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Magnetic induction at the centre of a circular loop of area $\pi \mathrm{m}^2$ is 0.1 tesla. The magnetic moment of the loop is ( $\mu_0=$ permeability of air $)$
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Verified Answer
The correct answer is:
$\frac{0.2 \pi}{\mu_0}$
Magnetic induction at the centre of circular loop
$$
B=\frac{\mu_0}{2} \frac{n i}{r}
$$
Magnetic moment of the loop
$$
\begin{array}{rlr}
M & =n i A=\frac{2 B r A}{\mu_0} & \\
& =\frac{2 \times 0.1 \times 1 \times \pi \times(1)^2}{\mu_0} & {[\because r=1]} \\
& =\frac{0.2 \pi}{\mu_0} &
\end{array}
$$
$$
B=\frac{\mu_0}{2} \frac{n i}{r}
$$
Magnetic moment of the loop
$$
\begin{array}{rlr}
M & =n i A=\frac{2 B r A}{\mu_0} & \\
& =\frac{2 \times 0.1 \times 1 \times \pi \times(1)^2}{\mu_0} & {[\because r=1]} \\
& =\frac{0.2 \pi}{\mu_0} &
\end{array}
$$
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