Electric potential in the classical Hall effect: An unusual boundary-value problem

Matthew J. Moelter, James Evans, Greg Elliott, Martin Jackson
1998 American Journal of Physics  
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
more » ... onstruct 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.
doi:10.1119/1.18931 fatcat:ch5zvkei7jfbzoblzdbqsaimra