- #1
patrickmoloney
- 94
- 4
Homework Statement
Find the magnetic moment of a crystal when placed
(i) in a weak field at high temperature
(ii) in a strong field at low temperature
Homework Equations
This is the last part of a question which I feel I have solved correctly up until this point.
The mean magnetic moment I found is
[tex]\langle M \rangle = N_{\mu} \frac{2 \sinh \Big{(}\dfrac{\mu \beta}{kT}\Big{)}}{1+ \cosh \Big{(}\dfrac{\mu \beta}{kT}\Big{)}}[/tex]
The Attempt at a Solution
Well at high temperature and low magnetic field strength
[tex]\dfrac{\mu \beta}{kT} \ll 1[/tex]
And at low temperature high magnetic field strength
[tex]\dfrac{\mu \beta}{kT} \gg 1[/tex]
What happens to the hyperbolic functions as one goes to [itex]0[/itex] and one goes to [itex]\infty[/itex]?
EDIT: I know what happens as [itex]\lim_{x \rightarrow \infty}\sinh x = e^x[/itex] and [itex]\lim_{x \rightarrow \infty}\cosh x = e^x[/itex]