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What happens microscopically when an electrical current starts to flow? I'd like to understand microscopically what happens in detail when electrons start moving (quasi-classically).

Electrons can have different velocity, they can produce electromagnetic fields, leads have free electrons and rigid atom cores and there exist electromagnetic fields. That's all the ingredients you should need?

Electrons only move due to EM fields, so basically this question boils down to what the EM fields look like and how they build up?! In steady state, what is the electric and magnetic field distribution in/around the lead? And what about the transient state?

What happens when you attack a battery to a lead? Are there EM fields between battery poles or why are electrons pushed? How do the EM field start to push electrons along an arbitraritly shaped long lead?

[EDIT: Ideally an explanation with the Drude model (which partly derives from Fermi model) or an explanation why that model isn't sufficient. Also stating the EM fields consistent with the electron density distribution would be important (i.e. $\vec{E}(r,\theta,z)$ and $\vec{B}(r,\theta,z)$) because otherwise it's hand-wavy arguments.]

(Please consider all remarks in this question. I know common arguments for parts of the question, but I've never seen a full microscopic in detail explanation.)

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I could swear that I saw the answer to your questions on this site summed up in a single answer even with a diagram. –  Alexander Mar 2 '12 at 10:25
    
possible duplicate of how does electricity propagate in a conductor? –  Qmechanic Mar 2 '12 at 15:51
    
I've looked at the question, but it is not going in the same direction. The most important part in my question is to state the EM field for all points in space and then explain how that drives the electrons. The answer there only mentions there is "voltage from the power plant", but it doesn't draw the whole picture. –  Gerenuk Mar 3 '12 at 9:18
    
If you like this question you may also enjoy reading this and this question. –  Qmechanic Mar 4 '12 at 12:16
    
I found Purcell's explanations of this kind of phenomena particularly easy to understand. –  Emilio Pisanty May 3 '12 at 13:44

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The conduction electrons in a length of wire can be modelled as a (Fermi) gas. Just like molecules in a gas, individual electrons wander around randomly, and a local increase in density of electrons causes a locally higher pressure. You can even get electron density waves that are analogous to sound waves.

Using this analogy, suppose you have a tube full of air and you suddenly increase the pressure at one end. You will generate a pressure wave that travels down the tube causing gas molecules to start moving as it reaches them. Assuming you maintain the pressure at the end of the tube, the gas molecules will on average move down the tube. I say "on average" because any individual gas molecule diffuses at random, but when there is a pressure gradient the net flow is down the gradient.

All this pretty much transfers straight to the electrons in the wire. Your battery has an excess of electrons at the negative terminal and a deficit at the positive terminal (just like a charged capacitor in fact). When you connect it to the wire the excess electrons at the battery negative terminal start diffusing into the wire. Electrons in the wire then start diffusing away from the negative terminal along the wire and the end result is a voltage wave that travels down the wire at a few tenths of the speed of light. Because there is some resistance to the electron motion (assuming the wire isn't a superconductor!) you end up with a pressure, i.e. voltage, gradient along the wire.

It feels like I say this for every answer, but Wikipedia has articles on the electron gas model. See http://en.wikipedia.org/wiki/Free_electron_model and the links in that article like http://en.wikipedia.org/wiki/Nearly-free_electron_model

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The problem with this explanation is that it isn't a pressure wave that pushes the electrons, it is an electromagnetic wave. A pressure wave travels at the speed of sound, and the response travels at the speed of light. Setting up the field is simple--- the field pushes all the electrons in the wire simultaneously, and excites a few electrons near the Fermi energy to move. The answer to the question linked in the comments explains how the field ends up following the wire. –  Ron Maimon Mar 4 '12 at 2:14
    
I also heard that the EM field plays a key role. But your other post doesn't really answer this particular question, as merely saying "there is a voltage" provides no concrete information. I added a comment to this question above. –  Gerenuk Mar 4 '12 at 11:43
    
@RonMaimon When molecules collide, they repel by a short range electric force. When electrons collide they repel by a long range electric force. And that's why speed of sound in electron gas is high. I would guess screening does not really change this. Can every electron in a wire be screened? I would say no. –  kartsa Mar 4 '12 at 13:15

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