Magnetization and magnetic susceptibility

  1. For magnetization which can be written as [itex]\vec{B}[/itex] = μ(o) ([itex]\vec{H}[/itex] + [itex]\vec{M}[/itex]) , 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 = ( [itex]\frac{K(b)}{μ}[/itex]) tanh-1([itex]\frac{M(z)}{N*μ}[/itex])

    M = μ tanh ( [itex]\frac{μ*B(effective)}{K(b) * T}[/itex] )

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

    M = N * μ * L([itex]\frac{μ * H}{K * T}[/itex] )


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

    xm = [itex]\frac{N*μ^2*B(o)*H}{K(b)*T}[/itex]

    xm = [itex]\frac{μ(o)}{V}[/itex] * [itex]\frac{∂M}{∂H}[/itex]

    xm = [itex]\frac{N}{V}[/itex] * [itex]\frac{μ(o)*μ(b)^2}{K(b)*T}[/itex]

    xm = [itex]\frac{C}{T}[/itex]

    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.
     
  2. jcsd
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