My question here is based on the following question in Physics for Scientists and Engineers (3rd edition) by Randall Knight:
An electroscope is positively charged by touching it with a positive glass rod. The electroscope leaves spread apart and the glass rod is removed. Then a negatively charged plastic rod is brought close to the top of the electroscope, but it doesn’t touch. What happens to the leaves?
a. The leaves get closer together.
b. The leaves spread farther apart.
c. One leaf moves higher, the other lower.
d. The leaves don’t move.
The answer given is a. Let's say that the total charge on the electroscope is +Q. I'm guessing that as you bring the negatively charged rod near to the electroscope, the positive charge on the electroscope "shifts" towards the negative rod, as follows: But it seems to me that there could (in theory?) be other possible configurations of the total charge, such as this: Here, the total charge on the electroscope is still +Q, but one end has charge +2Q and the other end has charge -Q. This would actually change the answer to the question (since the leaves would be further apart), but I'm more interested in the underlying physics than the answer to the question.
My question is simply this: how do we know (or, more accurately, how am I supposed to know) that the configuration of charge in the above image cannot occur?
Another question I have (on the exact same topic) is the following. If you take a spherical conducting shell (or basically any conductor with a cavity) and place a charge +Q in the cavity, then I know that the induced charge on the inner surface has to be -Q (by Gauss' law), as follows:
(Here I'm not worrying about the charge on the outer surface). But now my question is this: how do we know that the charge distribution on the inner surface is all negative? Couldn't there be an excess of negative charge on the part of the surface closest to the charge in the cavity, leaving a positive charge on the opposite side of the inner surface, while keeping the total charge on the inner surface -Q? That is, couldn't something like this happen: And if this is not possible, why not?
I guess the common theme underlying these two questions (as well as the previous one I asked) is that I have no idea how to "intuitively" work out how a charge will distribute itself over a conductor. And it seems intuitively that there could be multiple possible distributions and it's not obvious (to me) which is "correct". The books I'm looking at don't seem to have many guidelines about this.