Q126 / 200 · NEET 2021 · Physics

Two conducting circular loops of radii $R_{1}$ and $R_{2}$ are placed in the same plane with their centres coinciding. If $R_{1} ≫ R_{2}$ , the mutual inductance $M$ between them will be directly proportional to:

Solution

$M = \frac{ϕ_{12}}{I_{1}} = \frac{B_{1} A_{2}}{I_{1}} = \frac{(\frac{μ_{0} I_{1}}{2 R_{1}}) (π R_{2}^{2})}{I_{1}}$

$M = \frac{μ_{0} π R_{2}^{2}}{2 R_{1}}$

$∴ M \propto \frac{R_{2}^{2}}{R_{1}}$

Hence, the correct answer is option: 'C'.