements.…”