What is the Relative Permeability of Iron in a Solenoid?

[Mason98]

TL;DR

Hello, I was wondering how to tranpose this equation? I am sure that i'm doing it correctly but I am getting a wrong answer. Any help will be much appreciated

So the equation is
L=μoμrN^2A/l

I am wanting to make μr the subject and I think this is how i do it?

μr = L*l/μoN^2A

However when I type in this equation i am expecting to get about 200 for the relative permeability of iron. However, i am getting like 9x10-3 which is nowhere near 200.
For example here are my figures
μo = 4 * pi * 10-7
N^2 = 105^2
A = 0.00196
L= 57 mHenrys
l= 0.095

I assume to get 200 for relative permeability as when i use the first equation using 200 I get that L is 57 mH but when i try tranpose and find μr I don't get 200.

If anyone could help i'd really appreciate it thank you :)

 

[gneill]

When I plug the values into your equation I get essentially 200 for μ_r (well, 199.4). I suggest that you check your finger work on your calculator keypad

 

[Tom.G]

I suggest that you check your finger work on your calculator keypad

Specifically, you forgot to put parenthesis "()" around the denominator.

Cheers,
Tom

 

[zoki85]

Just out of curiosity: why are you expecting to get μr=200 for your piece of iron?

 

[Mason98]

Just out of curiosity: why are you expecting to get μr=200 for your piece of iron?

When I plug the values into your equation I get essentially 200 for μ_r (well, 199.4). I suggest that you check your finger work on your calculator keypad

Sorted now thanks, was typing it in wrong. lol

 

[Mason98]

Just out of curiosity: why are you expecting to get μr=200 for your piece of iron?

The Iron I've used in a lab experiment is supposed to be 200 so that's why i wanted to calculate it to confirm

 

[zoki85]

The Iron I've used in a lab experiment is supposed to be 200 so that's why i wanted to calculate it to confirm

Then such a close match between measured/calculated and expected value I would consider a luck (even in a carefully arranged experiment). Also have on mind the difference between permeability and apparent permeability:
https://en.wikipedia.org/wiki/Solenoid#Quantitative_description