Question

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.

Answer 1

In Biot-Savart law, magnetic field B is parallel to idl`xx`r and idl have its direction along the direction of flow of current.
Here. For the direction of magnetic field, At `O_(2)` due to wire carrying `I_(1)` carrying is
`B||"parallel "idlxxr" or "hatixxhatk" but "hatixxhatk=-hatj`
So, the direction at `O_(2)` is along Y-direction
The direction of magnetic force exerted at `O_(2)` because of the wire along the x-axis
`F=IlxxB=hatjxx(-hatj)=0`
So, the magnetic field due to `l_(1)` is along the y-axis the second wire is along the y-axis and hence, the force is zero.