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Magnetic induction at the centre of a circular loop of area $π$ square meter is 0.1 tesla. The magnetic moment of the loop is ( $μ_{0}$ is permeability of air)

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$\frac{0.2 π}{μ_{0}}$

$\frac{0.1 π}{μ_{0}}$

$\frac{0.3 π}{μ_{0}}$

$\frac{0.4 π}{μ_{0}}$

answer is B.

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Detailed Solution

$B = \frac{μ_{o} i}{2 r}$
$m = i π r^{2}$
$\frac{B}{m} = \frac{\frac{μ_{o} i}{2 r}}{i π r^{2}} = \frac{μ_{o}}{2 π r^{3}}$
$I f a r e a = π r^{2} = π$
$m = \frac{2 π r^{3}}{μ_{o}} (β) = \frac{2 π}{μ_{o}} (.1) = \frac{0.2 π}{μ_{o}}$

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