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A paramagnetic sample shows a net magnetization of 8 A/m when placed in an external magnetic field of 0.6T at a temperature of 4K.When the same sample is placed in an external magnetic field of 0.2T at a temperature of 16K, the magnetization will be

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a

$\frac{32}{3} A / m$

b

$\frac{2}{3} A / m$

c

6 A/m

d

2.4 A/m

answer is B.

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Detailed Solution

As $I = χ_{m} H and χ_{m} = \frac{C}{T}$ (Curie law),
$\begin{array}{l} I = \frac{CH}{T} or \frac{I_{1}}{I_{2}} = \frac{{CH}_{3} / T_{1}}{{CH}_{2} / T_{2}} = (\frac{H_{1}}{H_{2}}) (\frac{T_{2}}{T_{1}}) \\ Or M_{2} = M_{1} (\frac{H_{2}}{H_{1}}) (\frac{T_{1}}{T_{2}}) = 8 (A / m) [\frac{0 .2 T}{0 .6 T}] [\frac{4 K}{16 K}] \\ = \frac{2}{3} A / m \end{array}$

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A paramagnetic sample shows a net magnetization of 8 A/m when placed in an external magnetic field of 0.6T at a temperature of 4K.When the same sample is placed in an external magnetic field of 0.2T at a temperature of 16K, the magnetization will be