Calculate the capacitance of a parallel plate capacitor with a plate separation of 1nm in vacuum? i. If the space between the plates is filled with AlO3, an insulator with a relative dielectric constant k = 9, what is the new capacitance of the structure? ii. What is the electric field in the dielectric for an applied voltage V = 1V? iii. What is the charge stored in the capacitor? What is the density of electrons on the capacitor plate?