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

AI Thread Summary
To find the inductance of a coil with two concentric ferromagnetic cores, one must consider the arrangement and relative permeabilities of the materials involved. The inductance formula L = μN²A/l applies, but the presence of an air gap complicates the calculation. It is suggested that the outer core may dominate the inductance due to its shielding effect on the inner core. When an air gap is present, it increases leakage inductance and reduces magnetizing inductance, which should not be neglected. The contributions of different materials can be weighted based on the areas they occupy within the coil.
jam1234
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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?
 
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jam1234 said:

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?
 
berkeman said:
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.
 
jam1234 said:
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.
 
berkeman said:
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?
 
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