The aim of this project is to carry out a series of simulations of a Paul ion trap, also referred to as quadrupole ion trap, which takes advantage of the sinusoidal potential created by hyperbolic electrodes to confine charged particles. The current report includes the description of the discretization technique used to work with the main integral equations, known as Method of Moments (MoM); and the head steps made to get the final results, starting from the calculation of capacitances, the design of the hyperbolic electrodes and the calculation of the potential and electric field, and ending up with the representation of the trajectory of an ion inside the 3D trap, in addition to showing the relation between charge/mass of the particle with the characteristics of the potential 2019/2020