Evil Bunny said:
I guess I'm having a hard time wrapping my head around this. pulling the plates apart would really increase the voltage between them? Wow... The energy that you put into the system to pull the plates away from each other will increase the voltage on the plates... Seems like this might be a useful phenomenon in certain situations. Is there a component that utilizes this ability?
None that I know of -- an interesting idea, though.
Evil Bunny said:
Anyway... back to the capacitor... the charges only "built up" on the plates in the first place because they were attracted to each other by an electric field. Now... as the plates seperate, this field becomes weaker and weaker and one would assume that if the plates kept moving farther away from each other, they would escape the influence of the field altogether and they would simply become metal plates... presumably with a charge still on them.
Well, the electric field would get weaker, and I suppose at some point it would be negligibly small, but it won't disappear until the charge does. (Unless there's another conductor to interact with.)
Evil Bunny said:
We've basically just turned these two plates into a "static" situation where we could move them close to the ground and produce mini lightning bolts, right? Sounds like a neat science project.
Yeah, we're dealing with static electricity and if the voltage were high enough, you would get a noticeable arc.
brainyman89 said:
if we assume that these two charged plates are separated for a long distance in a way that the influence of the electric field no more exists, how could we calculate the voltage between these two plates?
There are two
easy models for dealing with capacitor plates. When the plates are very near each other, we can assume the field inside is uniform (which is only actually true when the plates are infinite planes), and when the plates are far away, we can look at them as point charges (which is only approaches reality as they get farther away).
Here's a simple formula for voltage due to point charges.
[URL]http://maxwell.byu.edu/~spencerr/websumm122/img213.gif[/URL]
where r is the distance, q the charge, and k a constant. OK, but this is a bad way to write this formula for our purposes, though, since we know V is maximum at infinity, then decreases as the plates move closer. We really want V = C - kq/r (we can add the constant both because voltage is relative and because this formula comes from an integration problem), where C is a constant that can be found if you know the voltage of the plates when they are at some distance r.
At distances where the infinite plate or point charge methods don't work well enough, the math would get more complicated; the charge distribution would no longer be uniform on the plates. To be honest, calculating voltage in that region is a little beyond my skill.