# Force between two neodymium permanent magnets

• MigMRF
In summary: J_z0Oa_9RRAIn summary, the conversation discusses the calculation of magnetic force between two magnets and the effects of two magnetic fields on each other. The first question is about the calculation of magnetic force, while the second question is about the interaction between two magnetic fields. The response suggests considering the magnetic field of one magnet as a dipole field and using dipole-dipole interaction to calculate the force. It also mentions the complexity of the topic and suggests looking at textbooks or experimenting to understand the concept better.
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

"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.

vanhees71 said:

"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?

vanhees71 said:
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.

You can see the inverse square law explained in Episode 34 of the The Mechanical Universe:

## 1. What is the force between two neodymium permanent magnets?

The force between two neodymium permanent magnets is the attraction or repulsion that occurs between them due to their magnetic fields. This force is dependent on the strength of the magnets, the distance between them, and the orientation of their poles.

## 2. How is the force between two neodymium permanent magnets calculated?

The force between two neodymium permanent magnets can be calculated using the formula F = (m1 * m2)/(4 * π * d^2), where m1 and m2 are the magnetic moments of the two magnets and d is the distance between them.

## 3. What factors affect the force between two neodymium permanent magnets?

The force between two neodymium permanent magnets is affected by the strength of the magnets, the distance between them, and the orientation of their poles. It is also affected by the magnetic permeability of the materials between the magnets and any external magnetic fields that may be present.

## 4. Can the force between two neodymium permanent magnets be increased?

Yes, the force between two neodymium permanent magnets can be increased by increasing the strength of the magnets or decreasing the distance between them. However, it is important to note that there is a limit to how close the magnets can be before they physically repel each other.

## 5. What are some common applications of the force between two neodymium permanent magnets?

The force between two neodymium permanent magnets is utilized in many everyday applications, such as magnetic closures on bags or purses, magnetic clasps on jewelry, and magnetic latches on cabinet doors. It is also used in more advanced technologies, such as magnetic levitation trains and magnetic resonance imaging (MRI) machines.

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