Question

A small square loop of wire of side l is placed inside a large square loop of side L $(L\gg l)$. The loops are coplanar and their centres coincide. The mutual induction of the system is proportional to

• A. $\frac{l}{L}$
• B. $\frac{l^2}{L}$
• C. $\frac{L}{l}$
• D. $\frac{L^2}{l}$

Answer 1

The correct option is B $\frac{l^2}{L}$

$\varphi =BA$

$\frac{\varphi }{i}=\frac{l^2}{L}$ --------- (1)
$\varphi =-Mi$
$\frac{\varphi }{i}=-M$ ---------(2)
$M\propto \frac{l^2}{L}$