A star shaped loop ( with `l=` length of each section ) carries current i. Magnetic field at the centroid of the loop is

Options

A. `(3mu_(0)i)/(pi l)`
B. `(3 mu_(0)i)/(2pi l)`
C. `(3-sqrt(3))(mu_(0)i)/(pil)`
D. `(3+sqrt(3))(mu_(0)i)/(pil)`

Answer

C

Explanation

`r=(sqrt(3)l)/(2)`
`B=6[(mu_(0))/(4pi)(i)/(r)(sin 60^(@)+sin60^(@))]`
`-6[(mu_(0))/(4pi).(i)/(r)(sin30^(@)+sin30^(@))]`
`=6xx(mu_(0))/(4pi).(i)/(r)(sqrt(3)-1)`
`=6xx(mu_(0))/(4pi).(i)/(((sqrt(3)l)/(2)))(sqrt(3)-1)`
`=(3-sqrt(3))[(mu_(0)i)/(pi l)]`