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jesuslovesu

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**[SOLVED] Electric Field and Charge Density**

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

## Homework Statement

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

## Homework Equations

## The Attempt at a Solution

I asked my professor about this and he said the [tex]\rho(x)[/tex] 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.

[tex]E(A) = Qin/e0[/tex]

[tex]E(2A) = \rho (x) * A * (2a)/e0[/tex]

[tex]E = \rho (x) * a/e0 [/tex]

Can I just plug in E and rearrange to get [tex]\rho (x)[/tex] ? 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.

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