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

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

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