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*From*: John Denker <jsd@av8n.com>*Date*: Tue, 4 May 2021 17:02:21 -0700

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:

https://en.wikipedia.org/wiki/Magnetic_circuit

**Follow-Ups**:**Re: [Phys-L] magnetic circuits ... was: change in inductance with iron core***From:*bernard cleyet <bernard@cleyet.org>

**Re: [Phys-L] magnetic circuits ... was: change in inductance with iron core***From:*Carl Mungan <mungan@usna.edu>

**References**:**[Phys-L] change in inductance with iron core***From:*Carl Mungan <mungan@usna.edu>

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