(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An infinite plane slab of thickness 2d lies in the xy-plane with −d<z<d. Its charge density is given

as ρ = kz^{2}for −d<z< d and zero otherwise.

(i) Find the electric field, E(z), for all z.

2. Relevant equations

Gauss' law

3. The attempt at a solution

This problem is pretty easy to do with a gaussian surface. However. I wanted to know if I could also do it by calculating the field directly from coulombs law (I know it would be far more tedious but I'm just curious) with the integral

1/4∏ε_{0}∫_{V}ρ/r^{2}dv = 1/4∏ε_{0}∫∫∫ρ/(x^{2}+y^{2}+z^{2}) dxdydx where the integrals of y and x run from -∞ to ∞ and the integral of z runs from -d to d.

But if so, this integral would only hold for being outside the slab right?

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# Calculate electric field of infinite slab

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