Q113 / 120 · VITEEE 2018 · Physics

A steel wire of length $\ell$ has a magnetic moment M. It is then bent into a semicircular arc. The new magnetic moment is

A
$\frac{\mathrm{M}}{\pi}$
Correct answer
B
$\frac{2 \mathrm{M}}{\pi}$
C
$\frac{3 \mathrm{M}}{\pi}$
D
$\frac{4 M}{\pi}$

Solution

Let pole strength $=\mathrm{m}$ So, $\mathrm{M}=\mathrm{m} \ell$ When wire is in form of arc, then the distance between poles $=\frac{2 \ell}{\pi}$ So, $M^{\prime}=\frac{m 2 \ell}{\pi}=\frac{2 M}{\pi}$

Hence, the correct answer is option: 'B'.

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