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I am trying to find the equation for calculating the direction and magnitude of $B$ and/or $H$ at a distance from a dipole magnet but my searches are proving impossible.

So far I have found the calculation for the magnitude of $B$ of a single wire at distance $r$ and I know the direction is found with the right-hand rule but I cannot find anything to do with permanent magnets, in particular the vector quantity.

I know the field will want to travel from the north pole to the south pole but the field doesn't take the shortest route, it has a sort of "trajectory" if you look at pictures?


Sod's Law

I make this post then I found this: http://en.wikipedia.org/wiki/Dipole#Field_of_a_static_magnetic_dipole

One thing I am unclear on is $\bf r$, which is:

$\bf r$ is the vector from the position of the dipole to the position where the field is being measured

What point on the dipole is this vector calculated from? The north pole, the south pole, the center of the dipole?

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  • $\begingroup$ I have the impression that he is interested especially in the short distance calculation, so a simple dipolfield formula won't be enough. $\endgroup$ – peterh says reinstate Monica Nov 26 '13 at 22:26
  • $\begingroup$ Most probably, and for that he would need to do numerical stuff instead of starting from an analytic expression. $\endgroup$ – Ignacio Vergara Kausel Nov 27 '13 at 9:48
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In principle you could think of it as the center of the dipole.

The solution given, is for the field far from the dipole (distance from the dipole to the point much bigger than the size of the dipole). Given that, the size of the dipole is rather irrelevant and it's considered as a point.

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  • $\begingroup$ Hmm, the distance I'm interested in is 0 - 1m, what formula should I use for these distances? $\endgroup$ – Lerp Nov 27 '13 at 8:54
  • $\begingroup$ It all depends on the size of the dipole. Certainly it won't work for distance close to 0 m for any size of dipole. $\endgroup$ – Ignacio Vergara Kausel Nov 27 '13 at 8:55
  • $\begingroup$ Okay, I will need to, first, model the field of a small bar magnet, either 6" x 4" x 1" Ferrite or 50mm x 50mm x 12mm NdFeB. Then I will need to model the field of a block made up of those magnets, which can be up to 800mm x 400mm. As a secondary question; at what distances is the dipolfield formula suitable? $\endgroup$ – Lerp Nov 27 '13 at 9:07
  • $\begingroup$ There should be some rule of thumb for that estimation, but I'm unaware of it. I would say that for distances 10 times bigger than the dipole size should be a good starting point. $\endgroup$ – Ignacio Vergara Kausel Nov 27 '13 at 9:47

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