Transport properties of cylinder pairs and of the square array of cylinders

Abstract

Abstract We evaluate the multipole coefficients B2n-1 in the potential expansion for a perfectly conducting cylinder pair separated by unit potential difference. We obtain a simple expression for the B2n-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.