Just out of curiosity, let's put some numbers to the idea and try to get some kind of a feel for the magnitude of a Coulomb.

The ClassE sstc has an input current of, say, 5 amperes. In other words, there are 5 Coulombs of charge, per second, passing through the ammeter on the front panel, doing whatever it does when it's in the ClassE circuit, and returning to the battery power supply... mostly.
And the AC RF part of the coil operates at a frequency of about 1 MHz. This means that, every one - millionth of a second, the current in the coil reverses direction, and if a capacity was filled by it going one way, it's drained by the current going the other way and then "refilled" with charge of the opposite sign (holes, really). So... every one millionth of a second, there are 5 millionths of a Coulomb of charge being sloshed around. Now if I try to stuff 0.000005 Coulomb onto a tiny surface like the point of the coil's breakout tower in a microsecond... it is not gonna be comfortable there and some part of it... a tiny part.... is going to spray off as corona, seeking neutral territory. And will find its way back to the system ground, through the air and the Earth itself, so charge conservation isn't violated and your battery doesn't shrink, get lighter or vanish into the seventh dimension.

Quote from: mrsean2k on July 17, 2012, 11:02:40 AM
I think that depends on how you define "maximally"?


In a circular room, if  you add one person at a time, I think you'd end up with:

n  = 1 - standing in the middle of the room.

n = 2 - standing at opposite ends of the diameter

n = 3 - at the points of the largest equilateral triangle the room can contain

n = 4 - this is where is gets tricky:
4a - at the corners of the largest square the room can contain or
4b - as for 3, but with the 4th standing dead center

4a maximises the minimum distance between any two people. But I think 4b maximises the overall sum of distances".

I'd think that generally, as N increases, they'd position themselves so they covered the floor with uniform density irrespective of the shape of the perimeter, as each individual jostled for position.

I'd need empirical evidence from a room and an endless supply of sworn enemies to be certain.

You are right, but you are also overwhelmed by the sheer numbers involved. As you put more enemies into the room, the Voltage increases, and there will be a point reached when the enemies will realise that they can simply jump through the walls or off the surface out in to space and get away that way. This means that there will always be a flow, from your enemy injection point, to the peripheral edges and points (where the voltage rises fastest) as the miserable repulsive cowards leap off into space to avoid being touched on the butt.

Here's your empirical evidence of this happening:
http://www.youtube.com/watch?v=FY-AS13fl30

Notice that there are only actually a few spots on the top toroidal capacity that emit the sparks. These will be found to be rough spots or sharper edges or projections on the surface of the otherwise smooth surface: field concentrations, places where the local voltage peaks due to the crowding effect described above.

Thanks for your comment... I'm not sure what the "humbug" referred to though.

I'll just get this down before I digest your response; it was a cry of anguish at not getting it, despite my private scribbled diagrams, and a vain attempt to stick my head in the sand and ignore the correct answer.

@MrSean2k: what the system seeks to maximise isn't exactly the intercharge spacing... it seeks to minimize the overall energy required to maintain the arrangement. So with n=4, a triangle at the periphery with one in the exact center is a _local_ minimum, with another deeper minimum nearby: the square, all at periphery. So the 3+1 arrangement is unstable and will "decay" or rather respond to the slightest perturbation, and flop "down" to the deeper energetic minimum represented by the square.

@TK


Ok, thanks, that makes sense (and keeps the analogy ticking along).