Equal currents `i=1` A are flowing through the wires parallel to y-axis located at `x=+1m, x=+2m, x=+4m` and so on...., etc. but in opposite directions as shown in Fig The magnetic field (in tesla) at origin would be

Options

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

Answer

B

Explanation

`vec(B)=(mu_(0))/(2pi)[(1/1+1/4+1/16+....) hatk-(1/2+1/8+....)hatk)]`
`=(mu_(0))/(2pi)[(1/(1-1/2))hatk-1/2(1/(1-1/4))hatk]`
`2/3.(mu_(0))/(2pi) hatk`
`=(2/3xx2xx10^(-7))hatK`
`=1.33xx10^(-7) hatK`