The solution of the Laplace equation in a two-dimensional case for a plate capacitor is analyzed. Analytical formulas for the potential and the field strength corresponding to a uniform charge distribution over two dielectric plates of finite width are derived. The case of an infinitely thin charge layers in two-dimensional space is also considered. The results of numerical calculations in the Mathcad program are presented. Graphs and the field line patterns are constructed, allowing for edge effects in the classical model of a uniform electrostatic field.
01.40.-d Education
02.30.Jr Partial differential equations
$^1$Moscow Technichal University of Communications and Informatics
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