Image solution for Poisson's equation in wedge geometry

The Poisson's equation for a dielectric wedge is solved by deriving a static image that corresponds to the potential contribution of the wedge. The problem is studied mainly in three dimensions but the solution for the analog two-dimensional problem is also provided. It appears that the use of image sources provides numerically a simple and efficient method to compute the potential inside and outside the wedge. Image sources for the exterior and interior regions consist of a line charge that decays exponentially as a function of complex angle and a set of point charges that can be interpreted as reflection or transmission images of a dielectric plane. All known closed-form solutions in terms of elementary functions are derived for an electrically and magnetically conducting half plane.<
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