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 co- planar and their centres coincide. The mutual inductance of the system is proportional to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\frac{l^2}{L}$
Given:
Small loop of side $l$ inside large loop of side $L$ ($L \gg l$), co-planar, centres coincide.
Mutual inductance $M$ is given by:
$M = \frac{\text{Flux through small loop due to current in large loop}}{\text{Current in large loop}}$
Magnetic field at the centre of a large square loop carrying current $I$:
$B \propto \frac{\mu_0 I}{L}$
Flux through small loop:
$\Phi = B \cdot \text{area of small loop} \propto \frac{\mu_0 I}{L} \cdot l^2$
Mutual inductance:
$M = \frac{\Phi}{I} \propto \frac{\mu_0 l^2}{L}$
Answer: Mutual inductance $M \propto \frac{l^2}{L}$