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[Phys-L] magnetic circuits ... was: change in inductance with iron core

On 5/4/21 3:36 PM, Carl Mungan via Phys-l wrote:

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?

Interesting topic. Most people have very little intuition about
how magnetic circuits work. I know a guy who earned a living
as a consultant designing such things.

Short answer: Here is a good way to visualize what's going on,
approximately: There is something roughly analogous to Ohm's
law for field lines. Electrical resistivity maps onto magnetic
reluctivity (which is the reciprocal of permeability). Iron
has a low reluctivity while air has a high (but not infinitely
high) reluctivity. Field lines are endless, so they always form
a complete circuit. The number of field lines you get depends
on not just the reluctivity of the chunk of iron, but of the
*complete circuit*

In the given situation, the total reluctance of the circuit
will be dominated by the air. You can change this dramatically
by using multiple pieces of iron to make a *closed path* that
the magnetic field lines can follow. You want the field lines
to stay within the iron.

Everything I've said is approximate. You can see where it comes
from by looking at the Maxwell equations plus the equation of
state of the iron.

There exists finite-element modeling software that will work
out the details.

For the next level of detail: