Explain Curie's law.

(N/A) Experimentally,it was found that the magnetisation $M$ of a paramagnetic material is inversely proportional to the absolute temperature $T$.
$\therefore M = C \frac{B_{0}}{T} \quad \dots (1)$ and $M = \chi H \quad \dots (2)$
Given that $B_{0} = \mu_{0} H$,substituting this into equation $(1)$ gives:
$M = \frac{C \mu_{0} H}{T}$
$\therefore \frac{M}{H} = \frac{C \mu_{0}}{T}$
Since $\chi = \frac{M}{H}$,we get $\chi = \frac{C \mu_{0}}{T} \quad \dots (3)$
This is known as Curie's law. The constant $C$ is called Curie's constant.
For a paramagnetic material,both the magnetic susceptibility $\chi$ and relative permeability $\mu_{r}$ depend not only on the material but also on the absolute temperature.
As the external magnetic field $B_{0}$ is increased or the temperature $T$ is lowered,the magnetisation increases until it reaches the saturation value $M_{s}$,at which point all the atomic dipoles are perfectly aligned with the field. Beyond this point,Curie's law is no longer valid.