Question

A circular coil of radius 'r' is placed on another circular coil whose radius is 'R' and the current flowing through it is changing and their centers coincide. (\(R≫r\)). If both the coils are coplanar, then the mutual inductance between them is proportional to

• A. \(\frac{r}{R}\)
• B. \(\frac{R}{r}\)
• C. \(\frac{R^2}{r}\)
• D. \(\frac{r^2}{R}\)

Hint:

The field of the big coil at its centre is nearly uniform over the small coil.

Answer 1

The Correct Option is D

Step 1: Dimensional check
$M$ must be a length times $\mu_0$. Only $\frac{r^2}{R}$ has the dimension of length among the options.

Step 2: Result
Option (D).

Final Answer:
r^2 / R. \[ \boxed{\text{(D)}\ M\propto\frac{r^2}{R}} \]