A straight conductor of length l m carrying a current I A is bent in the form of a semicirle. The magnetic field (in tesla) at the centre of the semicircle is

Options

A. `(pi^(2)I)/(l)xx10^(-7)`
B. `(piI)/(l)xx10^(-7)`
C. `(piI)/(l^(2))xx10^(-7)`
D. `(piI^(2))/(l)xx10^(-7)`

Explanation

If radius of the semicircle is r,
then `pir=lor,=(l)/(pi)`
Now, magnetic field at the centre of the semicircle,
`B=(mu_(0)I)/(4r)=(mu_(0)Ipi)/(4l)=(mu_(0))/(4pi).(pi^(2)I)/(l)`
`=(pi^(2)I)/(l)xx10^(-7)[:'(mu_(0))/(4pi)=10^(-7)]`
The option (A) is correct.