1First , we should realise that the torque developed on the ring is due to the induced electric field , not the magnetic field , as it is reduced to zero in an instant .
Having said this , let us find out that electric field .
∫ E . dl = dφBdt
Or , E . 2 π R = d [ B ( t ) π a 2 ]dt = B ' ( t ) π a 2
Hence , E = B ' ( t ) a 22 R
Now , the total torque developed due to this electric field -
Γ ( t ) = ( λ . 2 π R ) . E . R = λ B ' ( t ) π a 2 R
Since the angular momentum of the system remains conserved at all times , hence -
I ω = 0 ∫ t Γ ( t ) dt = λ ( Δ B ) π a 2 R
Or , ω = λ ( Δ B ) π a 2M R
Since , Δ B = B0 - 0 = B0
So , ω = - λ B 0 π a 2M R K
One possible doubt - Why did I use " B ( t ) " , while it is given that " B " is constant ? While the magnetic field is being reduced , the field will obviously depend on time , otherwise how can it be reduced to zero ?