What is the Relative Permeability of Iron in a Solenoid?

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SUMMARY

The discussion centers on calculating the relative permeability (μr) of iron in a solenoid using the formula L=μoμrN^2A/l. The user initially miscalculated μr, obtaining a value of 9x10-3 instead of the expected 200. After correcting the calculation by properly using parentheses in the denominator, the user achieved a result of approximately 199.4, confirming the expected value for the relative permeability of iron. The conversation highlights the importance of careful input in calculations and the distinction between permeability and apparent permeability.

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  • Understanding of electromagnetic principles, specifically solenoids
  • Familiarity with the permeability of materials, particularly iron
  • Proficiency in algebraic manipulation of equations
  • Basic knowledge of physical constants, such as μo (permeability of free space)
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  • Explore the derivation and applications of the solenoid equation L=μoμrN^2A/l
  • Learn about the differences between permeability and apparent permeability
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Mason98
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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 :)
 
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When I plug the values into your equation I get essentially 200 for μr (well, 199.4). I suggest that you check your finger work on your calculator keypad :smile:
 
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gneill said:
I suggest that you check your finger work on your calculator keypad
Specifically, you forgot to put parenthesis "()" around the denominator.

Cheers,
Tom
 
Just out of curiosity: why are you expecting to get μr=200 for your piece of iron?
 
zoki85 said:
Just out of curiosity: why are you expecting to get μr=200 for your piece of iron?
gneill said:
When I plug the values into your equation I get essentially 200 for μr (well, 199.4). I suggest that you check your finger work on your calculator keypad :smile:
Sorted now thanks, was typing it in wrong. lol
 
zoki85 said:
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
 
Mason98 said:
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
 

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