A paramagnetic sample shows a net magnetisation of 8 Am ^ -1 when… - Vidyadip

MCQ

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

A
$\frac{32}{3}\text{Am}^{-1}$
✓
$\frac{2}{3}\text{Am}^{-1}$
C
$6\text{Am}^{-1}$
D
$2.4\text{Am}^{-1}.$

✓

Answer

Correct option: B.

$\frac{2}{3}\text{Am}^{-1}$

From the Curie’s law explains, $\text{I}\propto\frac{\text{B}}{\text{T}}$
Here, $B$ is magnetic field induction, $I$ is the intensity of magnetisation and $T$ is absolute temperature.
$\Rightarrow\ \Big(\frac{\text{I}_2}{\text{I}_1}\Big)=\Big(\frac{\text{B}_2}{\text{B}_1}\Big)\times\Big(\frac{\text{T}_1}{\text{T}_2}\Big)$
Given,
$I _1=8 Am ^{-1}, B_1=0.6 T, T _1=4 K, B _2=0.2 T, T _2=16 K, I _2=?$
By putting values in equation $…(i),$ we have,
$\text{I}_2=\Big(\frac{2}{3}\Big)\text{Am}^{-1}.$

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