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):(adsbygoogle = window.adsbygoogle || []).push({});

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] = x_{m}* [itex]\vec{H}[/itex] should I use:

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

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

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

x_{m}= [itex]\frac{C}{T}[/itex]

x_{m}= 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.

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# Magnetization and magnetic susceptibility

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