# Finding Mutual Inductance of a Coil Inside Another Coil

#### Walks91

Joined Apr 28, 2018
20
The title is basically the question.

If I were to have two multi-turn coils, one placed inside the other with both of them being insulated from each other, do I just use the general equation for mutual inductance? Only the outer coil would be connected to the power source but would it matter if the two coils used the same ground?

Would they be considered as being in parallel, series or neither?

#### wayneh

Joined Sep 9, 2010
16,400
...do I just use the general equation for mutual inductance?
I doubt any simplified formula would give a decent estimation. I believe you'd need a lot of details to model the interaction with any precision. You'd get an answer faster by simply doing the experiment.

Only the outer coil would be connected to the power source but would it matter if the two coils used the same ground?
I don't think a shared ground would affect how current in the primary induces an EMF in the secondary. Somebody will probably come along and tell us why I'm wrong on that.

Would they be considered as being in parallel, series or neither?
Neither.

#### Walks91

Joined Apr 28, 2018
20
Thank you for the responses!

I have done some research and it did seem like most of the mutual inductance values were found from experimenting. I was just hoping to find a way to get an estimated value that would be of the same order of magnitude at the very least.

What if the inside coil was not grounded at all? Just like the equation for an iron core (or whatever else) that is placed inside a coil. The difference is that the core would be a hollow coil, or even just a hollow tube.

#### shortbus

Joined Sep 30, 2009
8,043
What if the inside coil was not grounded at all? Just like the equation for an iron core (or whatever else) that is placed inside a coil. The difference is that the core would be a hollow coil, or even just a hollow tube.
Wouldn't that make it an air core inductor?

#### wayneh

Joined Sep 9, 2010
16,400
I was just hoping to find a way to get an estimated value that would be of the same order of magnitude at the very least.
It's conventional to talk about the coupling factor, the degree to which the magnetic field of the primary is captured by the secondary. That's the limiting factor and I think you could make an order-of-magnitude estimate of that. In your scenario, the inner coil spans much less area than the outer one and a lot of the primary field passes outside the secondary coil.

#### Walks91

Joined Apr 28, 2018
20
I suppose the inner coil would be considered an air core inductor, but the outer coil would technically have a core (the inner coil). I know about the coupling factor and it's relation to mutual inductance. I'm just a little unsure what equation to use to give a decent estimation. Everything I've found so far has the coils separated in a different orientation.

I was looking into using the equation shown in this link for adjacent coils, where L would maybe be the gap between the inner and outer coil. https://www.electronics-tutorials.ws/inductor/mutual-inductance.html

#### Janis59

Joined Aug 21, 2017
1,232
Many cases it is far more rapid to measure instead of calculation, and sure better accurate. Instructions how to manage with shorted secondary and opened primary etc to get those measurements is full Google.