What exactly happens in a conducting conductor?

[Gerenuk]

How exactly do conductors conduct electrons?

I'm confident with Maxwell's equations and I can accept a classical treatment like
$$\sigma=\frac{nq^2\tau}{m}$$
where $$\tau$$ is the scattering rate. So actually I'd like to know what exactly happens with the electromagnetic fields when a voltage source is attached.

Where is the field? How does it build up? In the ideal case, conductors don't have a field inside? How to treat that problem here (internal fields,...)? How does the voltage source act microscopically when attached?

 

[ZapperZ]

How exactly do conductors conduct electrons?

I'm confident with Maxwell's equations and I can accept a classical treatment like
$$\sigma=\frac{nq^2\tau}{m}$$
where $$\tau$$ is the scattering rate. So actually I'd like to know what exactly happens with the electromagnetic fields when a voltage source is attached.

Where is the field? How does it build up? In the ideal case, conductors don't have a field inside? How to treat that problem here (internal fields,...)? How does the voltage source act microscopically when attached?

When you start asking this type of question, then you need to resort to solid state physics. Not sure if you have access to, say, Kittel's Solid State Physics text, but if you do, check out the Drude Model, somewhere in the first few chapters of that text. This gives you the simplest description of charge transport in a standard metal.

Zz.

 

[Gerenuk]

I'm actually a graduate student working on CMP, but that's not where I want more clarification. My electrons are classical and move according to the above equation.

I'd like to know how exactly the electric and magnetic field build up and how a current is sustained, if in the ideal conductor there is no electric field. And how does a voltage source create a field? Is between the poles all of the time? How does it attach to very long leads?

 

[ZapperZ]

I'm actually a graduate student working on CMP, but that's not where I want more clarification. My electrons are classical and move according to the above equation.

I'd like to know how exactly the electric and magnetic field build up and how a current is sustained, if in the ideal conductor there is no electric field. And how does a voltage source create a field? Is between the poles all of the time? How does it attach to very long leads?

Oh, OK.

The confusion here is that in the "no fields in a conductor", the conductor is placed in a static field, and the charges that rearrange themselves to shield the inside of the conductor remain on the surface. This is not the case for when you connect the conductor to a battery, for example. These charges flow into the battery (we are still keeping the classical scenario), or out from the battery, depending on the polarity. So you continue to have a sink and a source that continues to pull or push charges in the conductor. So whatever is going on close to the electrodes inevitably affects the charges close by.

Zz.

 

[Gerenuk]

The confusion here is that in the "no fields in a conductor", the conductor is placed in a static field, and the charges that rearrange themselves to shield the inside of the conductor remain on the surface. This is not the case for when you connect the conductor to a battery, for example.

So there is a constant "external" E field in the steady case or a "billard scenario" of electrons? Is there electric field outside the conductor (isn't the conductor overall neutral)?

I remember a calculation where the integrated Poynting vector on the surface yielded $$\iint_\text{surf} \vec{N}\cdot\mathrm{d}\vec{S}=VI=IR^2$$ and I was wondering what that means ($$P=A\,E\,H=lc\,E\,\frac{I}{c}=VI$$ where A is surface area, l is length and c is circumference of the conductor).

... So you continue to have a sink and a source that continues to pull or push charges in the conductor. ...

Is there is pull of nearby electrons in matter only or is there an electric field between unconnected battery poles? The only pull-force is the electric field. Does that mean that pole end are effectively positive ions which get reionized when electrons from other matter are pulled in?