# A question about electrons behavior in a conductor

1. Oct 19, 2009

### fluidistic

I'm only midway to finish my introduction to electromagnetism (level around Resnick-Halliday) so I understand the concepts I will talk about, but I never derived them.

For example, in the case of a spherical (not empty) conductor or any other solid conductor. If we charge it with extra electrons, they will move until being on the surface of the solid. I understand this result (however not why an electron cannot stay at the center of the sphere while the others go on the surface, but this is not my main question for now at least. I know I'd have to derive that in the formal EM course.).
Now if we take the case of a thin and long conductor (like a copper electric cable) and we apply a difference of potential between both extremes of the rod, the free electrons will move through the rod from a surface area to another. I don't understand why the density of electrons is the same for each cross area section. Shouldn't they move only at the surface of the conductor? Why is the case different from the static case I first described?

Thanks a lot.

2. Oct 19, 2009

### Bob_for_short

All free (additional) charges move to the fartherst distances from each other. A chanrge in a center is possible but this is unstable configuration. Any fluctuation destroys it.

Charges in conductor move in the whole volume according to two forces: electrical field and friction. Electrical field is directed along the wire axis so why only surface charges should move? All mobil charges move. Any piece of conductor has some electric field (potential difference) because there is a resistance. So the current is not infinite in real materials.

3. Oct 19, 2009

### fluidistic

I'm still not getting it. I guess I should wait next year when I'll have the formal EM course.
I don't realize that the farthest distance between charges is precisely when they are at the surface of the conductor. But It's not really important, I know I'll derive it.

However in the case of a conductor rod, although I realize all free charges (whether of not they are on the surface) must move under the action of a difference of potential, I don't understand the distribution of charges. Why is the distribution of charge different from the case of a charged conductor rod? (or a charged spherical conductor).

4. Oct 19, 2009

### hamster143

The difference is that your sphere is charged and your rod is not. So, if there's an excess of electrons on the surface of the rod, that means excess positive charge in the middle.

5. Oct 19, 2009

### fluidistic

I get it now. Thank you very much to both!

6. Oct 19, 2009

### Bob_for_short

Metallic rod is like lattice of positively charged ions (that stay still) and a negatively charged electron liquid. In equilibrium and in a neutral state the number of electrons in each volume is equal to the positive charge. They are distributed in the metal volume uniformly (any volume is neutral). One can add extra free electrons from exterior. These will cover surface. One can detract some electron from the metal. This will make a lattice tension due to non balanced positive charge.