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

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.

Included in

Physics Commons

Share

COinS
 

URL: http://digitalcommons.calpoly.edu/phy_fac/73