Abstract

In this paper, we have employed appropriate conformal maps to solve and analyze some harmonic Dirichlet problems in electrostatics. The technique involves the transformation of a given problem in the w plane onto one in the upper half of the z plane where it is identified as the imaginary part of the logarithmic function with branch cut at the ray -π/2 and efficiently solved or directly solving it in the w plane where it is posed. The equipotential lines and flux lines of the electric field were also generated to show the nature of the field and the features of the solution. The method gave exact general analytical solutions in closed form to the problems considered and could therefore be a useful alternative method for solving Laplace’s equation for two dimensional electrostatic problems.

Key words: Domain, Region, Conformal Map, Joukowski Map, Bilinear Transformation, Analytic Function, Branch Cut and Branch of a Multiple Valued Function, Electrostatic Potential, Equipotential Lines, Flux Lines, Electric field Intensity.