In this report, a simple erosion model of the discontinuous, stepwise mode of motion of a cold-electrode arc spot is proposed and applied to magnetically driven arcs as found in electric arc heaters. The model assumes that the macroscopic destruction of the electrode is initiated by the start of electrode fusion in the arc spot. The model takes into account the characteristic energy parameters of the arc spot, the thermophysical properties of the electrode material and the operational regimes of the electric arc. An effective erosion enthalpy is introduced, taking into account all elementary processes in the spot, ending up in electrode erosion. A reasonable agreement between the model and the copper cathode erosion experimental results is obtained.42852905294