流れ場の反転性を利用した二次元静電界の等電位線と電気力線の数値計算手法

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In this paper, a calculation method is presented to trace lines of force (electric field lines) and equi-potential lines in two dimensional electric fields, where no space charge distributes, as an aid in visualizing and analyzing electric field. This method is based on the idea that the role of electric field and equi-potential lines can be exchanged each other under the following conditions : (1) replace the electrode surface with a boundary surface parallel to an electric field line, (2) replace the boundary surface parallel to an electric field line with an equi-potential surface as contrasted with (1), and (3) make the inverse ratio of dielectric coefficients between two dielectric substances provided the boundary surface of different dielectric coefficients exists. The above conditions are derived from an inversibility of the fluid mapper which is used for visualizing stream lines of potential fields. This paper explains briefly the numerical calculation technique of electric field and equi-potential lines. The numerical calculation for practical use of the presented method is performed by the finite element method because of convenience for replacing boundary conditions. The application of this method is illustrated by an example of electric field analysis, in which the strict solutions can be easily obtained by coformal mapping. The presented method is particularly effective for the numerical calculation of electric field lines in complex dielectric substances having boundary surface of different dielectric coefficients.

流れ場の反転性を利用した二次元静電界の等電位線と電気力線の数値計算手法

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