A. Here's a follow-up to the lecture question that had you thinking about the workings of a capacitor. We were considering a capacitor with plates charged at +q/q, area A, and separation d. In physics, we strive to fit ideas together in as many ways as we can, and we have that opportunity here in relation to what's going on with elec- tric field (E), electric potential (V), capacitance (C), electric potential energy (U) and separated charge (q) when you pull the plates further apart to a distance of 2d. Describe what happens to these characteristics of the capacitor when you did pull the capacitor plates apart with the battery con- nected, while identifying key differences (connected vs. disconnected from battery).

B. Capacitors are electronic devices that can store energy in a cir- cuit and give it back whenever it's needed. In the prelectures, you saw how dielectric materials (polarizable insulators) can be placed between capacitor plates to increase capacitance. That just means that dielectrics can make it so that more charge is separated at a given po- tential difference between the plates. Show that the potential energy of the same capacitor will be more with a dielectric inserted than without by using the relevant expressions for the potential energy of a capacitor.