Exact and numerically stable closed-form expressions for potential coefficients of rectangular conductors

Existing exact closed-form expressions for the scalar mutual and self-potential coefficients for rectangular conductors may be ill-conditioned for certain geometries. We propose new, exact, closed-form expressions for potential coefficients that are much better-conditioned. The basic idea is to express all potential coefficients as weighted sums of mutual and self-potential coefficients of suitably defined virtual plates. Experimental results are presented to demonstrate the improved numerical stability of the new formulas