Question

A small square loop of wire of side $l$ is placed inside a large square loop of wire of size 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

Field at the center of outer square loop = $B=\frac{2\sqrt{2}\mu i}{\pi L}$ along the axis.

flux linking the smaller square loop= $\lambda =B{l}^2=\frac{2\sqrt{2}\mu i}{\pi L}{l}^2$

mutual inductance = $m\frac{\lambda }{i}=\frac{2\sqrt{2}\mu l^2}{\pi L}$