One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current passed in both, the ratio of the magnetic field at the central of the loop `(B_(L))` to that at the central of the coil `(B_(C))`, i.e. `(B_(L))/(B_(C))` will be :

Explanation

When there is only one turn, the magnetic field at the centre,
`B= (mu_(0) I)/(2 a)`
`2pia' xx n = 2pi a rArrr a' = a//n`
The magnetic field at its centre, `B_1 = (mu_(0) nI)/(2 a//n) = (mu_(0) nI)/(2a) = n^2 B`
The ratio is, `B_(1)//B=n^2`