# Is it possible to calculate the magnetic force between magnets?

## Main Question or Discussion Point

Hello
I am a a grade 11 learner and I am trying by all means to calculate force between magnets.
I know that the strength of a magnetic field is determined by the size of the magnet.

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mfb
Mentor
In general this is a very complicated problem and needs numerical simulations. Sometimes it is possible to get good analytic approximations, but it depends on the setup.

• mohau tshekoeng
CWatters
Homework Helper
Gold Member
+1

For some situations the equations have been done for you. Example...

https://en.m.wikipedia.org/wiki/Magnet#Force_between_two_bar_magnets

However I remember reading a comment once on a magnet manufacturers web site. Basically it said that their own experiments suggested such equations rarely matched reality very well. They advised that you may need to do your own experiment if the exact force is important.

+1

For some situations the equations have been done for you. Example...

https://en.m.wikipedia.org/wiki/Magnet#Force_between_two_bar_magnets

However I remember reading a comment once on a magnet manufacturers web site. Basically it said that their own experiments suggested such equations rarely matched reality very well. They advised that you may need to do your own experiment if the exact force is important.
Magnet manufacturers??
Well one thing for sure is that force is impacted by size,distance at which magnets are placed from one another and velocity...
If a formula can be constructed by those 3 factors there might be progress

mfb
Mentor
The force does not depend on the velocity, unless we are talking about relativistic speeds.
It does depend on the relative orientation between the magnets, and of course on the magnets itself and their distance.

CWatters
Homework Helper
Gold Member
Magnet manufacturers??
I was referring to comments like this...

https://www.kjmagnetics.com/calculator.asp

Many online calculators we've seen determine pull force based on a theoretical calculation of the flux density. With a few assumptions, flux density (in Gauss) can be related to the expected pull force. Unfortunately, this simplification often fails to match experimentally measured data.

The force does not depend on the velocity, unless we are talking about relativistic speeds.
It does depend on the relative orientation between the magnets, and of course on the magnets itself and their distance.
Does this mean I interpreted Lorenz force law in another way??

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mfb
Mentor
The Lorentz force allows to find the force between a magnet and a moving charge. Your magnets are not moving charges. If you have an electromagnet, then in principle you can apply the Lorentz force to the electrons moving in the conductor - but then you need the speed of the electrons in the object, not the speed of the object itself. A permanent magnet does not have moving charges in the classical sense, so even the approach with internal velocities does not work there.

Hesch
Gold Member
A magnetic field ( between two magnets ) has an energy density,

Edens= ½ * B * H [ J/m3 ].

If the magnets are close to each other, the magnetic field in the airgap will be almost homogenous. So the force on the magnets will be:

F = dE/ds , where s is the width of the airgap, and E = Edens * (volume of airgap).

In the above line 2, remember that H = B/μ0 ( in air ).

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