An analysis based on numerical solutions to the three moments of the Boltzmann equation is presented for magnetron discharges used in plasma processing of electronic materials. A chlorine discharge at 13.56 MHz is studied and the results are compared for discharges with and without the magnetic field. The charged particle densities increase by a factor of 5 and the ionization rate increases by an order of magnitude with the application of a 100 G magnetic field in a 50 mTorr discharge. The sheaths in the magnetron discharge are thin and the sheath electric field decreases with increasing magnetic field. The bulk ohmic heating is the dominant mechanism for power deposition under the conditions investigated here.