Question

Two conducting circular loops of radii R1 and R2 are placed in the same plane with their centers coinciding. If R1 > > R2, the mutual inductance M between them will be directly proportional to

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

Answer 1

Answer: (A)

$\frac{R_2^2}{R_1}$

Answer 2

Magnetic field at the center of primary coil
$B=\frac{\mu_0i_1}{2R_1}$
Now, considering it to be uniform, magnetic flux passing through secondary coil is
$\phi_2=BA=\frac{\mu_0i_1}{2R_1}(\pi R_{2}^2)$
Now, $M=\frac{\phi_2}{i_1}$
$=\frac{\mu_0\pi R_{2}^2}{2R_1}$
$\therefore\ \ M \propto \frac{R_2^{2}}{R_1}$
Therefore, the correct option is (A) : $\frac{R_2^2}{R_1}$.