Influence of shape variation on capacitance matrices

We theoretically determine the per-unit-of-length N × N capacitance matrix of a set of N conductors w.r.t. a reference conductor, obtained when expanding the cross-section of one or more of these conductors w.r.t. some nominal configuration. It is shown that certain relationships between the individual matrix elements of the nominal and of the expanded configuration exist. For the N ≤ 2 case, the expansion leads to the increase of the absolute value of all matrix elements. For N > 2 no such general conclusion is shown to exist. The results remain valid in three dimensions. A number of numerical examples illustrate the theory.