# Electric Field and Charge Density

1. Feb 23, 2008

### jesuslovesu

[SOLVED] Electric Field and Charge Density

Oops, nevermind I guess I just use div(E) = rho/e0

1. The problem statement, all variables and given/known data

A layer of charge fills the space between x = -a and x = a. The layer has a charge density $$\rho (x)$$. The electric field intensity everywhere inside the charge distribution is given by $$E(x) = \hat{x} Kx^3$$ where K is a constant[/tex]

2. Relevant equations

3. The attempt at a solution

I asked my professor about this and he said the $$\rho(x)$$ should be a volume charge density. So basically it's an infinite slab (in the y and z dir) Having some difficulty in finding the charge density.

I am assuming the charge density is NOT constant everywhere, correct?
I recognize that this requires a Gauss's Law formulation. Similar to an infinite plane if I am not mistaken.
$$E(A) = Qin/e0$$
$$E(2A) = \rho (x) * A * (2a)/e0$$
$$E = \rho (x) * a/e0$$
Can I just plug in E and rearrange to get $$\rho (x)$$ ? Am I handling the ends correctly? I am basically following the same procedure for finding the E of an infinite plane except I am using 2a as the thickness.

Last edited: Feb 23, 2008