# Calculating the force acting between to magnets

I am using neodymium N52 magnets in a project I'm working on, and I have been attempting to calculate the force between them. I just wanted to double check my results with the community and hopefully get some advice as the graph looks as expected, but the numbers are very very large.

This is the main equation i am using to calculate force. (as per Ravaud, R; Lemarquand, G; Babic, S; Lemarquand, V; Akyel, C (2010): https://ieeexplore.ieee.org/document/5458080 ; further information: https://en.wikipedia.org/wiki/Force_between_magnets )

$$F(x)\simeq \left[\frac {B_0^2 A^2 \left( L^2+R^2 \right)} {\pi\mu_0L^2}\right] \left[{\frac 1 {x^2}} + {\frac 1 {(x+2L)^2}} - {\frac 2 {(x+L)^2}} \right]$$

where

B0 is the flux density very close to each pole, in [T, = 0.71]
A is the area of each pole, in m2, [A = 3.142]
L is the length of each magnet, in m, [L = 0.005]
R is the radius of each magnet, in m, and [R = 0.01]
x is the separation between the two magnets, in m  ranges from [x = 0.1, to x = 0.57]


Finally, i used the following equation to calculate the magnetic flux density (according to Chikazumi, Sōshin (1997)):https://en.wikipedia.org/wiki/Magnetization

$$B_0 \,=\, \frac{\mu_0}{2}M$$

such that $$\mu_0 = 4\pi\times 10^-7$$ and $$M = mv$$. V being the volume of the magnet ($$0.126m^3$$) and m being magntisation $$M=(1/\mu_o)B_r$$

at the maximum distance of 0.57m, the force produced by the two magnets is = 16.5148088143021N, at the minimum distance, i get a force = 15581.3960030775N.

I have managed to fix a few mistakes this morning, so the numbers are looking a bit more reasonable, but wanted to double check with the community if that's ok. I am just looking for advice on my line of thought, or whether I missed the mark entirely.

Many thanks Tony

## migrated from math.stackexchange.comJul 2 at 14:08

This question came from our site for people studying math at any level and professionals in related fields.

• I think this question would fit better into the physics or the engineering stackexchange. – klunkean Jul 2 at 9:14
• Looks more like physics as opposed to math to me? Also, the tag description tells us that electromagnetism should never be the only tag. – Jyrki Lahtonen Jul 2 at 9:14
• thanks.. i'll move it over there – Tony GR Jul 2 at 9:16
• Can you give a reference to where this equation is derived for curiosity's sake – Nadide Jul 2 at 9:20
• Hi Nadide, i added a few links in a recient edit, but this is the paper Cylindrical Magnets and Coils: Fields, Forces, and Inductances; Ravaud et al. (2010): ieeexplore.ieee.org/document/5458080 there is more information on a wiki page: en.wikipedia.org/wiki/Force_between_magnets – Tony GR Jul 2 at 9:28