In the given figure net magnetic field at O will be

Options

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

Answer

B

Explanation

Magnetic field at 0 due to
Part(1) : `B_(1)= 0`
Part(2): `B_(2) = (mu_(0))/(4pi).(pi i)/((a//2)) ox` (along-Z-axis)
Part(3) `B_(3) = (mu_(0))/(4pi) .(i)/((a//2))(darr)` (along-Y-axis)
Part (4): `B_(4) = (mu_(0))/(4pi).(pi i)/((3a//2)) o.` (along +Z-axis)
Part (5): `B_(5) =(mu_(0))/(4pi).(i )/((3a//2))(darr)` (along-Y-axis) (along-Z-axis)
`B_(3) + B_(5) = (mu_(0))/(4pi).(1)/(a) (2 + (2)/(3))= (8mu_(0)i)/(12pi a) (darr)` (along-Y-axis)
Hence net magnetic field
`B_("net") = sqrt((B_(2)- B_(4))^(2) +(B_(3)+ B_(5))^(2)) = (mu_(0)i)/(3pi a) sqrt(pi^(2) + 4)`