Physics - Magnetism Question with Solution | TestHub

Let the length of the wire$=L,$

then$L=2\pi r$

Where,$r=$radius of the loop.

$\therefore r=\frac{L}{2\pi }$

$\therefore$Area of the loop,$A=\pi r^2$

$=\pi \cdot \frac{L^2}{4{\pi }^2}=\frac{L^2}{4\pi }$

Thus, magnetic moment of the loop,

$M=IA=I\cdot \frac{L^2}{4\pi }$

$\therefore L=\sqrt{\frac{4\pi M}{I}}$