Aslab of charge with charge density p(z) = 2 poz/d extends from z = -d/2 to z= +d/2 and is infinite in extent in the x - and y directions. assume the permittivity in all regions is 80. (a) using the principle of superposition and results proved in lectures, write down an expression for the electric field e(z) everywhere within and outside the slab of charge. provide all working. (b) verify that your answer satisfies gauss' law in differential form. (c) write down an expression for the electric potential $(z) at points inside and outside the slab. (d) calculate the total energy per unit area stored in the slab using your answer to (a).