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. Calculate intensity of the electric field at a point midway between them.

Explanation

For first infinitely long straight wire, linear charge density `lambda=e`.
For second infinitely long straight wire, linear charge density `lambda'=2e`
distance between to infinite parallel straight wires `=r`.
Distance of point P from `1^(st)` and `2^(nd)` wire `=r/2`
electric field intensity at P due to `1^(st)` wire, `E_(1)=lambda/(2pi epsi_(0) (r/2))=e/(pi epsi_(0) r)` ...(1)
Electric field intensity at P due to `2^(nd)` wire, `E_(2)=(lambda')/(2pi epsi_(0) (r/2))=(2e)/(pi epsi_(0) r)`
`:. E_(2)=2E_(1)` [`:'` from (1)]
`:.` Electric field intensity at middle point due to second infinitely long wire
`E_(2)=(2lambda)/(pi epsi_(0)r)`