Question

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

• A. $\frac{R_1}{R_2}$
• B. $\frac{R_2}{R_1}$
• C. $\frac{R_2^2}{R_1}$
• D. $\frac{R_2}{R_1}$

Answer 1

Answer: (C)

(3)

Answer 2

The mutual inductance $M$ between the two concentric loops is derived by first calculating the magnetic field $B$ at the center of the larger loop due to a current $I$ flowing through it. Given $R_1 \gg R_2$, this field $B$ is assumed to be uniform across the area of the smaller loop. The magnetic flux $\Phi$ through the smaller loop is then $B$ multiplied by the area of the smaller loop ($\pi R_2^2$). Finally, using the definition $\Phi = MI$, the mutual inductance $M$ is found to be $\frac{\mu_0 \pi R_2^2}{2R_1}$, which shows a direct proportionality to $\frac{R_2^2}{R_1}$.