Question
A paramagnetic sample shows a net magnetisation of $8\ Am ^{-1}$ when placed in an external magnetic field of $0.6 T$ at a temperature of $4 K$ . When the same sample is placed in an external magnetic field of $0.2 T$ at a temperature of $16 K ,$ the magnetisation will be

Answer

$(b)\ \frac{2}{3} Am ^{-1}$
Explanation:
On increasing the temperature magnetic susceptibility of paramagnetic material decreases or vice versa .
According to Curie law, we can deduce a formula for the relation between magnetic field induction, temperature and magnetisation.
$i.e., I ($magnetization$) \propto \frac{B(\text { magnetic field induction })}{t(\text { temperature in kelvin })} $
$\Rightarrow \frac{I_2}{I_1}=\frac{B_2}{B_1} \times \frac{t_1}{t_2}$
Let us suppose, here $I _1=8 Am ^{-1}$
$ B _1=0.6 T, t _1=4 K$
$B _2=0.2 T, t _2=16 K$
$\Rightarrow \frac{0.2}{0.6} \times \frac{4}{16}=\frac{I_2}{8}$
$\Rightarrow I_2=8 \times \frac{1}{12}=\frac{2}{3} Am ^{-1}$

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