Problem Spring d Capacitor with area- A k Vo Battery A parallel plate capacitor with plate area A is hooked to a battery with voltage Vo to provide an initial charge and then the battery is disconnected by a switch. The plates are held a distance d apart during the initial charging process. After the switch disconnects the battery, one of the two plates is connected to a spring with spring constant k that is anchored to a wall. The plate is allowed to move on the spring to minimize its potential energy. The spring is not stretched when the separation is equal to d (i.e. Uspring = 0). Let x be the position of the left plate relative to the unstretched position. a) Before the switch is flipped, what is the charge on the capacitor? (3 points) b) After the switch is flipped and the spring is connected, find the electric potential energy, Ue, stored in the capacitor as a function of x and in terms of the other parameters given. (3 points) c) In terms of the parameters given, find the potential energy in the spring, Uspring, as a function of x. (3 points) d) Find the total potential energy in the system, U(x), using your results from parts (b) and (c). (3 points) Using the potential energy from (d), find the equilibrium value of x. (4 points) f) What is the voltage on the capacitor for the equilibrium value of x? If we doubled the spring constant, k, would the voltage on the capacitor increase or decrease? (4 points)