Perturbative Approach for the Analysis of Charge Distribution on Arbitrarily Shaped Conductors

In this paper, we analyze the electrostatic charge distribution on arbitrarily shaped conductor surfaces. Following a perturbative approach, derive an approximate analytical formulation of problem. We start from known case conducting ellipsoid, adopt deformed ellipsoidal coordinate system, and search for zero-order approximated solution also focus arbitrary-shaped thin foils, showing that density is divergent their borders. then define applicability range proposed approach expressing contour equation as Fourier series. Finally, present detailed error analysis several polygonal contours, comparing results with those obtained via numerical based Finite Element Methods (FEM).