A magnetized wire is bent into an arc of a circle subtending an angle 60° at its centre. Then its magnetic moment is 'x'. If the same wire is bent into an arc of a circle subtending an angle 90° at its centre then its magnetic moment will be

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$\frac{(2 \sqrt{2}) x}{3}$

$\frac{x}{3}$

$\frac{x \sqrt{3}}{3}$

$\frac{3 x}{2 \sqrt{2}}$

answer is C.

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Detailed Solution

$M^{1} = \frac{2 Msin (\frac{θ}{2})}{θ}$

$in the second case if moment is y$

$\frac{x}{y} = \frac{\frac{\sin 30^{0}}{π / 3}}{\frac{\sin 45^{0}}{π / 2}} = \frac{3}{2} \frac{1}{2} \sqrt{2}$

$y = \frac{(2 \sqrt{2}) x}{3}$

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