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

Answer

`1*33xx10^-7hatk`

Explanation

Mag. field induction at O due to current through one wire is
`vecB_1=(mu_0)/(4pi)(2I)/(r)hatk`, we have
`vecB=(mu_0)/(4pi)2xx1[1/1-1/2+1/4-1/8+1/16+…]hatk`
`=(mu_0)/(2pi)[(1+1/4+1/16+…)hatk-(1/2+1/8+…)hatk]`
`=(mu_0)/(2pi)[((1)/(1-1/4))hatk-1/2((1)/(1-1/4))hatk]`
`=(mu_0)/(2pi)2/3hatk=(mu_0)/(4pi)(4hatk)/(3)`
`=10^-7xx4/3hatk=1*33xx10^-7hatk`