Abstract
The in-plane magnetoresistance of columnar composites is studied for a class of three-constituent mixtures of normal conductor, perfect insulator, and perfect conductor, where the magnetic field $\mathbf{B}$ is applied in the plane perpendicular to the columnar axis. Exact relations are found between the bulk effective resistivity tensor ${\stackrel{^}{\ensuremath{\rho}}}_{e}$ of such a medium and that of a medium where the perfect insulator and perfect conductor have exchanged their spatial locations. Exact expressions are found in some cases for the leading order large $\mathbf{B}$ behavior of ${\stackrel{^}{\ensuremath{\rho}}}_{e},$ for periodic microstructures and certain directions and ranges of directions of $\mathbf{B}.$ Numerical calculations are used to compute ${\stackrel{^}{\ensuremath{\rho}}}_{e}$ in those microstructures for all directions of $\mathbf{B},$ and for various magnitudes of $|\mathbf{B}|.$ The different results are compared and their significance is discussed.
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