Abstract
Some general properties of the effective conductivity tensor \(\hat \sigma _e\) of a composite material placed in magnetic field H are considered. It is shown that the derivatives of the tensor \(\hat \sigma _e\) components with respect to their arguments can be expressed in terms of various bilinear characteristics, namely, the mean products of the electric fields in an initial system and the “transposed” system (which differs from the initial system in the substitution H → −H). At H → 0, the general formulas derived in this work yield the well-known expressions for the Hall coefficient and magnetoresistance that are valid for the case of weak magnetic fields.
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