Question

An infinitely long string uniformly charged with a linear charge density lambda 1 and a segment of length l uniformly charged with linear charge density lambda 2 lie in a plane at right angles to each other

Answer 1

well, your question is incomplete .
A complete question may be ------> An infinitely long string uniformly charged with a linear charge density lambda 1 and a segment of length l uniformly charged with linear charge density lambda 2 lie in a plane at right angles to each other . Find electric field at P , which are located x distance from first wire and y distance from 2nd wire ?

we know, electric field intensity due to infinite long wire is given by
E = λ/2π∈₀r , where r is distance between wire and observation point.

So, electric field due to 1st wire at P , E₁ = λ₁/2π∈₀x
electric field due to 2nd wire at P, E₂ = λ₂/2π∈₀y
So, Enet = √{E₁² + E₂²}
= 1/2π∈₀ [λ₁²/x² + λ₂²/y²]½

Hence, answer is Enet = 1/2π∈₀ [λ₁²/x² + λ₂²/y²]½