Force between two neodymium permanent magnets

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  • #1
MigMRF
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So I was wondering how I calculate the magnetic force between two magnets. When we learned about magnets, we only covered magnetic fields and electricity (laplace's law) and how electricity can create a B-Field. But how will two B-fields (or magnets) affect each other? Is there a simple formula (like F=L*IxB)? And how does the range between the mangets affect the force?

I hope that someome has the answer
 

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  • #2
vanhees71
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I'm a bit unsure what you are asking, because you ask to different questions. Let me start with the second:

"But how will two B-fields (or magnets) affect each other?"

As far as Maxwell's equations in a vacuum are concerned (and neglecting quantum effects) these are strictly linear, i.e., "two electromagnetic fields" (i.e., the two parts of the em. fields orginating from two independent charge-current distributions) superimpose themselves simply, i.e., ##\vec{E}=\vec{E}_1+\vec{E}_2##, ##\vec{B}=\vec{B}_1+\vec{B}_2##.

The first question is a bit more complicated.

If you have two permanent magnets at not too close distances the most simple idea is to consider the magnetic field of one of the magnets as a dipole field at the place of the other magnet, which you describe approximatelly by its magnetic moment. Then you have a dipole-dipole interaction, which you can find in many textbooks.
 
  • #3
MigMRF
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I'm a bit unsure what you are asking, because you ask to different questions. Let me start with the second:

"But how will two B-fields (or magnets) affect each other?"

As far as Maxwell's equations in a vacuum are concerned (and neglecting quantum effects) these are strictly linear, i.e., "two electromagnetic fields" (i.e., the two parts of the em. fields orginating from two independent charge-current distributions) superimpose themselves simply, i.e., ##\vec{E}=\vec{E}_1+\vec{E}_2##, ##\vec{B}=\vec{B}_1+\vec{B}_2##.

The first question is a bit more complicated.

If you have two permanent magnets at not too close distances the most simple idea is to consider the magnetic field of one of the magnets as a dipole field at the place of the other magnet, which you describe approximatelly by its magnetic moment. Then you have a dipole-dipole interaction, which you can find in many textbooks.

Thanks for the quick reply :)
Sadly I'm looking for a way to calculate the first question, how two magnets interact and what force magnet 1 will apply to magnet 2.
Correct me if I'm wrong, but are you saying, that i should let one of the magnets "act" like the B-Field and then let the second magnet be like a particle in this field?
The reason why I'm asking these question, is because I really want to calculate how a Gauss rifle works. So in fact it's now two neodymiummagnets that interact, but rather a neodymium magnet and a ferromagnet (a steel ball). Will this change anything. And lastly: You say, that many textbooks will tell me how to calculate a dipole-dipole interaction. I have been looking all over the internet, but I'm yet to find anything like that. Could you maybe tell me a bit more?
 
  • #6
Mister T
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You can see the inverse square law explained in Episode 34 of the The Mechanical Universe:

 

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