Two rods of length L carrying uniformly distributed charge q each are kept along x-axis and y -axis with one end at origin.Electric field at a point at distance L/2 from centers of both rods is?

Since being above the midpoint (for horizontal rod)horizontal component of electric field due to half rod will be cancelled  out by other half same with the vetical field of (vertical rod).hence only horizontal  field due to vertical and vertical  field due to horizontal  rod remain in action.

 

Horizontal field =qk/l×(l÷2) and same with vertical 

 Resultant is (2qk/l^2)(2^1÷2)