# Why the net field inside a conductor is zero?

1. Sep 10, 2014

### recomendacion

I do not really understand the big picture of gauss law. For what I know a conductor is a material where electrons can move freely, but I am reading my book and they show pictures where the protons are all right below the surface. My other question would be how can you describe the inside of a conductor? and how it is related to gauss law?

2. Sep 10, 2014

### Philip Wood

A few points to start off the discussionâ€¦

The 'net field' is a sort of average electric field strength over a region large enough to contain many atoms (at least several hundred).

The net field is not zero if there is a current in the conductor. A field is needed to keep the electrons moving with a constant mean drift velocity, because collision forces oppose their motion.

The net field is zero in electrostatic conditions, that is no current. If there were a field there would be a current. So that's why we talk about no net field in a conductor: it's the condition for electroSTATICs.

So no net field does NOT follow from Gauss's law, rather it provides an interesting settingg in which to apply Gauss's law.

3. Sep 10, 2014

### TrueColor

You can imagine a conductor as an object that contains infinite amount of free charge(electrons) that roam around the conductor. These electrons are actually valence electron, and they can roam freely cause we imagine that the energy required to tear them from their atom is zero. Total charge of an isolated conductor is zero, cause we assume there's equal amount of protons and electrons in atoms that constitute the conductor.

If you have any excess of charge inside a conductor, there exists electric field and push these free electrons around. By Earnshaw's theorem, system can't be held in a stable equilibrium by electrostatic forces alone so if you have excess of negative charge inside conductor, these free electrons will be repelled by it, and would go to infinity if they can, but they can't because they are bounded by the surface of a conductor. They can't leave surface cause they don't have enough energy to break through(theirs energy is below work energy of a conductor). If you put a positive charge inside, same argument goes, but now you imagine that when atttracted electrons come to that positive charge to "suppress" it, they leave lack of negative charge on a surface, which is equal to saying that you have excess of positive charge.

I hope this explanation sounds ok, please someone correct me if I'm wrong :)