A study is conducted on a magnetic field effect on electron heating in capacitive rf discharges under a collisional regime, where the electron mean collision frequency is much higher than the rf frequency. The evolution of an electron energy distribution function (EEDF) over a magnetic field range of 0-30 G in 300 mTorr Ar discharges is measured and calculated for the investigation. A significant change in the low-energy range of the EEDF is found during the evolution. The observed result reveals the application of the magnetic field to the high-pressure capacitive plasma gives rise to a cooling effect on the low-energy electrons. This is in contrast to the low-pressure case where the magnetic field enhances the low-energy electron heating. The calculated result of the EEDF is in good agreement with the experiment. (C) 2004 American Institute of Physics.