The calculation of Hall potentials in a rectangular Hall plate is treated for the case in which the device is subject to a magnetic field B that is inhomogeneous in the y-direction perpendicular to the direction of initial current flow. The potentials are presented in the form φH(→r′) = const. ∫widthB(y)G(y,→r′)dy for the normal Hall effect (→r′ is the position vector). Analytical expressions are given for the weight function G (which depends on the form of the device), together with graphs for a number of typical examples. An analogous expression is derived for the planar Hall effect in ferromagnetic thin films.
Fluitman, J. H. J. (1981). On the calculation of the response of (planar) hall-effect devices to inhomogeneous magnetic fields. Sensors and actuators, 2, 155-170. https://doi.org/10.1016/0250-6874(81)80035-2