Question

# A wire of length $\text{L}$ metre carrying a current of $\text{i}$ ampere is bent in the form of a circle. Its magnetic moment will be?

A

$\frac{\text{iL}}{4\mathrm{\pi }}$

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B

$\frac{{\text{iL}}^{2}}{4\mathrm{\pi }}$

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C

$\frac{{\text{i}}^{2}{\text{L}}^{2}}{4\mathrm{\pi }}$

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D

$\frac{{\text{i}}^{2}\text{L}}{4\mathrm{\pi }}$

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Solution

## The correct option is B $\frac{{\text{iL}}^{2}}{4\mathrm{\pi }}$Step 1: Given dataWire of length $\text{L}$ .The current of $\text{i}$ ampere .Step 2: To findWe have to determine the magnetic moment.Step 3: Calculating Magnetic momentWe know, $\mathrm{L}=2\mathrm{\pi r}\phantom{\rule{0ex}{0ex}}\mathrm{r}=\frac{\mathrm{L}}{2\mathrm{\pi }}$The magnetic moment will be:$=\mathrm{i}.\mathrm{\pi }.{\mathrm{r}}^{2}\phantom{\rule{0ex}{0ex}}=\mathrm{i}.\mathrm{\pi }.\left(\frac{{\mathrm{L}}^{2}}{2\mathrm{\pi }}\right)\phantom{\rule{0ex}{0ex}}=\frac{\mathrm{i}.{\mathrm{L}}^{2}}{4\mathrm{\pi }}$Therefore, the correct option is option ($\mathrm{B}$).

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