Modeling Magnetic Dipole Interaction Between Permanent Magnets

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Discussion Overview

The discussion revolves around modeling the interaction between permanent magnets, specifically focusing on the equations and software needed to simulate their behavior as they rotate and translate towards each other. Participants explore various approaches to represent the magnetic forces and motions involved, considering both theoretical and computational aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest modeling each magnet as a dumbbell with mass concentrated at the poles to analyze the forces and motion.
  • There is a discussion about the lack of equations for magnetic monopoles, with some participants questioning whether such equations can be derived from existing magnetic dipole equations.
  • One participant mentions that the basic equation of magnetic force is based on the concept of a monopole, while another challenges this by referencing the Biot-Savart law and its limitations.
  • Some participants propose that the magnetic field from a monopole follows Coulomb's law, drawing parallels between electric and magnetic fields, while noting differences in geometry.
  • There is a suggestion that Maxwell's equations are symmetric when monopoles are considered, leading to a discussion about the constants involved in replacing permanent magnets with electrons and their dipole moments.
  • Concerns are raised about the complexity of calculating the magnetic dipole moment, with one participant expressing uncertainty about the expected behavior of the dipole moment in relation to distance.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the modeling of magnetic interactions, the existence and implications of magnetic monopoles, and the appropriate equations to use. The discussion remains unresolved with no consensus on the best approach or the validity of certain claims.

Contextual Notes

Participants highlight limitations in existing models and equations, particularly regarding the treatment of magnetic monopoles and the complexities of calculating forces and motions in a magnetic dipole system. There is an acknowledgment of the need for further exploration and clarification in these areas.

tris_d
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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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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.
 
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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The basic equation of magnetic force (the inverse square law) is based on the concept of a monopole.
 
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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No - back before the dawn of time, when the unit of magnetisation was the Oersted. The world was a simpler place.
 
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?
 
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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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.
 

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