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 and may be treated as essentially infinite. The slab has a uniform positive charge density p.

(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.