What is Capacitance?

This is a question I thought I knew back when taking AP Physics II, but now I know for sure that I don't actually understand. And this lack of understanding honestly wasn't the most helpful for the 8.02 PSet due yesterday (today, but yesterday, as in before midnight). I'll re-ask Peter Dourmashkin about Problem 4 and if there is a convincing intuitive way to do this at some point, because there was this thing about separating the middle plate that Reece, Cindy, and I delved into at some point, but just never reached a conclusion. For reference, here's the stuff that happened on the board (not including the rabbit hole):

There was some idea to split the middle plate into two and put half of the charge 

And while going from left to center seemed reasonably possible, unfortunately, we are in the world of physics capacitance and circuits, not topology, which means the thing on the right is a definite "no bueno." There was also other attempts to split that middle plate into two, but stuff got ultra iffy when we tried calculating charge displacement when one plate could have more charge than another, and then even I would have to pause and think (yeah... there's no way this is right...)

God, I missed topology. Oh wait. MIT's 18.700 is probably so much more of a rigorous nightmare than my YSP topology class. Oops...

Anyways, I should probably sleep now so I can grind 6.009 tomorrow. But I don't feel like it, and by the time I see your comments telling me "GO TO SLEEEEEPPP!!!" it will already have been morning. So suck it.



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