How to Determine Inductance in a Magnetic Circuit with Varying Permeabilities?

[kevinb]

Homework Statement

I have a magnetic circuit with a coil wrapped around the centre "leg" of the core as follows.

I have been given average lengths, areas and permeabilities for the three legs and the airgap.

Homework Equations

L = (N^2*µ*A)/l

The Attempt at a Solution

For the core material permeability(µ) do I specifically use the permeability of the part of the core the coil is wrapped around? (As mentioned, in this example I was given different permeability for the different "legs")

Similarly for the coil area(A) and average coil length(l), if these are not specified separately, do I use the dimensions of the centre leg?

 

[rude man]

Homework Statement

I have a magnetic circuit with a coil wrapped around the centre "leg" of the core as follows.

I have been given average lengths, areas and permeabilities for the three legs and the airgap.

Homework Equations

L = (N^2*µ*A)/l

The Attempt at a Solution

For the core material permeability(µ) do I specifically use the permeability of the part of the core the coil is wrapped around? (As mentioned, in this example I was given different permeability for the different "legs")

Similarly for the coil area(A) and average coil length(l), if these are not specified separately, do I use the dimensions of the centre leg?

First, what are the relative permeabilities of the core material vs. that of air? What great simplification does that allow you to make? (If your teacher really wants you to take all permemabilities into account, this simplification is impossible but what follows is applicable nonetheless).

Then, you need to look at this as a magnetic circuit. Meaning flux, reluctance, magnetic potential difference. Relation of reluctance to permeability and the geometry? The basic definition of inductance is L = Ni/ψ where ψ = magnetic flux. What simple formula follows from that, relating reluctance to inductance in your situation?

PS - you obviously also need the number of turns.

 

[kevinb]

Many thanks for your reply. I have been given the number if turns and the current that is flowing. In an earlier question I am given the permeabilities so can work out flux. Now with the correct formula I can would out inductance.