Frequency dependence of hysteresis curves in conducting magnetic materials

An extension of the hysteresis model has been developed that takes into account the effects on the hysteresis curves of eddy currents in electrically conducting media. In the derivation presented it is assumed that the frequency of the applied field is low enough (or the thickness of the material medium small enough) that the skin effect can be ignored so that the magnetic field penetrates uniformly throughout the material. In this case, the dc hysteresis equation is extended by the addition of a classical eddy-current-loss term depending on (i) the rate of change of magnetization with time, (ii) the resistivity of the material, and (iii) the shape of the specimen; and on an anomalous (or excess) eddy-current-loss term which depends on (dB/dt)3/2. In the limit, as the frequency of the magnetic field tends to zero, the frequency-dependent hysteresis curve approaches the dc curve.