Two long wires carrying current `I_(1) and I_(2)` are arranged as shown in figure the one carrying current `I_(1)` is along is the x-axis. The other carrying current `I_(2)` is along a line parallel to the y-axis given by x=0 and z=d. Find the force exerted at `O_(2)` because of the wire along the x-axis.

Explanation

Magnetic field due to current `I_(1)` in long wire along X-axis at point `O_(2)` , (which is at a distanced from wire) is
`B_(O_(2)) = (mu_(0))/(4 pi) (2I_(1))/d `
It will be acting along the Y - axis.
Force at `O_(2)` due to wire along X-axis will be :
`F = I_(2) | vec l xx vec B_(O_(?))|`
` = I_(2) lB_(O_(2)) sin theta `
As second wire is along Y- axis , so the angle between `vec l " and " vec B_(O_(2)) " is zero, i.e., " theta = 0^(@) . rArr F = I_(2) lB_(O_(2)) sin 0^(@) = 0 `