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 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

Magnetic field at point `O_2` due to current `I_1` in long wire along x-axis is
`B_(O_2)=(mu_0)/(4pi)(2I)/(d)`, It will be acting along the y-axis. As second wire is along y-axis, so the angle between the directions of `I_2vecl` and `vecB_(O_2)` is zero, i.e., `theta=0^@`.
Force on wire lying along y-axis is,
`f=I_2|veclxxvecB_(O_2)|=I_2lB_(O_2)sin0^@=0`