Electric Potential in the Classical Hall Effect: An Unusual Boundary-Value Problem

Author Info

Matthew J. Moelter, University of Puget SoundFollow
James Evans, University of Puget Sound
Greg Elliot, University of Puget Sound
Martin Jackson, University of Puget Sound

Recommended Citation

Postprint version. Published in American Journal of Physics, Volume 66, Issue 8, August 1, 1998, pages 668-677.

NOTE: At the time of publication, the author Matthew Moelter was not yet affiliated with Cal Poly.

The definitive version is available at https://doi.org/10.1119/1.18931.

Abstract

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.

Disciplines

Physics

Copyright

1998 American Association of Physics Teachers.

Publisher statement

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.