The measurement of the erosion at the electrodes of an arc rotated between water‐cooled nonrefractory coaxial electrodes in an axial magnetic field has been made in air at atmospheric pressure. Values of erosion rate an order‐of‐magnitude less than those previously reported have been obtained. The effect of variation in axial magnetic flux density, arc velocity, rotational frequency, cooling‐water flow‐rate, and electrode wall thickness have been investigated. A steady‐state model, taking into account the nonuniform thermal distribution in the electrode below the arc root, has been obtained in terms of the electrode dimensions normalized with respect to the diameter of the arc root. The minimum conditions for the surface of a cold‐cathode electrode to be maintained below the melting point of the electrode material are deduced.