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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?