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

Answer

B

Explanation

If a wire of length `l` is bent in the from of a circle fo radius `r` then `2pir=l`

`implies r=l/(2pi)`
`vecF=i(vecLxxvecB)`
Magnetic field due to straight wire
`B_(1)=(mu_(0))/(4pi).(2i)/r=(mu_(0))/(4pi)xx(2xx2)/(1xx10^(-2))` also magentic field due to circle loop
`B_(2)=(mu_(0))/(4pi).(2pi i)/r=(mu_(0))/(4pi).(2pixx2)/(pi//2) implies (B_(2))/(B_(1))=1/50`