S COL A parallel plate capacitor consists of two isolated circular plates with diameter d separated by a distance s, as shown above (s < < d). The charge density of each plate has magnitude , and the top plate is positively charged. In terms of d, s, , and fundamental constants, derive expressions for: a. The charge stored on each plate. b. The electric field at the center of the capacitor. c. The capacitance of this capacitor. d. The potential energy stored in this capacitor. e. The plates are pulled so that the distance between them is now 2s. The plates are pulled apart in such a way that the charge on the plates is not disturbed (maybe someone was wearing insulating gloves...). How do the following quantities change relative to the original capacitor (doubled, halved, etc.)? i. The charge density of the plates ii. The capacitance of the capacitor iii. The potential energy stored in the capacitor f. The plates are again pulled apart so that the distance between them is now d. Explain why we cannot mathematically determine how the capacitance and energy of the capacitor change as a result of this process.