Abstract
The present paper deals with the spatial distribution of the electrostatic potential in a channel with two electrodes in the presence of the Hall effect. The velocity profile is inhomogeneous and corresponds to the velocity diminishing down to zero at the channel walls. The problem of determining the electric field in the channel is reduced to that of solving a boundary value problem with mixed boundary conditions for an elliptic type equation. One of the versions of the Wiener-Hopf method is used in the course of solution. The three-dimensional distribution of the electric field in a MHD channel has been studied, because of considerable difficulties of mathematical nature encountered, only for the simplest cases of isotropically conducting media, i. e. for the cases when the walls have uniform conducting properties, or when an electrode zone is present in the channel [1–7]. For the anisotropic conductivity of the medium only plane problems have been studied [8, 9].
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