Mutual inductance M between two concentric coils of radii 1 m and 2 m is

Magnetic field inside the smaller coil due to large coil is uniform and equal to µ₀i/2Rlarge
Thus, flux through the smaller coil due to this magnetic field = µ₀i/2Rlarge × πR²small
Thus,M = Φ/i = µ₀/2 × 2π(1)² = µ₀π4