A staright wire of length `(pi^(2))` meter is carrying a current of `2A` and the magnetic field due to it is measured at a point distant `1 cm` from it. If the wire is to be bent into a circles and is to carry the same current as before, the ratio of the magnetic field at its centre to that obtained in the first case would be

Options

A. `50:1`
B. `:50`
C. `100:1`
D. `1:100`

Answer

B

Explanation

`B_(P)=(mu_(0)i)/(4pid) (cos theta+ cos theta)=(mu_(0)i cos theta)/(2pid)`
`=(mu_(0)i)/(2pixx1xx10^(2)) (pi^(2)//2)/(sqrt((pi^(2)//2)^(2)+(0.01)^(2)))=(mu_(0)i)/(2pixx10^(-2))`

`2pir=L=pi^(2) implies r=(pi)/2 m`
`B_(0)=(mu_(0)i)/(2r)=(mu_(0)i)/(2.pi/2)=(mu_(0)i)/(pi)`
`(B_(0))/(B_(r))=2xx10^(-2)=2/100=1/50`