Q138 / 150 · MHT CET 2023 (10 May Shift 1) · Physics
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
- A$\frac{\mathrm{R}_1}{\mathrm{R}_2}$
- B$\frac{\mathrm{R}_2}{\mathrm{R}_1}$
- C$\frac{\mathrm{R}_1^2}{\mathrm{R}_2}$
- Correct answerD$\frac{\mathrm{R}_2^2}{\mathrm{R}_1}$
Solution
Mutual inductance of two concentric coplanar circular coils,
$\begin{aligned}
& \mathrm{M}=\frac{\mu_0 \pi \mathrm{N}_1 \mathrm{~N}_2 \mathrm{R}_2^2}{2 \mathrm{R}_1} \\
\therefore \quad & \mathrm{M} \propto \frac{\mathrm{R}_2^2}{\mathrm{R}_1}
\end{aligned}$
Hence, the correct answer is option: 'D'.