Question

A small square loop of wire of side l is placed inside a large square loop of wire of side L (L > l). The loop are coplanar and their centre coincide. The mutual inductance of the system is proportional to

• A. $l/L$
• B. $l^2/L$
• C. $L/l$
• D. $L^2/l$

Answer 1

The correct option is B $l^2/L$

Magnetic field produced due to large loop $B=\frac{{\mu }_0}{4\pi }\frac{8\sqrt{2i}}{L}$
Flux linked with smaller loop
$\varphi =B\left(l^2\right)=\frac{{\mu }_0}{4\pi }\frac{8\pi i{l}^2}{L}$
$\therefore \varphi =Mi\Rightarrow M=\frac{\pi }{i}=\frac{{\mu }_0}{4\pi }.\frac{8\sqrt{2}{l}^2}{L}\Rightarrow M\propto \frac{l^2}{L}$