Title

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

Document Type

Article

Publication Date

8-1-1998

Publication Title

American Journal of Physics

Department

Physics

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.

Volume

66

Issue

8

pp.

668-677

ISSN

0084-9812