Re: what happens on an atomic scale in a conductor carrying current?

Dear Klaus in Korea,

One thing to remember is that metal used in common cables allows the 
creation of "free electrons" that can act as carriers of electric 
charge.  What does that mean?  It means that the electrons are not bound 
in a specific atomic state of the metal atoms, but are freely randomized 
throughout the metal material.  You've probably heard of the "conduction 
band" in conductors or semiconductors.  It is in this high energy band 
where electron current resides. While free electrons (modeled as what's 
known as a "Fermi free electron gas") exhibit magnetic and orbital spin 
character, their spins are also randomized.  The primary momenta of charge 
carriers that generate common current are linear, not spin.

The quantum mechanical momentum of a free electron is mv = ©¤k. What 
happens when we apply an electromagnetic field to a system of free 
electrons? They feel a "Lorentz" force described by the following 
relation:

  

If we have only an electrical field exerting the electromotive force (as 
in common cable), the magnetic field is zero (B = 0) and,

   

Over a time period, t,

   

That results in,

   

Now, with this simple theory, the longer we leave the field on, the faster
and faster the electrons start to move (the k-values, which are 
proportional to the momenta, keep on increasing in the x-direction)

This would mean that if you apply a field to a copper wire, and create an 
electrical current (movement of electrons), the current would grow as a 
function of time, apparently without a limit. What stops the electrons 
from moving faster and faster in this electric field? (they are 
accelerating under this force).

Collisions. These occur because of impurities in the cable, lattice 
defects or defomitites, and phonons (acoustic and optical particles 
characteristic of the cable material).  Experiments have shown that at 
room temperature (300 K), the electrical resistivity is dominated by 
electron collisions with phonons.


Here is the URL of a website with a nice pictorial view of current at the 
atomic level in a copper cable with a great discussion of drift 
velocity...

=> http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html


Another thing to consider is if a cable conducts high-frequency 
alternating current then the effective cross sectional area of the wire 
available for current conduction is diminished. The "skin effect" is the 
tendency of an alternating electric current to distribute itself within a 
conductor so that the current density near the surface of the conductor 
is greater than that at its core. That is, the electric current tends to 
flow at the "skin" of the conductor. 

A type of cable called litz wire (from the German Litzendraht, woven 
wire) is used to mitigate the skin effect for frequencies up to about one 
or two MHz. It consists of a number of insulated wire strands woven 
together in a carefully designed pattern, so that the overall magnetic 
field acts equally on all the wires and causes the total current to be 
distributed equally among them. Litz wire is often used in the windings 
of high-frequency transformers, to increase their efficiency.

Interesting new research on using individual atoms as conducting "cables" 
has given fresh insight into charge carrier flow on a nanometer scale. 
Conduction properties of these "cables" at the atomic scale are very 
different from the common cable we've discussed here.  It turns out to be 
possible to send extremely strong currents (corresponding to current 
densities of ~10e14 A/m2) through such devices without damaging them.

See the website at the URL

=>  
http://www.physics.leidenuniv.nl/sections/


Hope this helps Klaus in your investigation of electric current,

---* Dr. Ken Beck