modeling the magnetic field of multiple magnet bars

- L
- laura
  
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posted
17 years ago

Wed, Aug 23, 2006 5:19 PM

Hi all,

I have several magnets (bars) of well known size.

These magnets are placed on a table and they can rotate around their center until they reach a stable state.

I want to know if there are some mathematical formulas which can describe the interaction in this system.

I've found a formula which describes the force between two identical cylindrical bar magnets placed end-to-end.

But, I need a more general formula where multiple magnets are involved and are not always placed end-to-end.

Is there such formula?

thanks, laura

- J
- John Woodgate
  
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posted
17 years ago

Wed, Aug 23, 2006 5:55 PM

In message , dated Wed, 23 Aug 2006, laura writes

Possibly, but I can assure you, you WOULD NOT like it.

It's similar, but not identical, to the n-body problem in gravitics, which is analytically insoluble in the general case.

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John Woodgate, J M Woodgate and Associates, Rayleigh, Essex UK

- P
- Phil Hobbs
  
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posted
17 years ago

Wed, Aug 23, 2006 6:59 PM

If they're far enough apart that the interactions are weak, you can model them as magnetic dipoles of constant strength. Higher-order multipoles aren't that terrible either. See *Classical Electrodynamics* by J. D. Jackson or whatever your favourite E&M text is. With some measurements, you can fit the multipole coefficients and make this as accurate as you like.

If you have significant nonlinear interactions (i.e. one magnet causing significant magnetization in another one) then this problem doesn't have a unique solution, because all the magnets' strengths will depend on previous history. For example, if you put an alnico magnet and a NdFeB together N to N, they will repel at long distances and attract at smaller ones, as the NdFeB first induces magnetization in the alnico, and then permanently reverses its remanent magnitization.

Cheers,

Phil Hobbs