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little neutrino
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Homework Statement
A slab of insulating material has thickness 2d and is oriented so that its faces are parallel to the yz-plane and given by the planes x = d and x = -d. The y- and z- dimensions of the slab are very large compared to d and may be treated as essentially infinite.
Homework Equations
The charge density of the slab is given by ρ(x) = ρ0 * (x/d)^2 , where ρ0 is a positive constant. Using Gauss Law, find the electric field due to the slab (magnitude and direction) at all points in space.
The Attempt at a Solution
Attached is a picture of my attempted solution. I don't know why both my answers are off by a factor of 2, could somebody explain?
The answer given is: |x| > d: (ρ0d)/(3ε) ; |x| < d: (ρ0x^3)/(3εd^2).
Thanks![/B]