Abstarct: The potential traps for trapping of the charged particles are one of the most conventional systems used for fundamental research and perecise measurements on trapped charged particles. The Penning trap is a potential trap that with a static electric potential and a superimposed magnetic field can confine the charged particles in three dimensions. These systems have applications such as study and measurement of the fundamental constant of the particles, energy states studies, study of particles decay, study of charged particles interaction and Quantum Information. In this thesis, classical evolution of electron and ion in a Penning trap is studied.......