Question

Two concentric circular coils having radii \(r_1\) and \(r_2\) (\(r_2<<r_1\)) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, \(μ_0\) = permeability of free space)

• A. \(\frac{μ_0πr_2}{2r_1}\)
• B. \(\frac{μ_0πr_1^2}{2r_2}\)
• C. \(\frac{μ_0πr_1}{2r_2}\)
• D. \(\frac{μ_0r_2^2π}{2r_1}\)

Hint:

Large coil gives a nearly uniform field mu0 I/(2 r1) through the small coil.

Answer 1

The Correct Option is D

Step 1: Field of outer coil
$B = \mu_0 I/2r_1$ at the common centre.

Step 2: Flux
Through the small area $\pi r_2^2$: $\phi = \mu_0I\pi r_2^2/2r_1$.

Step 3: M
$M = \phi/I$, option (D).

Final Answer:
Option (D). \[ \boxed{\frac{\mu_0\pi r_2^2}{2r_1}} \]