# Transport Properties of Cylinder Pairs and of the Square Array of Cylinders

R. C. McPhedran

## Abstract

We evaluate the multipole coefficients B$_{2n-1}$ in the potential expansion for a perfectly conducting cylinder pair separated by unit potential difference. We obtain a simple expression for the B$_{2n-1}$ when the cylinders approach each other, and show that this expression also holds for a square array of cylinders. We derive a formula linking ratios of multipole coefficients from Green's theorem, and use this to obtain an estimate for the effect of changing the cylinder conductivity from infinity to a large, finite value on the array conductivity.