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: Field of the big coil
At the centre, \(B = \frac{\mu_0I}{2R}\). It is almost uniform over the tiny area of the small coil.

Step 2: Flux through the small coil
\(\Phi = B\cdot\pi r^2 = \frac{\mu_0I\pi r^2}{2R}\).

Step 3: Mutual inductance
\(M = \frac\Phi I = \frac{\mu_0\pi r^2}{2R}\), so \(M\propto\frac{r^2}{R}\). Option (D).

Final Answer:
M is proportional to r squared over R. \[ \boxed{\text{(D)}\ M\propto\frac{r^2}{R}} \]