Electric currents I₁ and I₂ are set in two concentric circular coils in a plane as shown. The radii of two coils are 1 cm and 100 cm respectively. The mutual inductance of the arrangement is about (μ₀ = 4π × 10⁻⁷ T m A⁻¹)

Correct option is A

Correct answer is A
Explanation:
The mutual inductance M for two concentric coils can be approximated using:
M = μ0 × (N1 × N2) × A / 2r2
Here:
N1 and N2 are the number of turns in the inner and outer coils (assumed to be 1 turn each).
A = π r12 is the area of the inner coil.
r2 is the radius of the outer coil.
Substituting the values:
M = (4π × 10-7) × (1 × 1) × (π × (1 × 10-2)2) / 2
⇒ M = (4π × 10-7) × (π × 10-4)/2
⇒ M = 2π2 × 10-11 H
Approximating π2 ≈ 10, we get:
M ≈ 2 × 10 × 10-11 H = 2 × 10-10 H