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Physics/A follow up question on calculating the required strength of an electromagnet


Hi Steve,

Thanks very much for your reply to my question found here on calculating the required field strength of an electromagnet.
I seem to be having trouble with getting my emails from allexperts, so I am trying using a different one now - hopefully this will work as normal. (Unfortunately that means I was not able to rate your answer, which would be ten out of ten on all fronts as usual. Thanks again.)

Your answer had so much to it, that I am only going to ask a question about some of the elements for now, as I am going over it one step at a time!

I had not considered the distance between the electromagnet and the permanent magnet as a factor in determining the required strength of the electromagnet, thank you for putting me on to it.
I looked at the link you sent me and my eye was drawn to the sentence  "For small values of , the results are erroneous as the force becomes large for close-to-zero distance." The distance between my electromagnet and the permanent magnet is 0.5 mm, however the magnets themselves are also very small. The electromagnet is 2.7 mm long and 1.4 mm in diameter, for example, and the permanent magnet is of similar dimensions. In this case, should I assume that a distance of 0.5 mm is not a "close-to-zero distance" given the small dimensions of the magnets I am using, or will the magnetic field likely experience little/no decrease over this distance?

Actually, I will have a number of these electromagnet/permanent magnet tube combinations sitting next to each other, spaced 2.5 mm apart. I want to activate them independently, and I really do not want the field of one magnet tube interfering with an adjacent tube.

I am assuming that the minimum field strength produced by the electromagnet required to repel the permanent magnet at 0.5 mm will be too weak to affect another identical magnet 2.5 mm away, given that the electromagnet's field strength would decrease by a factor of 25. My reasoning being that 2.5 is five times as large as 0.5 - and five squared is 25. Have I got that correct? (I am really not sure of myself here!)
I have read in other places people saying that the square becomes cube as the distance increases. If this is correct, it is still very hard to know what constitutes the distance at which this happens, just as it is hard to know whether a distance of 0.5 mm is a close-to-zero distance, or indeed whether 2.5 is a close-to-zero distance as well.
Can I still use the formula on the link you sent me under the section, "Force between two cylindrical magnets" when dealing with these distances? If so, can you tell me - when the page says of the formula that "M is the magnetization of the magnets and x is the distance between them", how can I put M into the formula? Is that the combined magnetic fields of both magnets in Tesla?

Sorry for such a long question. As ever, thank you kindly for the considered, thorough and clearly explained answers you have given me. It is not easy to find someone who knows about this stuff, and can also explain it well. I appreciate it.


Hello Eddie,

I'll address each of your questions with a quote from your post as a heading for each new topic.

For small values of , the results are erroneous:
They are saying that the intent of the formula is to give an approximation of the resulting force but that the accuracy of the approximation diminishes when x is less than h. I would expect the approximation to work as well on your small scale dimensions. Meaning that I think the accuracy of the formula would deteriorate according to the value of x/h, regardless of the size of the magnets. So I believe the formula would be as good with your dimensions as it would be if all dimensions were increased by a factor of 100. When you said your distance was 0.5 mm, is that the condition when the permanent magnet is repelled? If so, then I would expect the force to be greater than the formula predicts. Notice that I don't really know at what value when decreasing x the discrepancy becomes significant. I think I have suggested before that experimentation is important.

My reasoning being that 2.5 is five times as large as 0.5 - and five squared is 25:
You are correct in that analysis. Another thing in your favor here is that the formula applies best when the axes of the magnets are aligned. Electromagnets in the adjacent tube would definitely not be  aligned, therefore unlikely to cause you a problem, provided the magnetic fields are not significantly stronger than required to do the job.

Can I still use the formula ... when dealing with these distances?:
Yes, the size of x compared to h is the important thing.

how can I put M into the formula?:
It is M^2 in the formula because they assume 2 equal magnets. If they are unequal, you would multiply the 2 values together. M is magnetization, one of many magnetic properties. The unit for M is amperes/meter.

Is that the combined magnetic fields of both magnets in Tesla?:
Similar. 1 T = 10^4 G = 10^7/(4*pi) ampere/meter = 795774 a/m
Perhaps these sites will help.

I hope this helps,


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Steve Johnson


I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.


I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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