Two concentric circular coils having radii r₁ and r ₂ ( r ₂ r ₁ ) are placed co-axially with centres coinciding. The mutual induction of the arrangement is (Both coils have single turn, ₀= permeability of free space)

Step-by-step solution

Let I₁ be the current through the coil whose radius is r₁ . Magnetic field at the centre of the coil, B₁= ₀ I₁ 2 r₁ Magnetic flux passing through the coil of radius r ₂ is aligned & ₂= B ₁ r ₂^2 ( = B . A ) & = ₀ I ₁ 2 r ₁ r ₂^2 aligned Mutual inductance of the arrangement, aligned M & = ₂ I ₁ & = ₀ I ₁ r ₂^2 2 r ₁ I ₁ & = ₀ r ₂^2 2 r ₁ aligned