B, H fields due to a magnetized material everywhere

[AxiomOfChoice]

If we consider a material with uniform magnetization [tex]\vec M[/tex], what are the [tex]\vec B[/tex] and [tex]\vec H[/tex] fields everywhere in the magnetic material? My first inclination is to say that [tex]\vec H = 0[/tex] since there are no free currents and that therefore [tex]\vec B = \mu_0 \vec M[/tex] everywhere, but I can think of situations where there's no free current but there's still an [tex]\vec H[/tex] field (e.g., inside and outside a uniformly magnetized sphere), so I'm probably wrong.

 

[Vailanor]

The answer is that \vec B = \mu_0 \vec M everywhere in the magnetic material, but \vec H can be non-zero depending on the geometry of the material. For example, inside a uniformly magnetized sphere, \vec H will be non-zero due to the presence of surface currents induced by the uniform magnetization. Outside the sphere, \vec H will be non-zero due to the presence of free currents induced by the uniform magnetization.