# Electron motion in a wire

For my introductory course to electromagnetism (I'm an undergraduate student, so ELI5), I'm trying to get the right conceptual model of electron movement in a thin wire (with constant but non-zero cross section, like a cylinder) due to a constant current. It seems to me, that there are several contributing factors, and I wonder which dominate, and if some kind of order exists.

1. Electrostatic repulsion between electrons. If this was the only force at play, electrons should all travel on the surface of the wire.

2. Magnetostatic attraction caused by the magnetic field from charges in motion. If this was the only force then the electrons would all travel in the center of the cylinder.

3. Collisions with matter and thermal scattering, which would make the motion chaotic.

4. Material properties of the cylinder, and if in particular the cylinder is a metal, then I suspect that the lattice planes of the metal and orientation of these planes is somehow relevant.

Basically 1 and 2 create order, 3 and 4 seem to destroy it. I can't seem to find anything relevant in my courseware or online. Specifically I'm interested in common DC household wires.

• If all electrons transferred to surface positive ions that remain will pull them back, so no even if only electrostatic forces exist, not ALL electrons would go to surface. Also please elaborate your question, are you giving an answer and asking whether it is correct or a question hidden in there somwhere is hard to comprehend. – Rijul Gupta Oct 21 '13 at 11:23
• @rijulgupta I'm just trying to picture how the electrons are actually moving in my head. My question is if there is some kind of order to their motion or if there isn't. I list several factors that I suspect to contribute, but I don't know which dominate or are relevant. – Gleno Oct 21 '13 at 11:26

1 and 3 are the major players here, and chaotic/brownian/random movement with lots and lots of collisions is what the electrons do even when they are being pushed from one place to another as a current.

The electrostatic repulsions and attractions tend to both bring them close and separate them at the same time, while heating just gives them a kinetic energy which makes them move randomly in any direction.

They just continue to do their random motion in different parts of wires as they are transferred from one location to other under the applied electric field.

The movement of the electrons comes from the electric field (or equivalently the voltage : $\mathbf E = - \nabla V$), not the current. The current itself is merely the average movement of the electrons, caused by the applied voltage.

So what makes the current? The electric field accelerates the charges, but they are randomly deflected by collisions so that the energy the electric field gives them ends up as increased random motion of particles: heat (that's the Joule effect).

Now for an ideal (perfect) conductor, point 3 vanishes and there is no electric field : the most simple picture would be that electrons have a constant motion in the wire that is determined by whatever else there is in the circuit.

A last note: your point 4 is usually accounted for as part of point 3.