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A paramagnetic sample showing a net magnetization of 0.8Am^-1, when placed in an external magnetic field of strength 0.8T, at a temperature 5K. If the temperature is raised to 20 K, then the magnetization becomes..

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$0.5 A m^{- 1}$

$0.2 A m^{- 1}$

$0.1 A m^{- 1}$

$0.4 A m^{- 1}$

answer is B.

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Detailed Solution

$χ = \frac{M}{H} = \frac{C}{T}$ , $where B = μ_{0} H$ ; $χ is susceptability, M is magnetic moment$

$∴ \frac{{Mμ}_{0}}{B} = \frac{C}{T}$

$⇒ MT=constant$

$\Rightarrow M_{1} T_{1} = M_{2} T_{2}$

$∴ M_{2} = \frac{M_{1} T_{1}}{M_{2}}$ $= \frac{0.8 \times 5}{20} = 0.2 {Am}^{- 1}$

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