Positive charge distribution in a conductor

[Yugeen]

Hi experts,

I still do not understand how positive charge is distributed inside a conductor. In case of extra electrons is it quite evident, as they are free to move and repel each other, so they go as far away as they can. But what exactly happens if electrons are removed from a conductor, let's say by induction and grounding?

I have already read that positive and negative extra charges are distributed on the surface, but how to describe the physics for the lack of electrons? Is there a tiny (one to two atoms) layer on the surface with no electrons? How to "feel" that this distribution has the least potential energy?

Thank you in advance.

 

[kuruman]

Start with a neutral conductor. In it you have a "gas" of electrons that are free to move and cannot be considered to belong to any particular atom. Note that not all atomic electrons are free to move; only one or two per atom. Within a volume element $dV$ inside the conductor, in any time interval the same number of electrons will enter the volume as will exit. The total number of moving negative charges within that volume will be, on average, the same as the total number of fixed positive charges.

Now what will happen if we somehow and all of a sudden (by magic means if necessary) we remove $N$ electrons from a volume element $dV$ right at the center of, say, a conducting sphere of radius $R$. All of a sudden there will be charge $+Ne$ with that volume which all attract the free moving electrons and eventually that volume element at the center will go back to its original situation of neutrality and inside it the total number of negative charges will be equal the total number of positive charges. In fact, this will be the case for all the elements $dV$ making up the sphere. Any element that does not meet the neutrality condition will attract or repel electrons until it does.

But what then is the effect of removing $N$ electrons? Who's left holding the bag? All the volume elements on the surface of the sphere although they are neutral inside have a deficit of negative charge on their edge that is part of the surface. It is incorrect to imagine that there are no electrons on the surface. Electrons from one part on the surface are free to move to another part on the surface but not under the surface. In any time interval, the same number of electrons will enter a surface element $dA$ as will exit. If one electron from the surface dives under, another electron will rise up to take its place. The end result is that there will be a deficit of charge $-Ne$ on the surface which is equally distributed in the case of a sphere. In other words the removal of electrons from the center of the sphere when all was said and done produced deficit of electrons on the surface which is equivalent to having charge $+Ne$ placed on the surface.

Just think, how is the picture of removing charge $-Ne$ from the sphere (what I described above) different from placing charge $+Ne$ on the surface of the sphere? In both cases you have an electrically neutral volume under the surface and positive charge $+Ne$ on the surface. The only difference, which does not affect the electrical behavior, is that one sphere has slightly less mass than the other.