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. $\frac{\text{iL}}{4\mathrm{\pi }}$
• B. $\frac{{\text{iL}}^2}{4\mathrm{\pi }}$
• C. $\frac{{\text{i}}^2{\text{L}}^2}{4\mathrm{\pi }}$
• D. $\frac{{\text{i}}^2\text{L}}{4\mathrm{\pi }}$

Answer 1

The correct option is B

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

Step 1: Given data

Wire of length $\text{L}$ .

The current of $\text{i}$ ampere .

Step 2: To find

We have to determine the magnetic moment.

Step 3: Calculating Magnetic moment

We know,

$$\begin{gathered} \mathrm{L}=2\mathrm{\pi r} \\ \mathrm{r}=\frac{\mathrm{L}}{2\mathrm{\pi }} \end{gathered}$$

The magnetic moment will be:

$$\begin{gathered} =\mathrm{i}.\mathrm{\pi }.{\mathrm{r}}^2 \\ =\mathrm{i}.\mathrm{\pi }.\left(\frac{{\mathrm{L}}^2}{2\mathrm{\pi }}\right) \\ =\frac{\mathrm{i}.{\mathrm{L}}^2}{4\mathrm{\pi }} \end{gathered}$$

Therefore, the correct option is option ($\mathrm{B}$).