Abstract
AbstractThe following electrostatic potential problem is considered: arbitrary potential distribution is given on a spherical cap, the electric charge distribution is to be determined. The closed form solution is obtained by a special integral representation of the kernel of governing integral equation. Two examples are considered: uniform potential distribution over a spherical cap, and the case of earthed conducting spherical cap in a uniform electrical field. The expressions for the electric charge distribution and the total charge are given. The general results of this paper may be also applied to the related problems of a fluid flow and thermoconductivity.
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