Electric Potential in the Classical Hall Effect: An Unusual Boundary-Value ProblemAmerican Journal of Physics
AbstractThe 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.
Copyright1998 American Association of Physics Teachers.
Citation InformationMatthew 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
Available at: http://works.bepress.com/mmoelter/10/