The planar concentric rings of metal wire having radii r₁ and r₂ (with 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 magnetic field at the centre of a loop is given by B= ₀ N I 2 R ...(i) Magnetic field produced by ring A, B_A= ₀ I 2 r₁ Magnetic flux produced in ring B due to B _ A , _B=B_A A_B ( A _ B . is area) _B= ₀ I 2 r₁ r₂^2= ₀ r₂^2 2 r₁ I ...[From(i)] Mutual Inductance M= I M= _B I = ₀ r₂^2 I 2 r₁ I = ₀ r₂^2 2 r₁