Ncert Exercises & Solutions

A paramagnetic sample shows a net magnetization 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 magnetization will be:

1. 32/3 ${Am}^{- 1}$
2. 2/3 ${Am}^{- 1}$
3. 6 ${Am}^{- 1}$
4. 2.4 ${Am}^{- 1}$

(b) Hint: The magnetisation depends on the external field and the temperature.

Step 1: As Curie law explains, we can deduce a formula for the relation between magnetic field induction, temperature, and magnetization;

$\begin{array}{l} i.e., I (magnetisation) \propto \frac{B (magnetic field induction)}{t (temperature in kelvin)} \\ \Rightarrow \frac{I_{2}}{I_{1}} = \frac{B_{2}}{B_{1}} \times \frac{T_{1}}{T_{2}} \end{array}$

Step 2:

$Let us suppose, here, I_{1} = 8 {Am}^{- 1}$

$B_{1} = 0 .6 T, T_{1} = 4 K$

$B_{2} = 0 .2 T, T_{2} = 16 K$

$I_{2} = ?$

$\Rightarrow \frac{02}{0 .6} \times \frac{4}{16} = \frac{I_{2}}{8}$

$\Rightarrow l_{2} = 8 \times \frac{1}{12} = \frac{2}{3} {Am}^{- 1}$

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