Magnetization and magnetic susceptibility

1. Nov 17, 2013

smantics

For magnetization which can be written as $\vec{B}$ = μ(o) ($\vec{H}$ + $\vec{M}$) , how would it be expressed as a function of N (number density N atoms per unit volume), μ , magnetic-field Bo, T, and some constants (Boltzman's constant, Curie constant)? I have found similar set ups from different sources, but I am unsure which I should use. What I have come up with so far is (some of these are equivalent to others):

B/t = ( $\frac{K(b)}{μ}$) tanh-1($\frac{M(z)}{N*μ}$)

M = μ tanh ( $\frac{μ*B(effective)}{K(b) * T}$ )

M(z) ≈ $\frac{N*μ^2*B}{K(b)*T}$ = $\frac{n*μ(b)^2 * H}{K(b) * T}$

M = N * μ * L($\frac{μ * H}{K * T}$ )

Then to find the low-field magnetic susceptibility which is $\vec{M}$ = xm * $\vec{H}$ should I use:

xm = $\frac{N*μ^2*B(o)*H}{K(b)*T}$

xm = $\frac{μ(o)}{V}$ * $\frac{∂M}{∂H}$

xm = $\frac{N}{V}$ * $\frac{μ(o)*μ(b)^2}{K(b)*T}$

xm = $\frac{C}{T}$

xm = μ(o)*μ(b)^2*g(E(f))

I feel like the 3rd equation for the Magnetization would be the correct one to use, and the 1st equation for the magnetic susceptibility would be the correct one to use.