Electric field computation inside a rectangular petrol tank

In the paper was developed a hybrid method (analytic–numeric) for the electric field computation inside a rectangular petrol tank. For this problem it will be assumed a static state and all the computations will be developed in a Cartesian coordinate system. Two regions will be delimitated: first one is the free space and second one is the liquid electro-statically charged (petrol) inside the tank. For solving the Laplace equation in the first region, variable separation method will be applied and the electric potential will be determined. In the second region the Poisson equation will be solved, assuming a particular solution and then the electric potential will be obtained. To determine the constants from the potential expressions the zero potential condition at the tank surface and the continuity conditions at the separation surface was considered. Using mathematical manipulations (series development, numerical approximations etc.) an ill conditioned matrix system (23 × 23) resulted. This system will be numerically solved/discussed using a developed MathCad algorithm. The condition number of the coefficients matrix is being computed and the regularization methods applied to the system will be discussed.