Two conducting circular loops of radii $R_{1}$ and $R_{2}$ $(R_{1} >> R_{2})$ are placed in the same plane with their centres coinciding. Find the mutual inductance between them.

\frac{μ_{0} π R_{1}^{2}}{R_{2}}

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\frac{μ_{0} π R_{2}^{2}}{R_{1}}

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\frac{μ_{0} π R_{1}^{2}}{2 R_{2}}

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\frac{μ_{0} π R_{2}^{2}}{2 R_{1}}

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Solution

The correct option is D $\frac{μ_{0} π R_{2}^{2}}{2 R_{1}}$
Assume current i passes through outer loop. Then $B = \frac{μ_{0} i}{2 R_{1}}$ and
$ϕ = B A$
$ϕ = \frac{μ_{0} i}{2 R_{1}} π R_{2}^{2}$ using $ϕ = M i$
Mutual inductance $M = \frac{μ_{0} π R_{2}^{2}}{2 R_{1}}$

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