Please clearly show the math work on how to get the answers. Thanks

2. (10) A parallel plate capacitor of area A and separation d has capacitance C when the gap between the plates is filled with air. a) Suppose the area of the capacitor is divided into two areas A, = - A, and A2 = = A. Find the capacitance Ca if the gaps for these two regions are filled with materials that have dielectric constants of K1 = 3, K2 = 2, as in the figure. b) Suppose the gap is divided into two layers with thicknesses di = - d, and d2 = = d. Find the capacitance C, if these layers are filled with materials that have dielectric constants of K1 = 3, K2 = 2, as in the figure. Give Ca and C, in terms of C. a) b) Ca C Cb C