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

The Correct Option is A

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) : \(\frac{R_2^2}{R_1}\).