Modeling Magnetic Dipole Interaction Between Permanent Magnets

In summary, two permanent magnets will rotate and translate until they stick together if they have an arbitrary orientation. If you treat each magnet as a dumbbell of fixed length with all the mass concentrated in the poles, you can model the forces on each pole and iterate the motion. Some possible motions are chaotic, but treating each pole separately may solve the problem.
  • #1
tris_d
162
0
Two permanent magnets are on the table some distance apart and having some arbitrary orientation relative to each other. When we let go of them they will rotate and translate until they stick together. I am looking for suitable equations to model this interaction on a computer. Also, if anyone knows some software that can already do this please let me know.
 
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  • #2
I would suggest to treat each magnet as a dumbbell of fixed length with all the mass concentrated in the poles.
It's then possible to model all of the forces on each pole and iterate the motion.

Some possible motions could be chaotic though.
 
  • #3
AJ Bentley said:
I would suggest to treat each magnet as a dumbbell of fixed length with all the mass concentrated in the poles.
It's then possible to model all of the forces on each pole and iterate the motion.

Some possible motions could be chaotic though.

You mean to treat each pole separately? I don't think there is such equation since magnetic monopoles are not supposed to exist, but that does seem to be the right direction to approach this problem.


So far I only found this equation:
http://en.wikipedia.org/wiki/Magnetic_dipole_moment

87ee5b0ca7607534ce921bb60738a13c.png


The problem is that only tells me how much will they attract, but not how much will they rotate and how much will they translate. You suggestion might solve this problem as instead of one force I would have two, and that would hopefully model rotation and thus possibly solve the whole problem. All I need now is some equation for it. Do we have equation for magnetic monopoles, or can it be derived from the equation above?
 
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  • #4
The basic equation of magnetic force (the inverse square law) is based on the concept of a monopole.
 
  • #5
AJ Bentley said:
The basic equation of magnetic force (the inverse square law) is based on the concept of a monopole.

733b90b9f3344eb6393eba29284d3447.png


You mean Biot-Savart law, magnetic field due to moving charge? That's cylindrical magnetic field rather than "spherical", and is defined by the velocity vector. Right in front and behind magnetic field goes to zero as it gets aligned with the velocity vector (doughnut), so I don't think that would work as I don't think that's how individual poles of a magnetic dipole look like.
 
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  • #6
No - back before the dawn of time, when the unit of magnetisation was the Oersted. The world was a simpler place.
 
  • #7
AJ Bentley said:
No - back before the dawn of time, when the unit of magnetisation was the Oersted. The world was a simpler place.

What do you mean "no"? What equation are you talking about?
 
  • #8
Seems like the knowledge has been lost. lol!

The magnetic field from a monopole follows the coulomb law just like the electric field. Originally these two subjects were treated identically. You can substitute a pair of electric charges for your magnetic dipole and except for a few constants the mathematics are identical.
 
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  • #9
AJ Bentley said:
Seems like the knowledge has been lost. lol!

The magnetic field from a monopole follows the coulomb law just like the electric field. Originally these two subjects were treated identically. You can substitute a pair of electric charges for your magnetic dipole and except for a few constants the mathematics are identical.

I see. But the geometry should be different, field lines of an electric field are straight and radial, but magnetic field lines are circular. Still, the force lines might come up to be about the same, so it actually might work. It certainly is the best solution I have so far. Cheers!
 
  • #10
tris_d said:
I see. But the geometry should be different, field lines of an electric field are straight and radial, but magnetic field lines are circular. Still, the force lines might come up to be about the same, so it actually might work. It certainly is the best solution I have so far. Cheers!

The geometry is identical. The fields are identical. Maxwell's equations are symmetric (when monopoles are allowed) . Electric filed lines are not necessarily straight (Curl E ≠ 0). Everything is exactly the same except for the values of a few constants.
 
  • #11
AJ Bentley said:
The geometry is identical. The fields are identical. Maxwell's equations are symmetric (when monopoles are allowed) . Electric filed lines are not necessarily straight (Curl E ≠ 0). Everything is exactly the same except for the values of a few constants.

That's wonderful.

Ok, so if I wanted to replace the two permanent magnets with two electrons and their intrinsic dipole magnetic moment, how would I get the value I need to use for my monopoles?
 
  • #12
Well, the only change is that you use μ (permeability) in place of ε (permittivity)

You can use ε.μ = 1/c2 so it's just a case of sticking in a factor of c2
 
  • #13
AJ Bentley said:
Well, the only change is that you use μ (permeability) in place of ε (permittivity)

You can use ε.μ = 1/c2 so it's just a case of sticking in a factor of c2

That's a bit too much for me. I expected some actual number as electron's dipole moment is constant value. I think magnetic dipole moment drops with inverse cube not inverse square law, and both poles are taken into account, so I expected it would be more complex to obtain the value for each pole separately.
 

What is magnetic dipole interaction?

Magnetic dipole interaction is the force between two magnetic dipoles. A magnetic dipole is a small magnet with a north and south pole, similar to a bar magnet. This force is responsible for the attraction or repulsion between magnets and is also involved in the behavior of compass needles.

How does magnetic dipole interaction work?

Magnetic dipole interaction is caused by the alignment of the magnetic dipoles in the presence of a magnetic field. Like poles (north and north or south and south) repel each other, while opposite poles (north and south) attract each other. This interaction is described by the inverse square law, meaning the force decreases as the distance between the dipoles increases.

What are some real-world applications of magnetic dipole interaction?

Magnetic dipole interaction has several practical applications, such as in electric motors and generators, where it is used to convert electrical energy into mechanical energy and vice versa. It is also used in MRI machines, which use strong magnetic fields to create images of the inside of the body.

Can the strength of magnetic dipole interaction be changed?

Yes, the strength of magnetic dipole interaction can be changed by altering the strength of the magnetic field or by changing the orientation of the dipoles. For example, the strength of an electromagnet can be controlled by adjusting the current flowing through it, which changes the strength of its magnetic field.

How does temperature affect magnetic dipole interaction?

Temperature can affect the strength of magnetic dipole interaction. As the temperature increases, the thermal energy of the particles in a material also increases, causing them to vibrate more and interfere with the alignment of magnetic dipoles. This can weaken the strength of the interaction between dipoles, making them less magnetic.

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