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 ( ₀= permeability of free space) (Both coils have single turn)

Step-by-step solution

The magnetic field at the centre of a loop is given by B= ₀ N I 2 R 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 aligned & A_B= r₂^2 & _B = & ₀ I 2 r₁ r₂^2= ₀ r₂^2 2 r₁ I aligned Mutual Inductance M = I (from MI = M ) We can write, M= _B I = ₀ r₂^2 I 2 r₁ I = ₀ r₂^2 2 r₁