A current ' $\mathrm{I}$ ' is flowing in a conductor of length ' $\mathrm{L}$ ' when it is bent in the form…

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
  1. $\frac{\mathrm{IL}}{4 \pi^2}$
  2. $4 \pi \mathrm{IL}^2$
  3. $\frac{4 \pi}{\mathrm{IL}^2}$
  4. $\frac{\mathrm{IL}^2}{4 \pi}$

Solution

$\begin{aligned} & \mathrm{L}=2 \pi \mathrm{r} \\ & \therefore \mathrm{r}=\frac{\mathrm{L}}{2 \pi} \end{aligned}$ 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, $\mathrm{M}=\mathrm{IA}=\frac{\mathrm{IL}^2}{4 \pi}$ .

Asked in: MHT CET 2021 (23 Sep Shift 1)

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