now get the max 'r' .
then find max E.
Each of the two long parallel threads carries a uniform charge λ per unit length. The threads are separated by a distane l. Find the maximum magnitude of the electric field strength in the symmetry plane of this system located between the threads.
in the symmetry plane of this system , each point is at the same distance from the two threads
let the distance be r
then the eletric field due to both the threads = λ/2πrε0
but they will be inclined at 2θ where sinθ=l/2r
so the net electric field will be along the plane=
2cosθ(λ/2πrε0 )
differentiate it to get maximum