The Numerical Analysis of Laplaceu27s Equation in Cylindrical and Hollow Cylindrical Objects with Rotational Symmetry - Applying to Guard-Ring Capacitor -

摘要

Fundamental formulations are given for the potential distribution of a cylindrical and a hollow cylindrical objects with a rotational symmetry. This　procedure is performed by solving Laplaceu27s equation in polar coordinates using the method of separation of variables. By limiting the inner radius of a hollow cylinder to zero, it can be proved that all the formulations for the hollow cylinder become Lo those for the cylinder. A few examples of numericalanalysis are quantitatively done for the boundary conditions with constant potential value on the cylindrical and hollow cylindrical surface. The obtained data with respect to convergence of a series sum and resultant potential distribution are presented for the different boundary conditions.