A parallel plate capacitor has square plates of side length L. Plates are kept vertical at separation d between them. The space between the plates is filled with a dielectric whose dielectric constant (K) changes with height (x) from the lower edge of the plates as `K = e^(betax)` where b is a positive constant. A potential difference of V is applied across the capacitor plates.
(i) Plot the variation of surface charge density (s) on the positive plate of the capacitor versus x.
(ii) Plot the variation of electric field between the plates as a function of x.
(iii) Calculate the capacitance of the capacitor.