just b (a) Write down the integral and differential forms of Gauss' law in a dielec-tric, defining all quantities used.(b) A parallel plate capacitor is completely filled with a non-conductingdiclectric. Show that the electric displacement, D, is uniform betweenthe plates and calculate its value. (You may assume that the plates eachhave area A and are separated by a small distance d. Each plate carriesa surface charge density a C/m2.)·(c) The diclectric has a non-uniform relative permittivityK(x) = ax + bwhere a andb are constants and x is the perpendicular distance from oneplate. Using Gauss' law, show that the electric field between the platessatisfiesEoE(x) =K(x)-where Eo is a constant. Find the value of Eo-(d) Show that the voltage across the capacitor is given byEoIn 1+QdV =and calculate the-eapacitance.Find the volumme polarization charge density in the dielectric.

Electrical Displacement D Area of plates A distance between 2 plates = d

A parallel plate capacitor is completely filled with a non-conducting diclectric. Show that the electric displacement, D, is uniform between the plates and calculate its value. (You may assume that the plates each have area A and are separated by a small distance d. Each plate carries a surface charge density a C/m².)·