A paramagnetic sample shows a net magnetization of 8 A/m 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

Question

A paramagnetic sample shows a net magnetization of 8 A/m 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 (in m A ​ ) will be

TestHub · Accepted Answer

According to Curie's law, the magnetization $M$ of a paramagnetic material is directly proportional to the external magnetic field $B$ and inversely proportional to the absolute temperature $T$ .

$M \propto \frac{B}{T}$

$\frac{M _{2}}{M _{1}} = \frac{B _{2}}{B _{1}} \times \frac{T _{1}}{T _{2}}$

Substituting the given values:

$M_{1} = 8 A/m, B_{1} = 0.6 T, T_{1} = 4 K$

$B_{2} = 0.2 T, T_{2} = 16 K$

$\frac{M _{2}}{8} = (\frac{0.2}{0.6}) \times (\frac{4}{16})$

$\frac{M _{2}}{8} = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}$

$M_{2} = \frac{8}{12} = \frac{2}{3} A/m$

Answer: $\frac{2}{3}$

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