Nonlinearity in the effect of an inhomogeneous Hall angle Daniel W. Koon St. Lawrence University Canton, NY.
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The differential equation for the electric potential in a conducting material with an inhomogeneous Hall angle is extended outside the small-field limit. This equation is solved for a square specimen, using a successive over-relaxation [SOR] technique, and the Hall weighting function g(x,y) -- the effect of local pointlike perturbations on the measured Hall angle -- is calculated as both the unperturbed Hall angle, QH, and the perturbation, dQH, exceed the linear, small angle limit. In general, g(x,y) depends on position and on both QH, and dQH.
(a) Resistivity: D. W. Koon & C. J. Knickerbocker, Rev. Sci. Instrum. 63 (1), 207 (1992);
(b) Hall effect: D. W. Koon & C. J. Knickerbocker, Rev. Sci. Instrum. 64 (2), 510 (1993).
D. W. Koon & C. J. Knickerbocker, Rev. Sci. Instrum. 67 (12), 4282 (1996).
Increasing r Decreasing r
Fit curve (in white):
where a≈0.66 for entire specimen.
Small perturbation is equivalent to point dipole perpendicular to and proportional to local E-field. Linear.
But the perturbation changes the local E-field. Therefore there is a nonlinear effect.
either in the small-angle limit or in general?