Postprint version. Published in American Journal of Physics, Volume 66, Issue 8, August 1, 1998, pages 668-677.
Copyright © 1998American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers. The following article appeared in American Journal of Physics and may be found at http://dx.doi.org/10.1119/1.18931.
NOTE: At the time of publication, the author Matthew Moelter was not yet affiliated with Cal Poly.
The classical Hall effect presents a surprisingly unusual and challenging problem in electrostatics, with boundary conditions that are not of Dirichlet, Neumann, or of mixed Dirichlet and Neumann type. These unusual boundary conditions create several difficulties not normally encountered in standard problems, and ultimately lead to expansion of the electric potential in a nonorthogonal basis set. We derive the boundary conditions for the potential in a rectangular geometry, construct a solution for the potential, and discuss the relation between this problem and problems of the standard mixed type. We also address a commonly encountered misconception about the current distribution.