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We are covering capacitors now, and there are a couple of things that confuse me. As we just finished the chapter covering simple circuits and resistance, we learned that no current would flow across an open circuit. Now, we are given a description of a device that essentially sounds like it "opens" the circuit--a gap between two plates that somehow "stores" energy by accumulating opposite charges on both plates.

How does charge accumulate on the plates if no current flows?

We have learned that in conductors, charges will automatically redistribute to outer layers and align themselves in such a way as to "cancel out" electric fields, or minimize the force exerted on them by neighboring charges. But then, we heard that the "drift velocity" of charges is incredibly slow. When these charges redistribute, is current flowing? If so, does it flow for a decent amount of time, since it takes time for the charges to migrate toward the surface?

My professor is content to prove everything mathematically, but I'm not the kind of person that can "divide everything by E" and all of a sudden it makes sense. As I don't have a good conceptual understanding of what the mathematical symbols represent, I'm hesitant to put any faith in them whatsoever (although definitions aren't a problem).

Can anyone tell me where I'm messing up?

Thanks