Let two long parallel wires, a distance d apart, carry equal currents I in the same direction. One wires at `x=0`, the other at `x=d` (as shown in Fig) Determine magnetic field at any point x-axis between the wires as a function of x.

Explanation

Let us consider a point P at a distance (x,y) from the wire 1.

`0lexled`
Hence `vecB_1=(mu_0i)/(2pix)hatj`
The point is at a distance d-x from wire 2.
`:. vecB_2=(mu_0i)/(2pi(d-x))hatj`
`:. vecB_("net")=vecB_1+vecB_2=(mu_0i)/(2pix)hatj-=(mu_0i)/(2pi(d-x))hatj`
`vecB_("net")=((mu_0i)(d-2x))/(2pix(d-x)) hatj`