Current distribution in a two dimensional electron gas exposed to a perpendicular nonhomogeneous magnetic field of a chess configuration

We have studied a finite two-dimensional electron system exposed to a normal nonhomogeneous magnetic field of a chess configuration. Using the conformal mapping method we obtain an exact analytical solution for the electric field distribution in terms of the Jacobi functions. The obtained formula is exploited to calculate the physical quantities of interest: the current density distribution, the linear density of charges accumulated along the magnetic interfaces, the magneto-resistance, and the Hall resistance.