Aplane dielectric slab of large face area a perpendicular to the x-axis has dielectric constant k(x), a general function ofx, between conducting plates carrying free charge of surface density fon their inner surfaces. (a) find d(x), e(x), and pc). (your formulas will be directly applicable in vacuum regions, with k(x) 1) (b) derive an integral formula for the capacitance; start by evaluating the potential difference between the plates from part (b). (c) check against the standard series circuit formula divide the slab into layers of infinitesimal reciprocal capacitance