# Force between two neodymium permanent magnets

MigMRF
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

Gold Member
2022 Award

"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.

MigMRF

"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?

Gold Member
2022 Award
• anorlunda
MigMRF
Well, it's pretty complicated. Maybe for a first overview Wikipedia is a good starting point:

https://en.wikipedia.org/wiki/Force_between_magnets
Well, thanks anyways. Might to it experimentally then and end up with a inverse square or cube relation.