Potential in bidimensional wedge domains

Abstract

Potential function due to lineal charge distribution C/m in bidimensional wedge domains bounded by two planes with zero potential and angle 2Ф, can be obtained by means of classical images theory or infinite series solution. However images theory solutions are limited to wedge angles entire submultiples of π. In this paper is shown that general problem solution can be expressed by the Sommerfeld-Malyughinetz integral for any value 0 < 2 Ф ≤ π in the complex plane through a convenient integration path. It is shown that solution for Laplace problem is a particular case of the more general Helmholtz problem with identical boundary conditions. It is shown that images theory is a particular case of the integral solution for 2Ф = π/n where n is an natural number.

Keywords

• singular domain potentials
• bidimensional potentials
• bidimensional Dirichlet problem