Deriving the magnetic moment of a specimen in a given magnetic field

[1v1Dota2RightMeow]

Homework Statement

I'm working on a problem that says that
>If $\varepsilon_{\pm}=\mp (\mu \mu_0 H + k \theta \frac{M}{\mu N} )$ is the energy of the atom of a specimen that can orient itself either parallel or antiparallel in a magnetic field, show that $ \frac{M}{\mu N}= tanh(\frac{1}{kT}( \mu \mu_0 H + k \theta \frac{M}{\mu N}))$.

I'm not really sure how to make the 2 equal.

Homework Equations

$M=\mu Ntanh(x)$
$x=\frac{\mu B}{kT}$

The Attempt at a Solution

I tried setting $\frac{\mu B}{kT}= \frac{1}{kT}(\mu \mu_0 H + k\theta \frac{M}{\mu N})$ but it ended up with $\muB=0$ which can't be true.

 

[MisterX]

This is just reformatting for you.

Homework Statement

I'm working on a problem that says that
> If $\varepsilon_{\pm}=\mp (\mu \mu_0 H + k \theta \frac{M}{\mu N} )$ is the energy of the atom of a specimen that can orient itself either parallel or antiparallel in a magnetic field, show that $\frac{M}{\mu N}= tanh(\frac{1}{kT}( \mu \mu_0 H + k \theta \frac{M}{\mu N}))$.

I'm not really sure how to make the 2 equal.

Homework Equations

$M=\mu Ntanh(x)$
$x=\frac{\mu B}{kT}$

The Attempt at a Solution

I tried setting $\frac{\mu B}{kT}= \frac{1}{kT}(\mu \mu_0 H + k\theta \frac{M}{\mu N})$ but it ended up with $\mu B=0$ which can't be true.

 

[1v1Dota2RightMeow]

This is just reformatting for you.

How do I format my questions like that?

 

[berkeman]

How do I format my questions like that?

Just see the LaTeX primer under INFO, Help/HowTo: https://www.physicsforums.com/help/latexhelp/