Additionl field proportional to magnetisation?

[jd12345]

Magnetisation of a sample is net dipole moment per unit volume i.e. M = m(net) / V

It turns out that magnetic field due to the material is proportional to magnetisation
i.e. B(magnetic field due to material) = μM
Any explanation to this? It should be proportional but any proof for this or is it just experimental

 

[tiny-tim]

hi jd12345!

Magnetisation of a sample is net dipole moment per unit volume i.e. M = m(net) / V

It turns out that magnetic field due to the material is proportional to magnetisation
i.e. B(magnetic field due to material) = μM
Any explanation to this? It should be proportional but any proof for this or is it just experimental

isn't it B = µ_o(M + H) = µH ?

M and H are measured in electric units, as electric current/distance (Am^-1),

(magnetic dipole moment is charge times distance/time, = distance times charge/time = distance times electric current, in A.m)

but B is measured in magnetic units, as magnetic flux/area (Wb.m^-2)

there's no fundamental reason for this … they're all the same thing! … it's just more convenient in practice!

so to convert between these different species of units, we must have a universal conversion factor, and that's µ_o (in Wb.A^-1m^-1 or T.m.A^-1)

µ (as opposed to µ_o) is just a trick to make it look as if B is proportional to H on its own​