Two very long uniformly charged lines with linear charge den

Two very long uniformly charged lines (with linear charge densities indicated) are separated by a distance D. What is the correct expression for the electric field strength at point P a distance r away from the positive line?

Solution

Field due to very long linear charge line at perpendicular distance d.

E = lambda / (2 pi e0 d )

due to left line.

d = r

E1 = (lambda ) / (2 pi e0 r )   to the right

due to right line.

field will be to the right.

d = D - r

so E2 = (lambda) / (2 pi e0 (D - r))

Enet = E1 + E2 = (lambda ) / (2 pi e0 r )    +   (lambda) / (2 pi e0 (D - r))

Ans(E)