Thought experiments in electromagnetic theory and the ordinary Hall effect

Thought experiments are effective tools of theoretical physics, and historically they have led to the discovery of many useful ideas and relations. Yet they also give rise to paradoxes that persist for long periods of time despite enormous efforts to resolve them. A problem par excellence, one that falls within the realm of classical electrodynamics and has been investigated exclusively by means of thought experiments, is the famous problem of hidden momentum. It concerns the conversion of the electromagnetic momentum generated by static electromagnetic fields into momentum of a non-electromagnetic nature and the resulting momentum balance. As a rule, this effect, which takes place in ponderable systems, is very subtle, of the order of ∼\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim$$\end{document} 1/c2; thus, until now it has only been studied theoretically and has never been demonstrated experimentally. The main subject of this paper is the analysis of a robust and experimentally well-established phenomenon operating in static electromagnetic fields—the ordinary Hall effect—which has been interpreted anew in terms of the Poynting vector and proven to be sufficiently sensitive for direct comparison with typical quantitative estimates encountered in the hidden momentum problem. Confrontation of hypothetical models with a real experiment enables us to formulate the general conditions and rules that should be observed when designing thought experiments in classical electrodynamics.