Two infinitely long thin straight wires having uniform linear charge densities `lambda` and `2lambda` are arranged parallel to each other at a distance `r` apart.The intensity of the electric field at a point midway between them is

Explanation

Distance between two parallel infinite long thin straight wires = r.
Electric field due to infinite long thin straight wire, `E=lambda/(2pi epsi_(0) r)`
`E_(1)` at `P=lambda_(1)/(2 pi epsi_(0) r_(1))`
`E_(2)` at `O=lambda_(2)/(2pi epsi_(0) r_(2))`
Given `r_(1)=r_(2)=r/2, lambda_(1)=lambda` and `lambda_(2)=2 lambda`
`implies E_(1)=lambda/(2 pi epsi_(0) (r/2))=lambda/(pi epsi_(0) r)`
`E_(2) =lambda/(2pi epsi_(0) (r/2))=(2lambda)/(pi epsi_(0) r)=2E_(1)`
`:.` Electric intensity at mid point, `E=E_(2)-E_(1)=2E_(1)-E_(1)=E`
`:. E=lambda/(pi epsi_(0) r)`