# Ideal conductor and charge movement

1. Jan 16, 2008

### Paul20

Hi

This question really matters me and I would like to someone to point me out (rigorously if possible) why and what makes charge move in ideal conductor.
All good conductors are modelled as being ideal so that the Maxwell equations inside the conductor needs not to be solved. So as electric field is zero in the conductor and that the tangential component of electric field on the surface needs to be zero why does current really flow? According to Ohm's law J the current density is proportional to the electrif field which is zero this implies that current density is zero and there is no charge movement as far as I know?

So what is the flaw im my reasoning?

Thanks!

2. Jan 16, 2008

### Staff: Mentor

That's only true in the electrostatic case. If there's current flowing, there's a non-zero field within the conductor.

3. Jan 16, 2008

### Paul20

I still don't get it...What I have understood is that it is the electric field which gets the charge moving. And everywhere in literature when they are speaking of ideal conductors it is always assumed that the electric field inside the conductor is zero.

Can you point more specificly from the Maxwell's equation what you mean?

4. Jan 16, 2008

### Staff: Mentor

True.
Not true. That's only true in the electrostatic case (no moving charges). If you think you've read otherwise, provide a reference.

5. Jan 16, 2008

### Troels

One comment: There *is* one case in electrodymanics where the electric field inside the conductor is zero, and that it for the case of an ideal conductor; ideal in the meaning of infinite conductivity.

In that case Ohm's law would imply infinite current for anything else than zero field in the conductor, which would be intolerant from a physical point of view. Hence, once you have gotten a current going in an infinitely conducting wire, no futher electromotive force is needed to sustain the current.

The example is of course rather artificial, save for superconductors, but I'm not sure the obey Ohm's law in the first place, and my course in quantum electronics and supercoductivity is scheduled a year from now :)

Last edited: Jan 16, 2008
6. Jan 19, 2008

### drv

Why current flows in a conductor

The movement of electric charges (electrons) in a conductor is similar to the movements of gas molecules. This assertion was made by Professor Max Planck over 100 years ago. The molecular movements is related to temperature and probability. The movement of molecules was defined by Boltzmann a few decades earlier. At a given temperature, various states of equilibrium exist within the material. The number of states and the degrees of movement are related by probability theory. Planck noted the similarity to atomic states and derived his famous Blackbody Radiation equation, partly on the basis of Boltzmann's probability calculations. These energy state equation shows that the energy level is proportional to kT. Similarly, the electron mobility of a conductor is inversely proportional to the square root of kT (proportional to an inherent actuating voltage). The electrons move in various directions, sideways, forwards and backwards, so there is no net movement to speak of in any direction (only low-level noise spikes). These moving electrons are sometimes referred to as "free electrons", although there has been some confusion, in the past, of the concept of a free electron.