Aslab 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 magnitude of the electric field due to the slab at the points 0< = x < = d. express your answer in terms of the variables p, x, d, and e_0.
d. using gauss's law, find the magnitude of the electric field due to the slab at the points x> = d. express your answer in terms of the variables p, x, d, and e_0.
e. what is the direction of the electric field due to the slab at the pints x > = d.