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 loops are coplanar and their centres 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

Answer: (B)

$l^2/L$

Answer 2

Magnetic field produced by a current $i$ in a large square loop at its centre $B \propto \frac{i}{L}$ say $B = K \frac{i}{L}$ $\therefore$ Magnetic flux linked with smaller looop, $\phi = B.S$ $\phi = \left( K \frac{i}{L} \right) ( l^2)$ Therefore, the mutual inductance $M = \frac{\phi}{i} = K \frac{l^2}{L}$ or $M \propto \frac{l^2}{L}$