A slab of insulating material has a thickness 2d and is oriented so that it faces parallel to yz - plane and given by planes x = d and x = -d it is treated to be infinite. A charged slab has a charge density given as \rho (x) = \ rho 0 (x/d)^2 where \rho 0 is a positive constant. (a) Why is the electric field E due to the slab x = 0? (b) Using Gauss' law, find the electric field due to the slab ( magnitude and direction) at all points in space.

A slab of insulating material has a thickness 2d and is oriented so that it faces parallel to yz - plane and given by planes x = d and x = -d it is treated to be infinite. A charged slab has a charge density given as \rho (x) = \ rho 0 (x/d)^2 where \rho 0 is a positive constant. (a) Why is the electric field E due to the slab x = 0? (b) Using Gauss' law, find the electric field due to the slab ( magnitude and direction) at all points in space.