this is not so simple to answer quickly in a forum page.
yes M depends on H in a complex way. in ferromagnetic materials you even have hysterysis, which means that the past history of H is also relevant. and if you don't have hysterysis, you may have nonlinearities. in superparamagnetic materials, meaning that in subdomain magnetic materials (which means that you are dealing with a really small ferrite particle), you don't observe hysterysis so we can safely ignore the effects of it for now.
now suppose there is some H field applied in one direction. if all of the magnetic moments of the particle alligns with the field (ignoring the effects of thermal agitations), you reach to saturation magnetization and you cannot get more than that even if you apply an infinite amount of H field. now suppose you decrease your field, H, to zero slowly. you will be likely to observe a linear dependence of magnetization to H. the slope of this dependence is likely to be determined by experimentation. so you can safely incorporate the value this slope to your model to determine the absolute permeability, in the case that you have low fields and you don't deal with hysterysis.
if you want to include the effects of thermal agitation, you have to solve for the boltzman distribition and so on, and you end up with the langevin equation. and if i remember correctly, in the case of low fields, it turns out that the dependence is also linear, just the magnitude of the saturation magnetization becomes less.
this was for the static case. as for the dependence of the magnetization to time varying H fields, the issue becomes complicated, in which case you have to incorporate some "phenomological" dynamic equations of the relaxation of the magnetization on the H field (this is similar to spin relaxation in magnetic resonance imaging), and also you have to account for the relaxation of the magnetization distribution into allowable thermodynamic equilibriums and eventually relaxing into one of the preferred direction and so on eventually ending up with some frequency dependent complex permeability.
hope this helps.
SuccessTheory said:
Homework Statement
I am doing a project for which I am learning some aspects of electromagnetism by myself, so you can imagine how lost I am. Well, not completely: I was searching for a ferrite with high permeability as a core material. I learned how the octahedral and tetrahedral sites and the unpaired electrons within the ferrite structure contribute to magnetization. So I went ahead and calculated the saturation magnetization of a ferrite that had a high magnetic moment per molecule.
μ: absolute permeability, μ0: permeability of free space, M: magnetization, H: magnetic field strength, B: magnetic flux density
Homework Equations
Now I don't know how to go from this saturation magnetization to absolute permeability. I know:
B = μ H and B = μ0 (H + M)
putting the two together I have:
μ = μ0 + (μ0 M)/H
The Attempt at a Solution
I don't know how to deal with H to solve for μ (I calculated M and μ0 is a constant). I know H is the applied field strength but I just read that generally M is also a complex function of H... so I don't think I can use any H but the H that gives my saturation magnetization, M. Any help on going from M to μ would be appreciated.
