CALC A Nonuniformly Charged Slab. Repeat Problem 22.54, but now let the charge density of the slab be given by ρ(x) = ρ0(x/d)2, where ρ0 is a positive constant.
22.54 . A Uniformly Charged Slab. 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; treat them as essentially infinite. The slab has a uniform positive charge density ρ. (a) Explain why the electric field due to the slab is zero at the center of the slab (x = 0). (b) Using Gauss’s law, find the electric field due to the slab (magnitude and direction) at all points in space.
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