Two positive charges of magnitude q are located on the y axi

Two positive charges of magnitude q are located on the y axis. The charges are separated by a distance s, and are located at 0.5s. Derive a general (symbolic) expression for the electric field strength at any point on the x axis. Show your work.

Solution

Given the charges are at 0.5s and -0.5s and are of same magnitude, the net electric field at a point on x axis will be only along the x axis and no component of it will be along y axis.

Now, for any distance x, net electric field = k[ q / (0.25*S^2 + x^2) + q/(0.25*S^2 + x^2)] * x / sqrt(0.25*S^2 + x^2)

[We multiply with x /(0.25*S^2 + x^2) to get the component along x axis]

Enet = 2KQx / (0.25*S^2 + x^2)^3/2

The above function can be plotted on a excel sheet.

The graph would be different from the one for a single charge on x axis, as in that case, the electric field will be inversely proportional to x^2 unlike the above function.