Say we have an AC in a magnetically lossy material, like iron. Because of iron's relatively high permeability, skin effect will be more pronounced than it is in say, copper, so this iron wire isn't so great a conductor, practically speaking.

However, skin effect arises due to eddy currents, which are themselves due to the time varying magnetic field due to the time varying current. So, this suggests there is a magnetic field at work, and there's the potential for magnetic hysteresis to be an additional source of loss in the material.

Yet, I'm not sure if this is true or not, if somehow the geometry of the conductor and the fields around it make this a non-issue. I would think that if a time-varying magnetic field exists inside the iron, then there would be hysteresis losses. Is this true? Does such a field exist?

To be clear: the issue is with iron as an electric conductor, not as part of a magnetic circuit such as a transformer core as is the more common application.


3 Answers 3


The skin effect tells us that the AC current in a conductor with high(ish) magnetic permeability will be confined to a region near the surface with characteristic thickness

$$\delta = \sqrt{\frac{2\rho}{\omega \mu}}$$

Since the current is effectively moving in a cylindrical sheet, there will be a region just inside that current sheet that will experience a tangential B-field (strongest close to the surface) that changes direction as the current changes direction.

Such a region will exhibit magnetic hysteresis, and this will increase the power dissipation due to the DC current. You would have to do the volume integral to see whether, for a particular scenario, this is a significant effect - but theoretically it is certainly possible.


In my opinion the contribution of hysteresis losses in an iron wire can be important when comparing with conductive losses, but this is an issue strongly dependent of the iron alloy used according to hysteresis loop, conductivity and permeability. The analysis of the induced current distribution in conducting wires subjected to a harmonic axial voltage is important in designing many electrical devices such as transformers and transmission lines. The azimuthal magnetic field induces axial electric currents and therefore the impedance of the wire depends on the excitation frequency. The current density, and the EM fields are increasingly confined to a thin layer at the boundary of the wire as the frequency increases in such a manner that the internal core is completely electromagnetically screened. To minimize this effect at higher frequencies it is necessary to enhance the surface-to-volume ratio by using thin high-conductivity wires. A correct evaluación of the two losses contributions can be made analitically or by numerical simmulations. Here http://scitation.aip.org/content/aapt/journal/ajp/77/11/10.1119/1.3160663 you can see the study for axial magnetic field and azimuthal currents. The problem you are interested is the reciprocal one: axial currents and azimuthal field, but the way you must approach this issue is practically the same.

  • $\begingroup$ So.....if the core is completely electromagnetically screened, how can there be hysteresis losses in it? $\endgroup$
    – Phil Frost
    Commented Jul 2, 2014 at 23:34
  • $\begingroup$ Very simple, losses are only present in regiones submitted to EM field. As the frequency increases conductive and magnetic losses take place only near the boundary and not in the core. $\endgroup$
    – user50378
    Commented Jul 3, 2014 at 21:08

Magnetic hysteresis losses are primarily associated with magnetic materials and occur when there are cyclic variations in the magnetic field. These losses are relevant in the context of magnetic cores used in transformers, inductors, and other electromagnetic devices where direct current (DC) or alternating current (AC) is involved.

In alternating current systems, the magnetic field changes direction periodically, which causes the magnetic domains within the material to realign themselves repeatedly. This process results in hysteresis losses, where energy is dissipated as heat due to the internal friction within the material.

However, the significance of hysteresis losses in alternating current systems depends on several factors, including the frequency of the alternating current, the magnitude of the magnetic field, and the properties of the magnetic material itself. At low frequencies or in materials with low hysteresis, the losses may be relatively small and not a dominant factor. In such cases, other losses such as eddy current losses or resistive losses in the wire may be more significant.

In practical applications, engineers often select magnetic materials and core designs that minimize hysteresis losses for a given operating frequency. This is achieved by using materials with low coercivity (the ability to resist changes in magnetization) and by properly designing the magnetic circuit to minimize the flux density variations and associated losses.

Therefore, while magnetic hysteresis losses can occur in alternating current systems, their relevance and impact depend on the specific conditions and materials involved.


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