Question

A paramagnetic sample shows a net magnetisation of $6\text{A/m}$, when it is placed in an external magnetic field of $0.4\text{T}$, at a temperature of $4\text{K}$. When the sample is placed in an external magnetic field of $0.3\text{T}$ at a temperature of $24\text{K}$, then the magnetisation will be :

• A. $1\text{A/m}$
• B. $4\text{A/m}$
• C. $2.25\text{A/m}$
• D. $0.75\text{A/m}$

Answer 1

The correct option is D $0.75\text{A/m}$

For paramagnetic material, according to curies law,
$\chi \propto \frac{1}{T}$

So, for temperatures $T_1\text{and}{T}_2$,
${\chi }_1{T}_1={\chi }_2{T}_2$

But, $\chi =\frac{I}{B}$

$\therefore \frac{I_1}{B_1}{T}_1=\frac{I_2}{B_2}{T}_2$

$\Rightarrow \frac{6}{0.4}\times 4=\frac{I_2}{0.3}\times 24$

$\Rightarrow I_2=\frac{0.3}{0.4}=0.75\text{A/m}$

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