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Elvis 123456789
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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. Let the charge density of the slab be given by ρ(x)=ρ0(x/d)^2 where ρ0 is a positive constant.Using Gauss's law, find the magnitude of the electric field due to the slab at 0<|x|<d.
Homework Equations
ρ=Q/V
=∫E*dA= (Q_encl)/ϵ0
The Attempt at a Solution
I started by choosing a cylinder as my gaussian surface; I placed one face of the cylinder on X=0(parallel with the yz plane) and the other on X=x <d. By symmetry, the electric flux simplifies to EA=(Q_encl)/ϵ0
=> EA=(ρ(x)V_encl)/ϵ0
=>EA=(ρ(x)Ax)/ϵ0
=> E=(ρ(x)*x)/ϵ0
=>E=(ρ0*x^3)/(ϵ0*d^2)
this is wrong and I don't know why. The correct answer contains a 3 in the denominator but I don't know why
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