Question

At a temperature of ${30}^{\circ }C$, the susceptibility of a ferromagnetic material is found to be $x$. its susceptibility at ${333}^{\circ }C$ is

Answer 1

Given, $T_1={30}^{\circ }C=273+30=303K$

$T_2={333}^{\circ }C=273+333=606K$

According to Curie's law,

${\chi }_m=\frac{{\mu }_{0}C}{T}$

Where $C$ is curie constant and $T$ is the absolute temperature.

$\therefore {\chi }_m\propto \frac{1}{T}$

$\Rightarrow \frac{{\chi }_{m_1}}{{\chi }_{m_2}}=\frac{T_2}{T_1}=\frac{606}{303}=2$

$\therefore {\chi }_{m_2}=\frac{{\chi }_{m_1}}{2}=0.5x$

$(\because {\chi }_{m_1}=x)$

Hence, option $\left(A\right)$ is the correct answer.