Magnetization and magnetic susceptibility

[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 $\vec{M}$ = x_m * $\vec{H}$ should I use:

x_m = $\frac{N*μ^2*B(o)*H}{K(b)*T}$

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

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

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

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.

 

[eljose79]

It looks like you have done some good research and have come up with several possible equations for expressing magnetization and magnetic susceptibility in terms of N, μ, magnetic field Bo, T, and constants. However, it is important to note that the exact equations to use may depend on the specific system you are studying and the assumptions you are making.

For example, the first equation you have listed for magnetization assumes a homogeneous magnetic field and uses the hyperbolic tangent function to account for the non-linear behavior of the magnetization. This may be a good choice for certain systems, but may not accurately reflect the behavior of others.

Similarly, the equations for magnetic susceptibility also make different assumptions and may be more or less appropriate depending on the system you are studying. It is important to carefully consider the assumptions and limitations of each equation before deciding which one to use.

Additionally, it is always a good idea to consult with other sources and experts in the field to ensure that your equations are accurate and appropriate for your specific research.