Two conducting circular loops of radii ' $\mathrm{R}_1$ ' and ' $R_2$ ' are placed in the same plane with…

Two conducting circular loops of radii ' $\mathrm{R}_1$ ' and ' $R_2$ ' are placed in the same plane with their centres coinciding. If $\mathrm{R}_1>\mathrm{R}_2$, the mutual inductance $\mathrm{M}$ between them will be directly proportional to
  1. $\frac{\mathrm{R}_1}{\mathrm{R}_2}$
  2. $\frac{\mathrm{R}_2}{\mathrm{R}_1}$
  3. $\frac{\mathrm{R}_1^2}{\mathrm{R}_2}$
  4. $\frac{\mathrm{R}_2^2}{\mathrm{R}_1}$

Solution

Mutual inductance of two concentric coplanar circular coils, $\begin{aligned} & \mathrm{M}=\frac{\mu_0 \pi \mathrm{N}_1 \mathrm{~N}_2 \mathrm{R}_2^2}{2 \mathrm{R}_1} \\ \therefore \quad & \mathrm{M} \propto \frac{\mathrm{R}_2^2}{\mathrm{R}_1} \end{aligned}$

Asked in: MHT CET 2023 (10 May Shift 1)

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