International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 60595, 9 pages
Research Article

Two-Dimensional Electrostatic Problem in a Plane with Earthed Elliptic Cavity due to One or Two Collinear Charged Electrostatic Strips

B. M. Singh,1 J. G. Rokne,1 and R. S. Dhaliwal2

1Department of Computer Science, The University of Calgary, Calgary T2N-1N4, Alberta, Canada
2Department of Mathematics and Statistics, The University of Calgary, Calgary T2N-1N4, Alberta, Canada

Received 16 August 2006; Accepted 23 November 2006

Academic Editor: Hans Engler

Copyright © 2007 B. M. Singh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A two-dimensional electrostatic problem in a plane with earthed elliptic cavity due to one or two charged electrostatic strips is considered. Using the integral transform technique, each problem is reduced to the solution of triple integral equations with sine kernels and weight functions. Closed-form solutions of the set of triple integral equations are obtained. Also closed-form expressions are obtained for charge density of the strips. Finally, the numerical results for the charge density are given in the form of tables.