A very small circular loop of radius 'a' is initially (at t = 0 ) coplanar and concentric with a much larger fixed circular loop of radius 'b'. A constant current I flows in the larger loop. The smaller loop is rotated with a constant angular speed about the common diameter. The emf induced in the smaller loop as a function of time t is ( ₀ = permeability of free space)

Step-by-step solution

The magnetic field produced by the larger loop at its centre is given by B = ₀ I 2b Since the smaller loop is very small ( a b ), the magnetic field over its area can be assumed to be uniform and equal to B . The magnetic flux linked with the smaller loop at any time t is = B A = B A ( t) Substituting A = a^2 and B = ₀ I 2b , we get = ( ₀ I 2b ) ( a^2) ( t) According to Faraday's law of induction, the induced emf is e = - d dt = - d dt [ ( ₀ I a^2 2b ) ( t) ] e = ( a^2 ₀ I 2b ) ( t) Answer: ( a^2 ₀ I 2b ) t