Asymptotic closed form for the capacitance of an arbitrarily shaped conducting plate

Closed-form results for the capacitance of an arbitrarily shaped conducting plate are presented. If the charge density suitable for fringe conditions and the appropriate charge barycentre are supposed, the asymptotic closed-form for the capacitance C can be achieved with high accuracy by simple curve integrals or the superposition of basic triangles. Some typical examples, such as an elliptical plate, a regular polygonal plate and a rectangular plate, are given.