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[Phys-L] change in inductance with iron core

I’m wondering about the following. Some multimeters can measure inductance. I have tried with a few coils lying around and I find that with nothing (ie. air) in the core, I get one value of the inductance, say maybe 0.1 H for things like Pasco coils or even some larger coils. If I now insert iron rods or laminated iron bars into them, the inductance increases by about a factor of 10, maybe a bit more or maybe a bit less.

My question is: Since the relative permeability of iron (even at low applied fields) can easily be 10 000 or more, why am I not seeing substantially bigger increases in the inductance when I insert these iron cores?

Carl E. Mungan, Professor of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363