Image solution for poisson's equation in wedge geometry
Abstract
Recently a novel static solution appeared for twodimensional electrostatic field excited by an infinite line charge in the vicinity of a dielectric wedge whose edge was parallel to the source. In the present paper Poisson's equation is studied mainly in three dimensions but the solution for the analog two dimensional problem is also provided. It appears that numerically a simple and efficient method to compute the potential inside and outside the wedge can be found by solving first image sources for the exterior and interior problem that give rise to the potential contribution of the wedge. Both the exterior and interior 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 a reflection or transmission images of a dielectric plane. All known closedform solutions in terms of elementary functions are derived for an electrically and magnetically conducting half plane.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 April 1994
 Bibcode:
 1994STIN...9522311N
 Keywords:

 Charge Distribution;
 Electric Fields;
 Half Planes;
 Imaging Techniques;
 Mathematical Models;
 Poisson Equation;
 Potential Theory;
 Three Dimensional Models;
 Wedges;
 Boundary Conditions;
 Dielectrics;
 Eigenvectors;
 Electromagnetism;
 Fourier Transformation;
 Green'S Functions;
 Laplace Equation;
 Communications and Radar