Testing the TK Tar Baby

[PhiChaser]

Yes... equally spaced apart and, because they are taking no chances whatsoever of being touched.... they will be maximally far apart, too. Which means they will be located..... exactly..... where?  Can you pin them down more precisely? ( the room is roughly square, I forgot to mention that, sorry)
In fact, please imagine several different perimeter shapes.  A circular room, a star-shaped room, etc.. Where will all the mutually repelling unit charges wind up, if they are left to their own tendencies, which are not only just to repel but to get as far apart from everybody else as possible?

If the room is square they will wind up in the corners (furthest apart). In a sphere they would keep moving along the outer perimeter since they would always be 'looking' for the furthest distance apart. When one would move the rest would also move in response to keep the maximum distance between them. I can see where a ring or sphere would be a beneficial shape using this analogy. So far so good?

PC

[TinselKoala]

If the room is square they will wind up in the corners (furthest apart). In a sphere they would keep moving along the outer perimeter since they would always be 'looking' for the furthest distance apart. When one would move the rest would also move in response to keep the maximum distance between them. I can see where a ring or sphere would be a beneficial shape using this analogy. So far so good?

PC

Bingo. Thank you for persisting. The charges will wind up concentrating along outer perimeters, in sharp corners, along edges.... and if you have a smooth spherical surface or a ring...like a toroid.... you can get the _most_ charge to fit on it comfortably per unit surface area.

Up until now I have talked about charges like they are small discrete quantized packets... and so they are. But a single Unit Charge is so tiny that it's just not practical to dump, say, four of them into a box. So usually I'll refer to "charge" as a kind of group noun: it represents a bigger lump of unit charges, some palpable portion of that Coulomb of charge that is a whole  ampere-second's worth. A Coulomb of charge is actually a huge amount of charge... if we could experience an entire Coulomb's worth of naked negative charges all at once we'd see a very strong electric field indeed and charge would be jumping off sharp points and edges of whatever surface we forced all that charge onto. If we have an ampere of current flowing in a circuit of wire and components, we really don't see the naked negative charge of an entire Coulomb of unit charges. We only see the effects of the moving charges, and since it's a current flow, what comes in one end (from the power source) goes out the other end (back to the power source) and the charge itself isn't depleted (charge is conserved !) but only the energy used to push it through the circuit is depleted.

So... the takehome message is: charge diverges. It tries to spread out, to get as far away from like charge as possible and on a conductor this means it will hog the surface, the edges and the points, until it's easier to just jump right off the surface than it is to "face" the crowded volume behind, that's full of all that jostling charge being pushed into the volume by the power source. (this jumping off can happen at any voltage but is usually not an important phenomenon until voltages... the relative pressure between the charges within the volume, and some lower outside reference level... start getting really high, like in excess of 6 kV. At 20 kV or more you start to see corona, which is an effect of charge actually spraying off the sharp points of your shape...your capacity.... into space.
We don't usually see this in low voltage circuits, even though they may be carrying entire whole Coulombs of charge circulating around in the wires, because we don't allow this charge to accumulate in a reservoir (a capacitance) without being neutralized by its equal and opposite charge. But we can, if we so desire.... please see my ClassE sstc for an example of a circuit with a low voltage DC supply that DOES take that charge, separate it from its opposite, and stuffs it into a capacitance at high voltage--- from where it sprays off into space, seeking some lower voltage area.

I want to thank PhiChaser again for bringing up this important point.

(To get some idea of just how huge an amount of charge a Coulomb really is.... Nikola Tesla believed that he could transmit power all around the globe of the earth, by using just 20 or 30 Coulombs of charge, sloshing around between his powerful Wardenclyffe transmitter and the Earth's ionosphere-ground cavity. And I believe it too. But charge is not energy; it takes a lot of energy to separate that much negative charge and manipulate it as Tesla sought to do.)

[mrsean2k]

.... they will be maximally far apart, too. Which means they will be located..... exactly..... where?

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.

[mrsean2k]

Humbug!

[MileHigh]

Mark:

Thanks for your nice comments and good luck with your ongoing investigations.  I really look forward to hearing about the testing on the buoyancy system also.

MileHigh