Editing Magnet (section)

==== Force between two bar magnets ====

The force between two identical cylindrical bar magnets placed end to end at large distance <math>z\gg R</math> is approximately:{{Dubious|date=September 2017}},<ref name="tri-c"/>
:<math>F \simeq \left[\frac {B_0^2 A^2 \left( L^2+R^2 \right)} {\pi\mu_0L^2}\right] \left[{\frac 1 {z^2}} + {\frac 1 {(z+2L)^2}} - {\frac 2 {(z+L)^2}} \right]</math>

where:

:''B<sub>0</sub>'' is the magnetic flux density very close to each pole, in T,
:''A'' is the area of each pole, in m<sup>2</sup>,
:''L'' is the length of each magnet, in m,
:''R'' is the radius of each magnet, in m, and
:''z'' is the separation between the two magnets, in m.

:<math>B_0 \,=\, \frac{\mu_0}{2}M</math> relates the flux density at the pole to the magnetization of the magnet.

Note that all these formulations are based on Gilbert's model, which is usable in relatively great distances. In other models (e.g., Ampère's model), a more complicated formulation is used that sometimes cannot be solved analytically. In these cases, [[numerical methods]] must be used.