Cálculo de potenciales electrostáticos en geometrı́as cilı́ndricas con Monte Carlo

Abstract

In the degree courses in science and engineering, it is usually not studied problems where the electrical potential has the following functional form φ = φ(ρ, z ), the mathematical part can become complicated in this type of problems, but from a numerical point of view there are several techniques, relatively easy to implement, in this work Monte Carlo is used to approach the calculation of electric potentials in cylindrical geometries independently of φ. It solves the Laplace and Poisson equations, for two problems with known solutions to validate the numerical solution with the exact one, the results are very good. The solutions are very similar, and so the method can be apply to more complex problems that have this type of symmetry but have no exact solution. The main limitation of the presented method is that the calculation of the potential has to be done at one point at a time..