To solve this problem, we need to determine the mutual inductance $M$ between two concentric circular loops.$\\$Given:$\\$• Radii of the loops are $R_1$ and $R_2$ with $R_1 >> R_2. \\$The mutual inductance $M$ between two loops is given by the formula:$\\ M = \frac{\mu_0 \cdot \pi \cdot R_2^2 \cdot N_1 \cdot N_2}{2 \cdot R_1} \\$where:$\\$• $\mu_0$ is the permeability of free space,$\\$• $N_1$ and $N_2$ are the number of turns in the loops (assuming both are single-turn loops, $N_1 = N_2 = 1). \\$Since $R_1 >> R_2,$ the magnetic field due to the larger loop is approximately uniform over the smaller loop.$\\$Substituting $N_1 = N_2 = 1$ into the formula, we get:$\\ M = \frac{\mu_0 \cdot \pi \cdot R_2^2}{2 \cdot R_1} \\$This shows that the mutual inductance $M$ is directly proportional to $\frac{R_2^2}{R_1}. \\$Therefore, the correct option is:$\\ \frac{R_2^2}{R_1}$ (Option 4)