Hall currents in inhomogeneous magnetic fields

A theoretical treatment of Hall currents in inhomogeneous magnetic fields is given, and both analytic and numerical procedures to calculate the effects are described. The conductor geometry studied is a long rectangular strip conductor with axial currents, and is subjected to a spatially varying magnetic field aligned perpendicular to the strip surface. The current density is described in terms of a T vector perpendicular to the strip surface. Current density components are derived from spatial derivatives of the T vector that depends upon the resistivity of the conductor and the Hall coefficient. Hall currents produce nonuniform current distributions due to the inhomogeneous magnetic fields that can create a significant increase in resistance in excess over that produced by magneto-resistance alone. Results are presented for aluminum at cryogenic temperatures. (Author)