Question

Hi experts, my question is regarding lecture 5 and charge distribution inside a conductor. It is evident that if extra electrons are transferred to a conductor, they just repel each other and go as far as they can (to the outside), as they are free to move. But what is the physics when there is a lack of electrons? How the positive charge can be distributed to the outside if they are not free to move? Moreover, is there an other way to make a conductor positively charged except removing some electrons (e.g. by induction when the conductor is grounded)?

Answer 1

The positive charge can be distributed to the outside when the electrons go to the center of the conductor by the same kind of logic. An analogy of thinking of this might be if the moon had a bunch of holes in it and you took a bucket of water and poured it on the moon. All the water would go through the holes, straight to the center of the moon. Similarly, in a conductor electrons travel to the center.

The only other way to make a conductor more positively charged by not removing electrons would be to add protons.

Answer 2

Hi Kainui,
Thank you for your response. Can we say in such a situation that the electrons left in the conductor goes to the place with the least potential energy? And the least is closer to center - let it be a solid sphere to ease the problem. If we theoretically make a sphere of only protons (it's clear that this is impossible) and put a single electron on its surface, then it goes directly to the center - is it correct? The second one, if placed, goes there as well, as the total force on the electrons is still much greater that they repel each other.
In case of the hollow "proton" sphere the electrons can only move inwards till they reach the internal body limit. Can we finally say for some kind of approximation that the positive charges can be replaced by a strong single charge placed in the center of both solid and hollow sphere and that makes the electrons move inside?

Answer 3

To your first question, yes. But don't over complicate this too much, just remember that you only need to know \[F _{e}=k _{e}q _{1}q_{2}/r^2\]So when you look at a single electron next to a large sphere of protons you'll see something like this: and now you see the electron really is forced into the protons. Where can it have the least amount of force on it? In the center, where it is in equilibrium with all the forces acting upon it. Now eventually if you add enough electrons you'll pass a threshold where it's neutral and then electrons will begin to accumulate on the surface.

Don't take my moon analogy too far, as electrons aren't actually water and gravity can never be a repulsive force. I only meant to use that to show how the center of a body will attract things to its center to be most stable in equilibrium.

As for modelling a charged object at its center of charge, similar to a graviational object at its center of mass, yes you can do this.

Answer 4

Thank you for the great explanation, it is clear now!

Answer 5

Glad I could help!