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I have an axially magnetized neodymium magnet of diameter $d$ and height $h$. The material is N42. I would like to derive a formula for the pull force.

This calculator does it: https://www.kjmagnetics.com/calculator.asp

So my question is basically: what formula does this calculator use for cylindrical magnets? It is enough to consider the pull force for magnet-steel for distance=0 and N42 grade.

Thanks.

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The website provides answers to FAQ, including 11. How is the pull force of each magnet determined? which explains that "All of the pull force values we specify have been tested in our laboratory."

FAQ #12 explains futher that "Most other online calculators are based on theoretical formulas, which are notoriously inaccurate, especially for very large or very small sizes. Our fanatical engineers have worked long and hard in the laboratory developing our online calculators that are VERY accurate based on thousands of test cases."

If your interest is practical, you could create a table of values from the website, covering the range which you intend to use, and interpolate between them. If your interest is theoretical, take a look at Force between two point dipoles.

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  • $\begingroup$ Can you explain the last sentence? If it induced a mirror image magnet, wouldn't they repel? $\endgroup$
    – mrk1357
    Commented Apr 30, 2017 at 21:35
  • $\begingroup$ Or is it mirror image, except the direction of the spins, which is the same as the original magnet? $\endgroup$
    – mrk1357
    Commented Apr 30, 2017 at 21:37
  • $\begingroup$ I am not very sure that the method of images can be applied to the magnet in the presence of an iron plate, so I have removed it from my answer. $\endgroup$
    – sammy gerbil
    Commented Apr 30, 2017 at 21:54

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