  A variational approach is used in order to study the stationary states of
Hall devices. Charge accumulation, electric potentials and electric currents
are investigated on the basis of the Kirchhoff-Helmholtz principle of least
heat dissipation. A simple expression for the state of minimum power dissipated
-- that corresponds to zero transverse current and harmonic chemical potential
-- is derived. It is shown that a longitudinal surface current proportional to
the charge accumulation is flowing near the edges of the device. Charge
accumulation and surface currents define a boundary layer over a distance of
the order of the Debye-Fermi length.
