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zezima1
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Homework Statement
An infinite plane slab of thickness 2d lies in the xy-plane with −d<z<d. Its charge density is given
as ρ = kz2 for −d<z< d and zero otherwise.
(i) Find the electric field, E(z), for all z.
Homework Equations
Gauss' law
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∏ε0∫Vρ/r2dv = 1/4∏ε0∫∫∫ρ/(x2+y2+z2) 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?