Equal currents A are flowing through the wires parallel to y-axis located at etc. but in opposite direction as shows.The magnetic field at origin (in teals) would be

Options

A. `-1.33xx10^-7hatk`
B. `1.33xx10^-7hatk`
C. `2.67xx10^-7hatk`
D. `-2.67xx10^-7hatk`

Answer

B

Explanation

(b) `vecB=(mu_0)/(2pi)[(1/1+1/4+1/16+....)hatk-(1/2+1/8+....)hatk]`
`=(mu_0)/(4pi)[(1/(1-1/4))hatk-1/2(1/(1-1/4))hatk]`
`=2/3 (mu_0)/(2pi)hatk=(2/3xx2xx10^-7)hatk=1.33xx10^-7hatk`