  The goal of this paper is to study the electrostatic field due to an
arbitrary charge distribution on a dielectric layer in a dielectric-loaded
rectangular waveguide. In order to obtain this electrostatic field, the
potential due to a point charge on the dielectric layer is solved in advance.
The high computational complexity of this problem requires the use of different
numerical integration techniques (e.g. Filon, Gauss-Kronrod, Lobatto, ...) and
interpolation methods. Using the principle of superposition, the potential due
to an arbitrary charge distribution on a dielectric layer is obtained by adding
the individual contribution of each point charge. Finally, a numerical
differentiation of the potential is carried out to obtain the electrostatic
field in the waveguide. The results of this electrostatic problem are going to
be extended to model the multipactor effect, which is a problem of great
interest in the space industry.
