The magnetic field at `O` is

Options

A. `((mu_(0)I)/(4R))sqrt(1+2/(pi^(2))+2/(pi))`
B. `((mu_(0)I)/(2R))sqrt(1+2/(pi^(2))+2/(pi))`
C. `((mu_(0)I)/(4R))sqrt(1+1/(pi^(2))+1/(pi))`
D. `((mu_(0)I)/(R))sqrt(1+2/(pi^(2))+2/(pi))`

Answer

A

Explanation

Magnetic field at `O:`
`B_(1)=(mu_(0)i)/(4piR)`, along `-z` axis
`B_(2)=(mu_(0)i)/(4R)`, along `-x` axis
`B_(3)=(mu_(0)i)/(4piR)`, along `-x` axis
`vec(B)_(0)=-B_(1)hatk-(B_(2)+B_(3))hati`
`|vec(B)_(o)|=sqrt(B_(1)^(2)+(B_(2)+B_(3))^(3))`
`=(mu_(0)I)/(4R)sqrt((1/pi)^(2)+(1+1/pi)^(2))`
`=(mu_(0)I)/(4R)sqrt(1+2/pi+2/(pi^(2)))`