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Magnetic Field Due to Current in a Solenoid

A paramagneti...

Question

A paramagnetic sample shows a net magnetisation 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 magnetisation will be

A

\frac{32}{3} A / m

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B

2.4 A / m

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C

6 A / m

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D

\frac{2}{3} A / m

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Solution

The correct option is D $\frac{2}{3} A / m$

Let, $B_{1} = 0.6 T,$ $B_{2} = 0.2 T$
$T_{1} = 4 K$ , $T_{2} = 16 K$
$I_{1} = 8 A / m$ , $I_{2} = ?$
From curie's law of magnetization,
$I \propto \frac{B}{T}$
So that,
$\frac{I_{2}}{I_{1}} = \frac{B_{2} T_{1}}{B_{1} T_{2}}$
Substituing the values, we get
$I_{2} = \frac{B_{2} T_{1}}{B_{1} T_{2}} I_{1} = \frac{0.2 \times 8 \times 4}{0.6 \times 16} = \frac{2}{3} A / m$

Final Answer:(b)

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