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Fundamental formulations are given for the potential distribution of acylindrical and a hollow cylindrical objects with a rotational symmetry.Thisprocedure is performed by solving Laplace's equation in polar coordinates usingthe method of separation of variables.By limiting the inner radius of ahollow cylinder to zero, it can be proved that all the formulations for the hollowcylinder become to those for the cylinder.A few examples of numericalanalysis are quantitatively done for the boundary conditions with constantpotential value on the cylindrical and hollow cylindrical surface.The obtaineddata with respect to convergence of a series sum and resultant potentialdistribution are presented for the different boundary conditions.

The Numerical Analysis of Laplace's Equation in Cylindrical and Hollow Cylindrical Objects with Rotational Symmetry. Applying to Guard-Ring Capacitor.