Abstarct: The potential traps for confinement of the charged particles are one of the most conventional systems used for fundamental research and perecise measuremnts on trapped charged paticles. The Paul and Penning traps are two categories of these traps. The Paul traps with a harmonic quadrupole electric potential and the Penning traps with a static electric potential and a superimposed magnetic field can confine the charged particles in three dimensions. These systems have broad applications such as measurement of the fundamental constant of the particles, mass spectrometry, ionic and nuclear excited states studies, measurement of the half life of the nuclear excited states, studing on decay of rare elements, charged particle intractions, Quantum Information and intanglement. In this study, the motion of the charged particles is studied both analytic and numeric. Also, simulation of the ion and electron trajectrory and study on confinement conditions are done. The static and harmonic magnetic field effects on the Paul trap are studied as a new work. It has shown that stability conditions of the Paul traps affected by magnetic field and stability regions can be controled too. Finaly, Simulation of the Planar Penning Traps and their electric well potentials are done and the effective factors on depth, width and shape of the potential wells are studies.