1. Tardigrade
  2. Question
  3. Physics
  4. 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 (let I is the current passing through larger square loop)

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 (let $I $ is the current passing through larger square loop)

Solution:

Magnetic field produced due to large loop $B=\frac{\mu_{0}}{4 \pi} \frac{8 \sqrt{2} i}{L}$
Flux linked with smaller loop
image
$\phi=B\left(l^{2}\right)=\frac{\mu_{0}}{4 \pi} \frac{8 \pi i l^{2}}{L}$
$\therefore \phi=M i$
$ \Rightarrow M=\frac{\phi}{i}=\frac{\mu_{0}}{4 \pi} \cdot \frac{8 \sqrt{2 l} l^{2}}{L}$
$ \Rightarrow M \propto \frac{l^{2}}{L}$