Wait... why exactly does farady's ice pail experiment prove Gauss's law?

Question

You'll notice there are no equations in this: that's because this is a question of morale, not of math. But a humble one at that! I come to learn, not to expound. But don't let that limit the form of your answer! Thank you in advance...

So, there are two aspects to the physics of electrostatics that I incidentally know confuse me right now. First off, it's the implications of these principles:

If there was an electric charge inside a conductor, it would induce motion in the charges. Therefore, we conclude that in electrostatic situations, there is no net charge inside the conductor.

Fair enough! Electrons move very easily in conductors. So I suppose this makes sense! But, that doesn't quite, in itself, give me enough information to predict the electric charge inside of a conductor can be electrostatic. Here's how I figure it:

If charge is evenly spread throughout a conductor, and out of balance, then the net excess charge (net field) inside of that conductor is going to be more "intense" (ie, ephemeral net electric field?) for charges inside rather than charges at the at the surface - they are "closer" and thus, the exact outside of the the conductor is where they will rapidly end up. (If there is no field outside the conductor, there is less "pressing" on the electrons from the outside.

Now that's fine, however: in a sufficiently huge hollow conductor, why don't they end up on the inside?

That works great for electrons! (Or, I thought it did.) However, my train of thought starts to break down for positive charges, and realistically, huge hollow conductors. If there is any stray charge outside of a certain conductor, couldn't there be some on an internal surface of a huge, hallow conductor? These would tend to cancel each other out, but in that non-ideal situation....

In the Faraday Ice Pail experiment shown in my physics book, it is a positive charge that is lowered into the pails.. ie, a lack of electrons. However, the positive charge stays on the surface as well... meaning their is a "lack" of electrons on the outside of the pail. Suddenly it's much harder to visualize my own crude "theory."

Would someone be so kind as to tell me what mechanism exactly, the electrons are propelled to such locations that they are in this situation?

I guess it seems consistent with conservation of energy (ie, moving electrons are doing doing work, whereas static charges do not? Thus again we can't have moving charges sustained in the conductor without an energy source?)

Answer 1

As you say: "If there is any stray charge outside of a certain conductor, couldn't there be some on an internal surface of a huge, hollow conductor?"

Certainly! I think your confusion arises from a misunderstanding of what "outside" means in this context. Outside does not mean "the furthest surface from the center of mass of an object." It means "the surface of an object." Likewise, the "inside" of a conductor refers to the actual matter of the conductor itself (the atoms making up the metal, that is), not to any hollow cavity in the middle of a larger conductor.

Suppose we have a spherical copper shell - that is, a sphere made of copper with a cavity in the middle. If we put a positive charge in the middle of this hollow cavity, then the inner surface of the shell will tend to become negatively charged (as the positive charge in the center will pull electrons to the inner surface) and the outer surface will become positively charged (in the absence of electrons). This is essentially the situation you have described, and it is completely accurate.

Your instinct about conservation of energy is also correct. The reason that moving charges cannot be sustained in a conductor is because no current in a conductor is indefinitely sustainable without some addition of energy. So eventually the charges in a conductor must move to some electrostatic position.

I'm not sure if this answers your question completely, because I'm not quite certain how the two aspects of your question ("what is the mechanism by which electrons are propelled" and "why do charges end up on the outside") fit together, so let me know if you need any clarification.

Answer 2

Faraday showed us a charged object inside a steel cylinder when touched Moves the charge to the outside when repeated builds the charge .which shows a lower moving to a higher.if for instance a 5 touched recharged and repeated 5 times there would be 25 outside and when charged again the 5 would create its own opposite of 5 with 30 outside.in other words everytime it touches it builds charge on outside of container.for some reason people aren't told this was part of the experiment.