A small square loop of wire of each side l is kept inside a large square loop of wire of each side ‘L’ (L > > l). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to (current i in the outer loop)

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$\frac{l^{2}}{L}$

$\frac{L^{2}}{l}$

L/l

l/L

answer is B.

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Detailed Solution

Given data:

A small square loop of side l and a large square loop of side L

Concept used: Magnetic field and flux

Detailed solution:

Magnetic field at the centre of large square $B = \frac{2 \sqrt{2} μ_{0} i}{πL}$

$ϕ = \vec{B} \cdot \vec{A}$

$\Rightarrow ϕ = {Bl}^{2}$

$ϕ= (\frac{2 \sqrt{2} μ_{0} {il}^{2}}{πL})$

$ϕ = Mi$

$M = \frac{ϕ}{i} = \frac{2 \sqrt{2} μ_{0} l^{2}}{πL}$

$\Rightarrow M \propto (\frac{l^{2}}{L})$

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