The magnetic field at `O` is

Options

A. `(mu_(0)i)/(2pi)((sqrt(3))/(pi)-1/3)`
B. `(mu_(0)i)/(2a)((sqrt(2))/(pi)-1/2)`
C. `(mu_(0)i)/(a)((sqrt(3))/(pi)-1/3)`
D. `(mu_(0)i)/(4a)((sqrt(3))/(pi)-1/3)`

Answer

A

Explanation

`B_(1)=(mu_(0)i)/(4piacos 60^(@))(cos30^(@)+cos30^(@))`
`=(mu_(0)i)/(2pia).sqrt(3), ox`
`B_(2)=(mu_(0)i)/(2a).(120^(@))/(360^(@))=(mu_(0)i)/(6a), o.`
`B_(O)=B_(1)-B_(2)=(mu_(0)i)/(2a)((sqrt(3))/(pi)-1/3), ox`