field of 2 attracting cylindrical bar magnets
field of 2 repelling cylindrical bar magnets
the force between 2 identical cylindrical bar magnets placed end end @ great distance
x
≫
r
{\displaystyle x\gg r}
approximately:
f
≃
[
b
0
2
a
2
(
l
2
+
r
2
)
π
μ
0
l
2
]
[
1
x
2
+
1
(
x
+
2
l
)
2
−
2
(
x
+
l
)
2
]
{\displaystyle f\simeq \left[{\frac {b_{0}^{2}a^{2}\left(l^{2}+r^{2}\right)}{\pi \mu _{0}l^{2}}}\right]\left[{\frac {1}{x^{2}}}+{\frac {1}{(x+2l)^{2}}}-{\frac {2}{(x+l)^{2}}}\right]}
where
b0 flux density close each pole, in t,
a area of each pole, in m,
l length of each magnet, in m,
r radius of each magnet, in m, and
x separation between 2 magnets, in m
b
0
=
μ
0
2
m
{\displaystyle b_{0}\,=\,{\frac {\mu _{0}}{2}}m}
relates flux density @ pole magnetization of magnet.
note these formulations based on gilbert s model, usable in relatively great distances. other models, (e.g., ampère s model) use more complicated formulation cannot solved analytically. in these cases, numerical methods must used.
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