How can the force between magnetic poles be accurately calculated?

[Jack123]

Hi, I was wondering if anyone could tell me how to calculate the attractive force between a pair of magnets. I orignally thought that this would involve a really simple formula (something of the 1 over r squared variety) but have struggled to find any equations dealling with the force between poles; they all seem to associate magnetic forces to charged particles.

The only formula I have found is located at this address:

http://geophysics.ou.edu/solid_earth/notes/mag_basic/mag_basic.html

In my experiment I was examining how the force of attraction between a solenoid and bar magnet of known strength (0.01 T) depended on current and number of turns of the solenoid as well distance between the two. I reasoned that the field of a solenoid is in effect the same as a bar magnet so I should be able to use the above formula.

However, the force I calculated was tiny, despite the fact that I could physically feel the attraction when I suspended the magnet over the solenoid. When I measured the force I found it to be on the order of around a tenth of a Newton, hundreds of times greater than the number I had obtained from the above equation.

So what am I doing wrong?

 

[MagnetDave]

The result is heavily dependent on the geometry and material of the situation. A "bar" magnet encompasses a wide variety of things that all perform very differently. If you envision your bar as a thin sheet, with the direction of magnetization in the thin axis, it will be close to useless. Conversely, if you make a baton, with the DOM in the long direction, it's quite powerful. Similarly, a Neo magnet will be different than a Samarium magnet, will be different than an Alnico...

In short, the situation is not very amenable to a quick-and-dirty formula. You should look into FEMM, which is a simple, free, 2D finite element code so that you can at least get some order-of-magnitude level calculation done.

 

[Meir Achuz]

That formula is for a pole far away from another pole.
The force depends on just where the magnet is put.
If the bar magnet is placed just at the end of the solenoid, then the force is given by
F=BB'A/(2pi), where B and B' are the strengths in gauss, and A is the cross-sectional area of the bar magnet
(in cm^2).