Question

Two coaxial coils A and B of radii \( R_1 \) and \( R_2 \) are placed in the same plane. (\( R_2 \geq R_1 \)). If a current is passed through coil B, the coefficient of mutual inductance between the coils is proportional to

• A. \( \frac{1}{R_1 R_2} \)
• B. \( \frac{R_2^2}{R_1} \)
• C. \( R_1 R_2 \)
• D. \( \frac{R_1^2}{R_2} \)

Hint:

The mutual inductance between two coils is proportional to the product of their radii. This is important when the coils are placed coaxially.

Answer 1

The Correct Option is C

Step 1: Understanding mutual inductance.
The mutual inductance \( M \) between two coils is given by: \[ M \propto \frac{R_1 R_2}{d} \] where \( R_1 \) and \( R_2 \) are the radii of the coils, and \( d \) is the distance between the coils.
Step 2: Conclusion.
Thus, the coefficient of mutual inductance between the coils is proportional to \( R_1 R_2 \), which corresponds to option (C).