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:
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:
Show Hint
- \( R_1/R_2 \)
- \( R_2/R_1 \)
- \( R_1^2/R_2 \)
- \( R_2^2/R_1 \)
The Correct Option is D
Solution and Explanation
For two co-planar coils, the mutual inductance \( M \) is inversely proportional to the distance between the coils and directly proportional to the areas of the coils. Given the radii \( R_1 \) and \( R_2 \), the mutual inductance is proportional to \( \frac{R_2^2}{R_1} \), assuming \( R_1 \gg R_2 \). This formula represents the effective coupling between the coils.
Step 2: Conclusion.
The correct answer is option (D) because the mutual inductance is proportional to \( R_2^2/R_1 \).
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