# Will a hollow ferromagnetic core for a solenoid yield any benefit as opposed to a solid metal core?

I'm creating solenoids for a project of mine, wrapping magnet wire around a ferromagnetic piece of pipe by hand. I've heard that the field strength of a solenoid can be increased by an order of magnitude by being wrapped around a solid ferromagnetic core. Since the pipe is obviously hollow, would a ferromagnetic piece of pipe have any benefit to the solenoid wrapped around it?

A thin wall tube can have a significant effect on coil performance. Unfortunately, for hollow core cylinders analytical solutions only exits for $$\lim \mu_\mathrm{r} \rightarrow 1$$ or better say $$\lim \chi \rightarrow 0$$ [Beleggia2009]. What is actually calculated is the demagnetizing factor. This can change significantly as a function of permeability [Chen1991]. Nevertheless, the general behavior of this solution gives you an idea of what is going on:

Due to the reduced capping surface the demagnetizing field is decreasing with increasing inner diameter. Therefore, the demagnetizing factor decreases, making it overall easier to magnetize the system. This means that the response to an external field increases, i.e. the relative permeability increases. At the same time the overall magnetic material decreases. This means more flux in less material. If those effects compensate (to what extend this takes place depends on $$\mu$$) the wall thickness actually does not matter.

A thin wall cylinder, however, will saturate much faster than a solid one.

[Beleggia2009] M. Beleggia, D. Vokoun and M. DeGraef Demagnetizing factors for cylindrical shells and related shapes, J. Magn. Magn. Mater. 321 (2009) 1306-1315

[Chen1991] D.-X. Chen and J.A. Brug, Demagnetizing factors for cylinders, IEEE Trans. Mag. 27 (1991) 3601-3619

Yes. The equation and relative permeability is based on solid cores.

The volume for the solid and hollow cores would differ greatly. Specially if you have a high perm material with a hollow air core vs a solid one.

Think of it this way:

Calculate the field for air and iron cores (use online calculator if you have to).

So IronField > AirField right? Cause Iron's relative permeability is higher. Air's permeability is around 1, where as Pure Iron is like 5000.

Now lets say you have a hollow core. From volume calculations and measurements you know that the hollow core is 50% Iron and 50% Air in terms of volume. Now to solve for that hollow core field:

IronField*50% + AirField*50%.

That is less then having a solid core. Hope this helps!

• If I understand this answer right, the main statement is that the effect changes in the same way the fill factor does. This is not correct. Commented Feb 4, 2021 at 6:35