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 :

Options

A. `N`
B. `1/N`
C. `1/(N^(2))`
D. `N^(2)`

Answer

C

Explanation

`B_(L)=((mu_(0))/(4pi))(2piI)/R 2piR=L`
`B_(L)=((mu_(0))/(4pi))(2pi)/((L/(2pi)))I, B_(L) prop 1/L`
For coil `N 2 pi r=L , B_(C) prop N/r, prop (N^(2))/L , (B_(L))/(B_(C))=1/(N^(2))`