Finite clusters with a small number of charged particles immersed in a plasmaenvironment have been numerically simulated with a dynamic method. Finite Coulomb clustersare systems of a small number of charged particles, N = 1 to 100, confined by a potential producedby plasma 2D-sheath. Under the action of net force each particle is in an equilibrium positionand together they form finite Coulomb clusters. The results of our study show the configurationof Coulomb clusters do not depend on their initial state. After theoretically studied and tested byusing the Monte Carlo technique we also prove the system energy is the determinant parameter ofthe configuration. In addition, the effect of the external magnetic field on the cluster configurationis analyzed.