Question

Four wires of equal lengths are bent in the shapes of four loops $\text{P},\text{Q},\text{R}$ and $\text{S}$ as shown in the figure. If each loop carries same current $I$ in the same sense, which loop will have highest magnetic moment ?

• A. $\text{P}$
• B. $\text{Q}$
• C. $\text{R}$
• D. $\text{S}$

Answer 1

The correct option is D $\text{S}$

For a current carrying loop:

$\overrightarrow{M}=NI\overrightarrow{A}$

For all loops, $N$ and $I$ are the same. So, the loop having the largest area will have the highest magnetic moment.

As each loop is made of wires having equal lengths, so the perimeter of each loop will be same.

For the same perimeter, circle has the largest area.

Hence, loop $\text{S}$ will have the highest magnetic moment.

Hence, option $\left(D\right)$ is the correct answer.