PYQ NEET- Magnetism And Matter L-2

Question: A wire of length $L$ metre carrying a current of I ampere is bent in the form of a circle. Its magnetic moment is#

A) $/ L^2 / 4 A m^2$

B) $/ \pi \mathrm{L}^2 / 4 \mathrm{Am}^2$

C) $2 I L^2 / \pi A m^2$

D) $I L^2 / 4 \pi A m^2$

Answer: $I L^2 / 4 \pi A m^2$#

Sol:#

When wire of length $L$ is bent in the form of a circle of radius $R$, then $$ \begin{aligned} L & =2 \pi R \ \Rightarrow \quad R & =\frac{L}{2 \pi} \end{aligned} $$ $\therefore$ Magnetic moment, $M=I A=I\left(\pi R^2\right)$ $$ =1 \cdot \pi\left(\frac{L}{2 \pi}\right)^2=\frac{1 \pi L^2}{4 \pi^2}=\frac{1 L^2}{4 \pi} \mathrm{Am}^2 $$