We study the relaxation of a classical gas of fully interacting two-dimensional charged particles under a transverse magnetic field. The gas is initialized in an artificial condition-the particles are placed randomly into a circle of a fixed radius and released-and the equations of motion are integrated numerically to find the long-time equilibrium configuration. The scattering mechanisms responsible for the relaxation are studied, revealing two distinct regimes: at short times, the gas expands and contracts as a whole at roughly the cyclotron frequency, and the interparticle scattering (being density dependent) shows a periodic ``scattering out'' of a small fraction of the constituent particles from the oscillating body. After roughly ten cyclotron periods, about two-thirds of the particles have been scattered out of the oscillating cloud, and the scattering becomes essentially a small group oscillating through (and colliding with) a thermalized region of randomly moving charges. We find that the overall relaxation time of the gas scales like the square root of the number of particles, and that for a fixed number of particles the relaxation time scales like the inverse square root of the initial radius.