Iron Core Solenoid: Calculating Applied Field and Magnetisation

[sa1988]

Homework Statement

Iron core solenoid, with 50 turns per cm (5000 per metre)
Current = 0.2A
Measured B field = 1.58T

Calculate:
i) The applied field, B_applied
ii) The magnitude of magnetisation, M, of iron alloy

Homework Equations

For a long solenoid, B_applied=μ₀nI
And, generally, B=B_applied+μ₀M

The Attempt at a Solution

I'm actually confused mainly on the first part because the answer isn't as it seems.

For a solenoid, the applied field is:
B=μ₀nI

So I get B = 1.26E-6 * 5000 * 0.2 = 1.26mT

This would then suggest, for part ii), that the magnetisation for the iron alloy is (1.58 - 0.00126)T = 1.579T

It seems the iron alloy has been rather hugely magnetised by such a small applied field!
I worry if this is actually correct, or I've done something wrong..?

Thanks

 

[TSny]

So I get B = 1.26E-6 * 5000 * 0.2 = 1.26mT

This would then suggest, for part ii), that the magnetisation for the iron alloy is (1.58 - 0.00126)T = 1.579T

Is this the value for M or for μ₀M?

It seems the iron alloy has been rather hugely magnetised by such a small applied field!

Yes. Ferromagnetic materials are amazing!

 

[sa1988]

Is this the value for M or for μ₀M?Yes. Ferromagnetic materials are amazing!

Ah, oops, yeah I missed out the μ₀ term.

Still I was shocked by the seemingly huge resultant B field from such a tiny current in the solenoid.

So M = (B-B_app)/μ₀ = (1.58-0.00126)/μ₀

However I'm now shocked again because this gives a magnetisation of 1.25E6... which is huge! (Or is it...?) I can't seem to find any examples online with actual numerical values for me to consider as a reference towards my own answer.

Simply, I don't know what a typical magnetisation value should look like. Should it be as huge as that?

Thanks

 

[TSny]

Yes, your numbers look reasonable for iron. It is amazing and it shows what a large group of entities (atoms) can accomplish when they cooperate.

 

[sa1988]

Yes, your numbers look reasonable for iron. It is amazing and it shows what a large group of entities (atoms) can accomplish when they cooperate.

Great stuff, thanks