Finding components of the electromagnetic field strength vector?

[amolv06]

2-dimensional components for vectors is easy if you have the magnitude and angle. x is just magnitude*cos, and y is magnitude*sin. But consider this:

Lets say you have a point charge q at (x, y, 0). You want to find the electric field at (0, 0, z). You know that the magnitude of the field is E. I can't figure out how to find the components for E.

I think that:

$$E_{z} = \left|E\right| \frac{z}{\sqrt{x^{2}+y^{2}+z^{2}}}$$

However, I can't see what the components for $$E_{x}$$ and $$E_{y}$$ would be.

 

[Hurkyl]

For the moment, ignore components relative to an origin and basis. Don't you have an explicit formula for the electromagnetic field strength vector at any given point?