On the basis of experimental investigations and a simple theoretical model that regards electrode erosion as ablation of the electrode material under action of intensive heat fluxes generated by an arc spot, we give estimations of the domain of copper cathode operating regimes with minimum erosion. It is shown that the magnetic field, which is utilized for arc displacement along the electrode surface, has a number of specific limitations from the point of view of electrode erosion. These limitations are related to the variation of the arc spot energy parameters with the magnetic field, which results in a variation in heat transfer between the electric arc and the electrode. As a consequence, an optimal magnetic field exists. For a copper electrode in air, an increase in the magnetic field above 0.08 T makes no sense, because it can only decrease the reliability of the cathode operation by growing erosion. Experimental investigations carried out confirm the results of theoretical analysis. The relationships and diagrams, which make it possible to estimate the domain of the operational conditions of a copper cathode with minimum erosion, are given.