How to Determine Electric Field and Potential in an Infinitely Charged Plate?

[dingo_d]

Homework Statement

Infinite plate is charged with symmetrically due to its central plane x = 0. Volume charge density is equal to \rho = \rho(| x |). Determine the electric field E and potential \phi within the panel. Take that the potential vanishes at points of the central plane.

Homework Equations

The electric field:

\vec{E}(\vec{r})=\int\frac{\rho(\vec{r}')(\vec{r}-\vec{r'})}{|\vec{r}-\vec{r}'|^3}d^3r', and potential is

\phi(\vec{r})=\int\frac{\rho(\vec{r}')}{|\vec{r}-\vec{r}'|}d^3r'

The Attempt at a Solution

What I'm having problem with is setting this up.

So I have an infinite charged plate, and I'm assuming it looks like this:

[PLAIN]http://img243.imageshack.us/img243/9877/73983825.png

And it goes to infinity in those directions. How to set up the coordinate system? Do I use some random point P away from the plate and look the E and \phi there or do I use the method of images?

I'm totally lost :\

 

[Bhumble]

I'd stick with Cartesian coordinates for it. Then use the differential form of Gauss' Law. \nabla\bulletE=\frac{\rho}{\epsilon_{o}}

 

[dingo_d]

Ok, but still I need to calculate the electric field, I could use \nabla\cdot\vec{E}=4\pi \rho but I'd still need to integrate it to get E...

 

[dingo_d]

Soo... Any help? :\

 

[Bhumble]

I think the point is that if you integrate along the x-axis you get \int\frac{\rho(x)}{\epsilon_0}dx\widehat{x}