Two planar concentric rings of metal wire having radii r₁ and r₂ ( r₁>r₂ ) are placed in air. The current I is flowing through the coil of larger radius. The mutual inductance between the coils is given by ( ₀= permeability of free space)

Step-by-step solution

The mutual inductance between two concentric coaxial circular coils is determined by the magnetic flux linkage. The magnetic field at the center of the larger coil of radius r₁ carrying current I is B₁ = ₀ I 2r₁ . Since the coils are coaxial and planar with r₁ > r₂ , this field is uniform over the smaller coil's area r₂^2 . The resulting flux is ₂ = B₁ r₂^2 = ₀ r₂^2 I 2r₁ . Mutual inductance is defined as M = ₂ I = ₀ r₂^2 2r₁ , corresponding to option B .