Electric field at point between two finite charged wires

[gruba]

Homework Statement

Two parallel charged wires are in vacuum. Width of wires is equal to the distance between them. Calculate electric field in the middle (point A).

Homework Equations

Superposition

The Attempt at a Solution

Using superposition, y components on vector E are cancelled. I get that the electric field at point A is
E_A=√2 λ/(πε₀a)
In my books solution, it is
E_A=λ/(2ε₀a)
Is my solution correct?
Note: I used integration by angle component.

Thanks for replies.

 

[TSny]

What direction are you calling y? If the y direction is vertical (perpendicular to the wires), then how do you get that the y-components of E cancel?

However, I do think your answer is correct for the magnitude of the net field at A and that the book solution is incorrect. We would need to see your steps in order to check that your method is correct.