Abstract
A differential scheme is proposed for the calculation of the components of the effective electrical conductivity tensor of a microinhomogeneous material taking into account the Hall effect. The presence of the Hall effect results in an appearance of asymmetry of the components of the conductivity tensor and a dependence of these components on the magnitude of the magnetic field applied to the material. In this case, the differential scheme leads to a system of matrix differential equations that were solved numerically in the current work. This solution was obtained for materials containing spherical or cylindrical inclusions. In the case of cylindrical inclusions, the results were obtained for inclusions with the symmetry axes parallel or orthogonal to the magnetic field. A comparison of the results obtained by the proposed methodology to the low concentration approximation was carried out.
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