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)hat(k)`
B. `1.33xx10^(-7)hat(k)`
C. `2.67xx10^(-7)hat(k)`
D. `-2.67xx10^(-7)hat(k)`

Answer

B

Explanation

`B_(1)=(mu_(0)i)/(2pi) o. " " B_(2)=(mu_(0)i)/(4pi) ox " " B_(3)=(mu_(0)i)/(8pi) o.`
`B_("net")=(mu_(0)i)/(2pi)+(mu_(0)i)/(8pi)-(mu_(0)i)/(4pi) ......`
`=(mu_(0)i)/(2pi)[1-(1)/(2)+(1)/(4)......oo]`
`=(mu_(0)i)/(2pi)[(1)/(1+(1)/(2))]=(mu_(0)i)/(3pi)=(4)/(3)xx10^(-7)=1.33xx10^(-7o.)`