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A current ' $\mathrm{I}$ ' is flowing in a conductor of length ' $\mathrm{L}$ ' when it is bent in the form of a circular loop, its magnetic moment will be
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Verified Answer
The correct answer is:
$\frac{\mathrm{IL}^2}{4 \pi}$
$$
\begin{aligned}
& \mathrm{L}=2 \pi \mathrm{r} \\
& \therefore \mathrm{r}=\frac{\mathrm{L}}{2 \pi}
\end{aligned}
$$
Area of the loop, $\mathrm{A}=\pi \mathrm{r}^2=\pi \frac{\mathrm{L}^2}{4 \pi^2}=\frac{\mathrm{L}^2}{4 \pi}$
Magnetic moment, $\mathrm{M}=\mathrm{IA}=\frac{\mathrm{IL}^2}{4 \pi}$
\begin{aligned}
& \mathrm{L}=2 \pi \mathrm{r} \\
& \therefore \mathrm{r}=\frac{\mathrm{L}}{2 \pi}
\end{aligned}
$$
Area of the loop, $\mathrm{A}=\pi \mathrm{r}^2=\pi \frac{\mathrm{L}^2}{4 \pi^2}=\frac{\mathrm{L}^2}{4 \pi}$
Magnetic moment, $\mathrm{M}=\mathrm{IA}=\frac{\mathrm{IL}^2}{4 \pi}$
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