saefroch wrote:When charged, electrons migrate from one side of a capacitor to another, according to a logarithmic function (IIRC), which tapers off dramatically. So they charge almost to a limited voltage.
The earth is normally considered an infinite source of positive and negative charges. So I conclude that I can use electrons from the earth and cram them onto one side of a capacitor, leaving zero charge on the other side, since it's connected to the earth, and as soon as electrons are taken off, they're replaced.
Nope. When you charge a cap you push one electron in one of it's wires and one single electron flows out the other wire. In this mode a cap looks like a short circuit, that is it does as long as an infinitly small current is flowing and the cap has zero charge across it. But electrons never cross between the two sides of the cap (if they do the cap has failed or is leaking).
The "logarithmic" function comes from the difficulty in shoving the second electron into the cap when there is already an excess electron on that plate of the cap. Electrons repel each other so it takes more work to push the second electron in than it did for the first. The second electron also ejects an electron from the other plate of the cap and out the other wire. Repeat
ad naseum since a typical cap holds zillions of electrons when charged.
Can a cap be discharged to ground? Depends on what you mean. If you take a cap and hook it up to a 1.5 V battery, then disconnect the battery and measure the voltage across the cap it'll read as 1.5V. (Depending on the internal resistance of the meter and the value of the cap the cap may discharge through the meter pretty quickly.)
Now if you connect one of the cap's two wires to ground and don't connect the other wire to anything ... nothing much happens. The cap is still charged. If the wire you touched to ground happened to have been the negatively charged wire you might think the excess electrons on that plate would flow to ground, ... but they can't because that would require that the electrons move away from the positive charge on the other plate of the cap.
Here is what a charged cap might look like, negative on one plate and positive on the other. Push one electron into the negative plate from the battery negative terminal (-battery is on the left) and one electron from the positive plate flows into the batteries positive terminal (+battery is on the right) .
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Electrical circuits always need a complete circuit (though sometimes that circuit isn't obvious) and electronic devices (almost) always have at least two electrical connections (antennas only have one but the universe is the other connection). One connection, or the absence of a complete circuit, means no current flows, hence the cap can't discharged. (The cap will slowly "leak", either electrons cross the internal insulator or current is carried by the air between the cap's two leads.)