Two conducting circular loops of radii R₁ and R₂ are placed in the same plane with their centre coinciding. If R₁ >> R₂ the mutual inductance M between them will be directly proportional to :

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$\frac{R_{2}^{2}}{R_{1}}$

$\frac{R_{2}}{R_{1}}$

$\frac{R_{1}^{2}}{R_{2}}$

$\frac{R_{1}}{R_{2}}$

answer is B.

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Detailed Solution

Let current i flow through the outer coil. Then magnetic field due to this loop at the center= $\frac{μ_{o} i}{2 R_{1}}$

Flux due to this magnetic field on inner coil= $\frac{μ_{o} i}{2 R_{1}} ({πR}_{2}^{2})$

Hence $M \propto \frac{R_{2}^{2}}{R_{1}}$

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