Finding Electric Field at Point x Away from Origin

[musicfairy]

How do I find the electric field at a point p distance x away from the origin?

I guess the y component cancels. I should use the equation E = kq/r² and add the electric field made by the 3 charges as vectors, but how do I do that?

My attempt:

r = x/√(x² + a²)

cosθ = x/r

E_x = 2kqx/√(x² + a²)^3/2 − kq/x²

Is this correct? I don't really understand the concepts well so if someone can explain that to me it'll be nice.

 

[Delphi51]

r = x/√(x2 + a2) can't be right - the dimensions aren't right; right side has distance over distance. Just use the Pythagorean theorem to find the distance.

Find the horizontal part of E = kq/r^2 using trigonometry.

 

[musicfairy]

Oops, I made a typo on that. I meant to say that r = = √(x² + a²)

 

[Delphi51]

Good show. Put in the trigonometry and you will be nearly finished.
Clever of you to notice that symmetry means you don't have to do the vertical part of the calculation.