# I How to calculate force caused by magnets?

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1. Jul 11, 2016

### maglove

I am trying to calculate the forces between a simple sphere neodymium magnet on other iron surfaces and magnets. I did a lot of research but still not sure what equation to use or how to apply them. I found the following equations here (https://en.wikipedia.org/wiki/Force_between_magnets)
F = μo* H² *A/2 = B² *A/(2*μo)
i am not sure what H and B are, how they are used and what is the difference between them. Also if perhaps there is a better equation (with the reference) for spherical magnets. I just want an estimate so the simpler the better. Thanks in advance
[ moderator note: minor presentation editing ]

Last edited by a moderator: Jul 12, 2016
2. Jul 11, 2016

### Hesch

H is the magnetic field strength, [ A/m ], that can be compared to electric voltage

B is the magnetic induction, [ Tesla ], that can be compared to elctric current density.

So the magnetic flux, [ Wb ], = ∫ B⋅dA can be compared to electric current.

The magnetic energy density = ½*B*H [ J/m3 ]. Through and between two magnets, the B-field will be constant ( as current through resistors in series ). But the H-field will not be constant ( as voltage across different resistors in series ). The H-field will be much higher in the airgap between two magnets, than inside the magnets, due to different magnetic permeabilities inside/outside the magnets.

B = μ * H → H = B / μ

Hence the magnetic energy density will be much higher in the airgap than in the magnets.

Now, the nature wants to get rid of high magnetic energy density, one way or another. So if the airgap could be substituted by magnet, the energy density will be lowered. That's why the magnets attrack each other.

Knowing the magnetic energy densities inside/outside the magnets and the volume of the airgap, You can calculate the force by:

F = dE/dV

where E is the energy and V is the volume of the airgap. In other words: How much magnetic energy will be used, when two magnets are closed up 1 mm.

If you calculate that, you will come up with something like your wiki-formula.

Last edited: Jul 11, 2016