How Does Gauss's Law Apply to the Electric Field in a Uniformly Charged Slab?

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Gauss's Law can be applied to determine the electric field within a uniformly charged insulating slab of thickness 2d. The charge density is uniform, and for the region between -d and d, the electric field is derived from the enclosed charge using the equation E = (ρ * x) / ε₀. The assumption that the electric field is zero inside the slab is incorrect; instead, the field is proportional to the distance from the center, indicating that the field is not zero in this region. The misunderstanding arises from the nature of the insulating material, which does not allow for free charge movement but still produces an electric field due to the fixed charge distribution. The correct electric field expression within the slab is E = (ρ * x) / (2ε₀).
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Hey guys I was wondering if anyone could help me with this problem

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. The slab has a uniform positive charge density p(rho). Using Gauss's law, find the electric field between -d<x<d

This is what I did but the system states I am wrong.

pV=Qenclosed

EA=Qenclosed/epsilon

E(r^2)=(rho*r^2*2d)/epsilon

E=rho*2d/epsilon

Thanks anyone :)
 
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I also thought it might be zero since its inside the material but I am getting that as an incorrect answer as well
 
This is how I trully feel about this problem: This slab is composed of insulating material, and insulating material does not permit easy movement of charge through them(can we assume that they don't move at all and are at rest?). Then, if all the charges are at rest, the field(E) at every point in the interior of the material is zero. With that, when -d < x < d wouldn't the field(E) be zero since for these x values we are talking about the interior of the slab?
 
Anyone please :)
 
E=[|Rho|x]/Epsilon naught
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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