In industry and in laboratory work oftentimes we are confronted with the problem of electromagnetic shielding between two bodies. In many ceases it is sufficient to have electrostatic shielding, and thus the interaction between two bodies can be determined by examining the mutual capacitance between them. When the interfering body is small and can be considered as a point source, its effect in the presence of another grounded conductor (in our case, the metallic shield) can be calculated by means of the Green's function for this grounded conductor surface. As the Green's functions for various surfaces are well established so these various forms of shielding can be handled by the method proposed in this paper.Green's functions for regions bounded by surfaces of oblate spheroidal as well as prolate spheroidal coordinate system are discussed with a mind to supplement a few formulas for the Legendre function with imaginary variables which are useful in physical and technical problems and which do not seem to appear in popular literatures.The problem of a hole of arbitrary shape on a conducting surface is then discussed with emphasis on the allowable size of the hole on a conducting surface of finite dimension, verifying the experimental results in literature. Finally the formula for calculating the mutual capacitance of two small bodies, one of which is enclosed by a closed metallic shield with a hole on its surface is given.
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