Two concentric circular coils having radii r₁ and r₂ ( r₂ << r₁ ) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, ₀ = permeability of free space)

Step-by-step solution

Let a current I flow through the outer coil of radius r₁ . The magnetic field at the centre of the outer coil is given by B = ₀ I 2r₁ . Since r₂ The magnetic flux linked with the inner coil of radius r₂ is = B A = ( ₀ I 2r₁ ) ( r₂^2) . The mutual inductance M of the arrangement is defined as M = I . Substituting the value of , we get M = ₀ r₂^2 2r₁ . Answer: ₀ r₂^2 2r₁