# Force between two permanent magnets at an angle

Hay all, first post (ohai2u! ^_^), so hope this is in the right place. I feel really stupid for having to ask this, because I'm sure the answer is really trivial, but here we go...

Ok so, imagine the scene - You have two permanent magnets on a table. Let's (for argument's sake) call these "Mag1" and "Mag2" respectively.

Now let's say that Mag1 is at position [0, 0] (x, y that is) and Mag2 is at say [5, 7].

Now let's say that Mag1 is at an angle of 0º to the x axis, and Mag2 is at 315º to the x axis. Of course these angles would be with respect to a line drawn from the south pole to the north pole of the given magnet.

Finally, let's say that all we know about the magnets are their length L in meters and their strength B in Gauss.

So simple question - what on earth is/are the equation(s) to calculate the force between these two magnets?

Calculating the force between two magnets when their poles are face-on is simple GCSE physics, but figuring out how to do it for any position / angle / orientation of the two magnets is proving elusive to me.

The one thing I have found is this article on magnetic moments on wikipedia:

http://en.wikipedia.org/wiki/Magnetic_moment#Forces_between_two_magnetic_dipoles

The diagram there (particularly the "local co-ordinates" part) appears to be pretty much exactly what I'm describing, but I'm unsure which equation would be most appropriate (if any), and I'm unsure how to get the values m1 and m2 described there (further up it mentions that m=pl, but what is p? Is p = B? Or is there some other equation somewhere to work it out from B?)

It feels like I'm close, I just need that extra nudge to get me over the hill lol. Hoping one of you can help me out here?

In case you're curious - I've always been a bit weak on my magnetics knowledge, but I've always found them interesting, so I'm currently trying to build a program to assit me in strengthening that understanding by letting me play with values and see what happens in response. The first step obviously is getting some basic / fundamental equations into it. Lol, stuck at the first hurdle, not a good start right? :P

CWatters
Homework Helper
Gold Member
Not really my subject but...

Perhaps consider that the force is not "between two magnets" but one magnet and the field that it's in. So you would need to work out the field at magnet 2.

I suspect it's horribly complicated for real world magnets. Might be easier if one was very small or a wire?

Lol sorry for my poor choice of phrase there - what you describe is exactly what im after (the force vactor acting on one of the magnets. Doesnt matter which one as assumedly an equal but opposite force would be acting on the other), in appose to the force at some point between them as I may have implied =)