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# modeling the magnetic field of multiple magnet bars

## modeling the magnetic field of multiple magnet bars - Physics Forum

### modeling the magnetic field of multiple magnet bars - Physics Forum. Discuss and ask physics questions, kinematics and other physics problems.

#1
08-23-2006, 05:18 PM
 laura Guest Posts: n/a
modeling the magnetic field of multiple magnet bars

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

#2
08-23-2006, 06:38 PM
 pom Guest Posts: n/a
modeling the magnetic field of multiple magnet bars

laura a écrit :
Hello,
I wonder if you want the magnet arrangement of the lowest energy or the
whole process of attaining this minimum.
Anyway, such a system takes a finite time to reach stability (the
experiment has been done with compass needles - very simple to build and
very nice).
In this case,you can calculate the state step by step, there is a
typical time constant of the modeled system. This has been done and is
still being done by research workers.
I think that there is an algorithm "floating" around. It takes big
amounts of computing resources , depending on complexity or scale.
At the moment, I cannnot say more as people are not back from the big
french holidays.
You can perhaps find something by searching for papers by authors like
Miltat or Thiaville.
I hope, that helps.
pom
#3
08-23-2006, 10:26 PM
modeling the magnetic field of multiple magnet bars

laura wrote:

Magnetic fields are tensor fields (i.e. pseudovector fields). Save for
a conventional definition of direction (N vs S) a simple magnetic
dipole field assigns a vector to every point in the space around it.

The 'magic' is that these fields are additive, so any magnetic field of
arbitrary complexity can be modeled by simple addition of the dipole
fields of individual magnets, to whatever degree of precision is
required. The situation is analogous to that of a series expansion of
a mathematical function. If you pick the components carefully it
becomes easy.

B(total)[x,y,z] = summation(i = 1 to infinity) B(i)[x,y,z]

summed over all dipoles, where B(i)[x,y,z] is the magnetic field
measured at the point (x,y,z) if the only magnetic dipole present is
the ith dipole.

Tom Davidson
Richmond, VA

#4
08-24-2006, 01:02 AM
 operator jay Guest Posts: n/a
modeling the magnetic field of multiple magnet bars

there will be regions of 'ferromagnet' and regions of 'air' upsetting
superposition, and also nonlinear magnetic / saturation properties of the
ferromagnets, no?

#5
08-24-2006, 08:23 AM
 pom Guest Posts: n/a
modeling the magnetic field of multiple magnet bars

operator jay a écrit :
Hello,
well I think that the size of the permanent magnets (ferromagnetic
region) was supposed negligible in respect to the distance of the dipoles.
Also: those permanent magnets should be of sufficiently high coercivity
to be able to neglect their change of magnetization in presence of an
external field.
Under these conditions, the dipole fields are well superposable as
pointed out (and implied in my previous answer).
Pom
#6
08-24-2006, 07:07 PM
 pom Guest Posts: n/a
modeling the magnetic field of multiple magnet bars

operator jay a écrit :

Hello,
I would say yes to all your remarks.
Energy minimum can be thought of as the final stable configurations.
There might be several on account of frustration, eg. triangular lattice
of dipoles.
So long
pom

 Tags bars , field , magnet , magnetic , modeling , multiple

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