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Electric Potential in the Classical Hall Effect: An Unusual Boundary-Value Problem
American Journal of Physics
  • Matthew J. Moelter, University of Puget Sound
  • James Evans, University of Puget Sound
  • Greg Elliot, University of Puget Sound
  • Martin Jackson, University of Puget Sound
Publication Date

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.

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.
Citation Information
Matthew J. Moelter, James Evans, Greg Elliot and Martin Jackson. "Electric Potential in the Classical Hall Effect: An Unusual Boundary-Value Problem" American Journal of Physics Vol. 66 Iss. 8 (1998) p. 668 - 677
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