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What are the accepted units of magnetic pole strength?


Feynmanfan85

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I was reading Maxwell's treatise on electromagnetism, and on Page 3 of Volume 2, he does a bit of dimensional analysis on the units of magnetic pole strength, using the following formula:

f = (m1 m2)/l2,

where m1 and m2 are the strengths of two magnetic poles, l is the distance between the poles, and f is the resultant magnetic force between the two poles.

The full treatise is available here (see page 3):

https://archive.org/details/electricityndmag02maxwrich

Let F denote the units of force, L denote the units of meters, and m denote the units of magnetic pole strength. 

Maxwell notes that,

F = m2 / L2,

which implies that,

m = L√F.

Because force equals mass times acceleration, it follows that F has units of (kg L)/T2, where kg is kilograms and T is seconds. Therefore,

m = L√((kg L) / T2) = (L3/2√kg) / T.

Interestingly, Maxwell's treatise was published in 1881, prior to Einstein's Special Theory of Relativity, which was published in 1905.

Armed with the fact that E = Mc2, we can continue Maxwell's analysis. Let J denote the units of Joules. It follows that,

m = √(J L).

That is, this analysis implies that the strength of a magnetic pole has units of the square root of Joules times meters.

Has anyone come across similar analysis on the units of magnetic pole strength?

What are the accepted units of magnetic pole strength?

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The formula was originally due to Michell in 1750.

The actual units have varied over time and there should be  constants added depending upon the system of units you are working in.

 

In modern MKS units the formula is

 


[math]F = \frac{{{{\bar Q}_1}{{\bar Q}_2}}}{{4\pi {\mu _0}{r^2}}}[/math]

 

where the pole strengths Qbar are measured in ampere-metres (amps times metres)

 

Does this help?

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Yes, thanks, I'm aware of the modern formulation. I was really more interested in the dimensional analysis Maxwell put forward. Working with his units, we obtain a relationship between magnetic strength and energy that I thought was interesting, and was wondering if anyone has carried that analysis forward. Do people view Maxwell's units as wrong, or deficient? Or have they simply fallen out of favor?

For some reason I didn't get a notice about your response, apologies for the delay in responding. 

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You need to make up your mind.

Maxwell did not work in kg and metres.

I gave you the modern answer because you posted a couple of paragraphs of working using modern units.

Edited by studiot
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Maxwell's equations are expressed in generic units of mass, time, and length. Using kg, seconds, and meters should not impact his analysis, so long as those units are used consistently.

My question is, his analysis, making use of mass, time, and length, is that analysis viewed as incorrect or deficient? 

 

If not, then we necessarily have a connection between energy and magnetic pole strength, which I found intriguing. I am open to the possibility that his analysis is dated, which is really the question I am posing.

Edited by Feynmanfan85
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13 minutes ago, Feynmanfan85 said:

Maxwell's equations are expressed in generic units of mass, time, and length. Using kg, seconds, and meters should not impact his analysis, so long as those units are used consistently.

If you say so, I suppose it must be true and the discussion can proceed no further.

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