I need to know how to calculate force between two bar magnets. I searched and found an answer on Wikipedia, but I don't really trust Wikipedia, a lot of crazy stuff is posted there.

So I searched again and didn't find an answer that matches Wikipedia's. So my question: Is Wikipedia's answer right?

  • $\begingroup$ It seems the source link for the wiki is also dead. All I can dig up is "it's difficult". This question has bothered me since high school. $\endgroup$
    – rubenvb
    Oct 23, 2013 at 7:54
  • $\begingroup$ It looks plausible and a "nice" exercise in integrating stuff. One way to check out if it works, would be to see what happens with the expression if you make the bars look like small dipoles and if the dipole force is recovered in such limit. $\endgroup$ Oct 23, 2013 at 9:26
  • $\begingroup$ More on force between two magnets: physics.stackexchange.com/search?q=is%3Aq+force+two+magnets $\endgroup$
    – Qmechanic
    Aug 21, 2014 at 7:48

1 Answer 1


Maybe using the electrostatic analogue you can get approximately valid results. As we know we can consider a magnet as a magnetic dipole and then do the maths for interaction of two dipoles as we would have done in the electrostatic realm.

The magnetic field due to a magnet at axis is taken to be as

$B_a= (2\mu m)/(4\pi r^3)$

And equatorially as $B_e = (\mu m)/(4\pi r^3)$.

Here $m$ is magnetic moment of magnet, $\mu$ is permeability of medium and $r$ is distance from centre of magnet. There is also the assumption that the magnet is small as compared to distance on which force is considered.

Now you can simple consider one magnets field at some distance and do simple calculations for magnet-field interaction for the other magnet.

Added as response to comment :

You can find fields at distance r-a and r+a from an electric dipole by either using this simplified formula or that long one from which this one is approximated. Then you can multiply them by charges that you have placed by placing the dipole, this will give you force on individual charges on added then you will get force on the dipole. This you can then use for analogue with magnetic dipole, replacing p by m (electric dipole moment by magnetic dipole) and the constant of electric force with that of magnetic one.

Note : i have omitted the mathematical proof here because of the various permutations in which the dipoles could be with respect to one another, still if some help is needed regarding a particular case i would be more than happy to help.

  • $\begingroup$ I already know how to calculate magnetic fields , i need to know how 2 will interact together and how to calculate the force between them. $\endgroup$
    – user28324
    Oct 23, 2013 at 11:44
  • $\begingroup$ last question : i found this ( en.wikipedia.org/wiki/… ) after finding the dipole moment , if i used this equation , will it be correct? $\endgroup$
    – user28324
    Oct 23, 2013 at 20:12
  • $\begingroup$ Sorry for not being of much help here, but since I do not have any idea of how they got the mentioned equations I can not make any comments. $\endgroup$ Oct 24, 2013 at 1:35
  • $\begingroup$ this equation only excited 15 years ago ,here's a reference if u want to read it en.wikipedia.org/wiki/… $\endgroup$
    – user28324
    Oct 24, 2013 at 4:43

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