A pair of stationary and infinitely long bent wires is placed in the `X-Y` plane as shown in figure.The wires carry currents of `10A` each as shown.The segments `L` and `M` are along the `x`-axis.The segments `P` and `Q` are pallel to the `Y`-axis such that `OS=OR=0.02 m`.Find the magnitude and direction of the magnetic induction at the origin `O`.

Explanation

i =10 A
OS=OR =r=0.02 m Since O lies on the line of the segments L and M, the magnetic induction at O due to currents in L and M is zero.
`B_(1)` =magnetic induction at O due to RP
`=mu_(0)/4pi 1/r (cos90^(@)+cos0^(@))=mu_(0)4pi 1/r` outward from the plane of the wires
`vec B_(2)`= magnetic induction at O due to SQ =`mu_(0)/4pi 1/r` outward from the plane.
Net magnetic induction at O due to the whole system is `vec B = vec B_(1) +vec B_(2) = 2xxmu_(0)i/4pir =2xx10^(-7)xx10/0.02 =10^(-4)T` = 10 T outward the plane
Net magnetic induction at O due to the whole system is
`vec B=vec B_(1) + vec B_(2) =2xx mu_(0)i/4pi r =2xx10^(-7)xx10/0.02=10^(-4)T`out of the plane.