In this paper, we analyze the relation between the surface curvature of an isolated charged conductor and resultant electrostatic potential. The study will be performed for a long conductor with uniform cross section. It will be demonstrated by geometric arguments that a correlation between curvature and potential exists. This relation will be obtained for a set of polar coordinates that parameterize the surface of the isolated conductor. Two examples will be discussed based on quasi-circular conducting cylinders, whose cross sections are obtained firstly perturbing the equation of the circle by a cosine function and secondly by a more general function including a Fourier series expansion.
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