Problem 2: A dielectric rectangular slab has lengths, width w, thickness d, and dielectric constant K. The slab is inserted on the right hand side of a parallel-plate capacitor consisting of two conducting plates of width w, length L, and thickness d. The left hand side of the capacitor of length L - s is empty. The capacitor is charged up such that the left hand side has surface charge densities to, on the facing surfaces of the top and bottom plates respectively and the right hand side has surface charge densities to on the facing surfaces of the top and bottom plates respectively. The total charge on the entire top and bottom plates is + Q and -Q respectively. The charging battery is then removed from the circuit. K -L-s a) Find an expression for the magnitude of the electric field E, on the left hand side in terms of G, ,, K, s, w, L, E, and d as needed. b) Find an expression for the magnitude of the electric field E, on the right hand side in terms of G , G, K, s, w, L, &, and d as needed. c) Find an expression that relates the surface charge densities o, and o in terms of, s, w, L, &, and d as needed. d) What is the total charge +Q on the entire top plate? Express your answer in terms of 5 , 0, K, s, W, L, &, and d as needed. e) What is the capacitance of this system? Express your answer in terms of K, s, w, L E, and d as needed. f) Suppose the dielectric is removed. What is the change in the stored potential energy of the capacitor? Express your answer in terms of Q, K, s, w, L, &,, and d as needed