How to find inductance of a coil with two concentric ferromagnetic cores?

[jam1234]

Homework Statement

This isn't exactly a homework question so there aren't any data/numbers to work with. I just want to know what to do if there are two ferromagnetic cores inside a coil of wire, arranged as concentric cylinders. Or how to account for the air gap between the core and the coil?

Homework Equations

L = μN²A/l

The Attempt at a Solution

Should it be treat as a series circuit? Or maybe parallel? Or do you weight the contributions of the relative permeabilities by the fraction of the area inside the coil they occupy?

 

[berkeman]

Homework Statement

This isn't exactly a homework question so there aren't any data/numbers to work with. I just want to know what to do if there are two ferromagnetic cores inside a coil of wire, arranged as concentric cylinders. Or how to account for the air gap between the core and the coil?

Homework Equations

L = μN²A/l

The Attempt at a Solution

Should it be treat as a series circuit? Or maybe parallel? Or do you weight the contributions of the relative permeabilities by the fraction of the area inside the coil they occupy?

Depending on the arrangement, I would guess that the outer core would dominate the inductance -- that is, very little of the B-field would be coupled to the inner core. The outer core would act as a shield for the inner core, IMO.

Do you have an application in mind?

 

[jam1234]

Depending on the arrangement, I would guess that the outer core would dominate the inductance -- that is, very little of the B-field would be coupled to the inner core. The outer core would act as a shield for the inner core, IMO.

Do you have an application in mind?

Well for example to account for the ring of air around a metal core in a solenoid. In some cases this may not be negligible.

 

[berkeman]

Well for example to account for the ring of air around a metal core in a solenoid. In some cases this may not be negligible.

That's a different situation than the question in your original post (OP). If you have an air gap between the windings and a single core, then that increases the leakage inductance Lk and reduces your magnetizing inductance Lm.

 

[jam1234]

That's a different situation than the question in your original post (OP). If you have an air gap between the windings and a single core, then that increases the leakage inductance Lk and reduces your magnetizing inductance Lm.

I did put the air gap bit in my original question as well. How would you find the inductance of a coil with a metal core and an air gap around it? I don't want to assume it is negligible because it isn't always. Do you just use the relative permeabilities weighted by the areas occupied by the core and air gap?