Question

Consider two, single turn, co-planar, concentric coils of radii \( R_1 \) and \( R_2 \) with \( R_1 \gg R_2 \). The mutual inductance between the two coils is proportional to: 

• A. \( R_1/R_2 \)
• B. \( R_2/R_1 \)
• C. \( R_1^2/R_2 \)
• D. \( R_2^2/R_1 \)

Hint:

When calculating mutual inductance, the ratio of the coil radii, especially when one radius is much larger than the other, is important.

Answer 1

The Correct Option is C

Step 1: Understanding the mutual inductance.
For two co-planar coils, the mutual inductance \( M \) depends on the geometrical configuration of the coils. It is proportional to the square of the radius of the larger coil \( R_1 \) and inversely proportional to the radius of the smaller coil \( R_2 \), assuming \( R_1 \gg R_2 \). This relationship can be derived from the formula for mutual inductance in terms of coil radii.
Step 2: Conclusion.
The correct answer is option (C) because the mutual inductance is proportional to \( \frac{R_1^2}{R_2} \).