Ironically, this is EXACTLY the scenario that I was wondering about - it was the inspiration for my post. So you've hit the nail right on the head. My suspicions are the same as yours, that even though the activated carbon has a surface area orders of magnitude larger than the polished metal...
You can google "capacitance of an isolated sphere" and "charge on an isolated sphere" for all kinds of examples, but here one I've lifted from the bunch because it actually states, "Note there is only one surface, but the formula still works" which emphasizes that there's no second plate. This...
Lets say that the sharp edges have been "rounded" somehow. My point is more that we have a huge surface area and I described it using the term "fractal" because that concept allows us to create a huge surface area in a tiny volume, which is what I really wanted to emphasize.
You said, "The concept of capacitance does not really make sense if there is only one conductor," however it was in that context that I was asking the question. I'm actually pretty comfortable and familiar with real electronic circuit capacitors and their "two plates" and how they work. But what...
I understand how to calculate the capacitance of an isolated conductor, say a sphere, and I know that the associated formula involves the surface area of the conductor. Does all of this make the assumption that the surface in question is convex, or at least "non-concave"? More specifically, what...
I finally did watch the video. Walter Lewin is fantastic and I've watched most of the Physics8.02 video lectures that he made on that site. I always quote bits and pieces from his videos for my students. (I'm actually a math/compsci professor with an engineering background and a PhD in...
Oh, I should add that allowing the device to have a spark arc-ing across the air gap is not acceptable, so this is why I calculated Vmax for the device based on whatever maximum total voltage would be just below the amount that would cause a breakdown of either dielectric. I guess its always...
What I still can't tell from your reply is if the statement is flawed generally, or if you meant it was flawed only when the gap starts to become small. So let me rephrase: If the air gap is sufficiently large so that the breakdown voltage is indeed 3e6V/m, then should the maximum charge be...
Let me check to make sure I'm understanding what you said:
So the 3e6V/m for air is only valid until the gap gets below some threshold whereupon it actually gets significantly higher - and this was the fact that I was missing?
Finally, when you said, "But that must indeed be flawed," what...
I'll spare you all the details, but suppose for some reason (too complicated to get into here) I needed to design a capacitor with certain fixed parameters and only one adjustable aspect, and I wanted the design to maximize the total charge the device could store. According to my calculations...