Influence of shape variation on capacitance matrices

• We model the capacitance matrix of N conductors.
• We examine what happens when the cross-sections of these N conductors increase.
• For N = 1 and N = 2 it is proven that all elements of the capacitance matrix increase.
• For N > 2 the diagonal elements increase.
• For N > 2 the other elements might either decrease or increase.

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.