Justify the discontinuity

(b) (2 points) An innitely thin surface charge does not exist in the real world. It can be considered as an idealization of a charge distribution within a layer of small but nite thickness. Let us consider a simple model of this situation: as shown in the right gure of Figure 2, a volumetric charge density p(z) is stratied along the normal direction ( or the z axis) and is localized within a small range of z. p(z) is otherwise arbitrary. Far away from this surface layer, the normal component of the electric eld asymptotes to E,\" and En,, respectively, along the positive z or negative z direction, respectively. Show that the total electric force per unit area along the normal direction acting on this charge distribution is f. = g (En,+ + E...) a, (4) where 0' = f dz p(z) is the surface charge density integrated across the surface layer. [Hint Consider applying Gauss's law.]