**Conduction Electrons**Some points gleaned from various sources:

**1)** In a vacuum the electric field would cause a charge to accelerate. In a wire, collisions of the conduction charges with impurities, imperfections, and vibrations of the atomic lattice causes the motion of the conduction charges to be slowed down. This represents a loss of energy which is dissipated as heat.

**2)** Within a metal conductor, even though there are free electrons, there is still resistance to current flow. This can be described by simple models, but apparently only quantum electron theories accurately deal with the behavior of metals under extreme conditions such as very low temperatures. Replacing the idea of electrons as particles with electrons as waves solves the problems of the simpler models. You can picture these electron waves oscillating through the metal lattice (which can also be pictured as a wave-like structure) - the interference of the lattice structure with the electrons causes resistance. This resistance is caused mainly by two things. One is impurities in the metal, which cause irregularities in the periodicity of the lattice. The other is the disturbance or "vibration" of the lattice caused by heat. Since some heat is always present (except at absolute zero) there is always some resistance from this source which prevents the electrons from sailing through.

**3)** The drift speed of electric charges

The mobile charged particles within a conductor move constantly in random directions. In order for a net flow of charge to exist, the particles must also move together with an average drift rate. Electrons are the charge carriers in metals and they follow an erratic path, bouncing from atom to atom, but generally drifting in the direction of the electric field. The speed at which they drift can be calculated from the equation:

I=nAvQ

where

I is the electric current

n is number of charged particles per unit volume

A is the cross-sectional area of the conductor

v is the drift velocity, and

Q is the charge on each particle.

Electric currents in solid matter are typically very slow flows. For example, in a copper wire of cross-section 0.5 mm², carrying a current of 5 A, the drift velocity of the electrons is of the order of a millimetre per second. To take a different example, in the near-vacuum inside a cathode ray tube, the electrons travel in near-straight lines ("ballistically") at about a tenth of the speed of light.

However, we know that electrical signals are electromagnetic waves which propagate at very high speed outside the surface of the conductor (moving at the speed of light, as can be deduced from Maxwell's Equations). For example, in AC power lines, the waves of electromagnetic energy propagate through the space between the wires which is usually filled with insulating material, moving from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance. The velocity of the flowing charges is quite low.

The associated electromagnetic energy travels at a speed which is much faster. The velocity factor is a measure of the speed of electromagnetic propagation compared to the speed of light in a vacuum. The velocity factor is affected by the nature of the insulating medium surrounding the conductor, and also the magnetic properties of the materials of the conductor and its surroundings.

The nature of these three velocities can be clarified by analogy with the three similar velocities associated with gases. The low drift velocity of charge carriers is analogous to air motions; to wind. The large signal velocity is roughly analogous to the rapid propagation of sound waves, while the large random motion of charges is analogous to heat; to the high thermal velocity of randomly vibrating gas particles.

**4)** Metals

Metals are good conductors of electricity and heat because they have unfilled space in the valence energy band. (The Fermi level dictates only partial occupancy of the band.) In the absence of an electric field, conduction electrons travel in all directions at very high velocities. Even at the coldest possible temperature — absolute zero — conduction electrons can still travel at the Fermi velocity (the velocity of electrons at the Fermi energy). When an electric field is applied, a slight imbalance develops and mobile electrons flow. Electrons in this band can be accelerated by the field because there are plenty of nearby unfilled states in the band.

Resistance comes about in a metal because of the scattering of electrons from defects in the lattice or by phonons. A crude classical theory of conduction in simple metals is the Drude model, in which scattering is characterized by a relaxation time τ. The conductivity is then given by the formula

sigma = {ne^2 \tau}/{m}

where n is the density of conduction electrons, e is the electron charge, and m is the electron mass. A better model is the so-called semi-classical theory, in which the effect of the periodic potential of the lattice on the electrons gives them an effective mass (ref. band theory).

**5)** William Beaty's

**Speed of Electricity****6)** In the classical model of electric conduction, a conductor (ie.

metal bar, wire, etc.) is pictured as a three dimensional array

of atoms or ions and the electrons are free to move about the

conductor. In the absence of an electric field the elctrons

move about in the same manner as gas molecules move about in a

container. The free electrons collide with ions of the 3-D

array and are in thermal equilibrium with them. The speed

with which the electrons are "bouncing" around is on the order

of 10^7 cm/s.

When a potential electric field is applied, the electron

experiences a force and subsequently it is accelerated. The

velocity of that electron is proportional to the force and the

duration that the force is applied. It is inversely proportional

to the mass of the electron.

velocity = q * E * t / m

where q is the charge, E the field strength, t the duration, and

m the mass. So in other words there is no "constant" speed for

electricity.

The net speed with which electrons travel under some field is

called the drift velocity. Here is an example of how to calculate

the drift velocity for electrons in a conductor carrying current:

example

-------

Say you have a piece of 14 gauge copper wire (radius 0.0814 cm)

and that wire is carrying 1 A. We can assume one free electron

for every copper atom in the wire. The density of free electrons

in the wire, n, is

n = (6.02 x 10^23 atoms/mol)(8.92 g/cc) / 63.5 g/mol

= 8.46 x 10^22 atoms/cc

and the drift velocity, v, is

v = 1 C/s / (pi * 0.0814 cm * 0.0814 cm)(8.46x10^22 atoms/cc)(1.6x10^-19 C)

= 3.55 x 10^-3 cm/s

= 0.00255 cm/s

Note that this drift velocity is very small when compared to the

velocity the electron at thermal equilibrium is at "bouncing"

around.

[Moderator note: Another way to look at this is from the perspective of an

electron. For the wire mentioned above, when the current flows, it is just one

electron being pushed into the wire at one end, and another electron popping out

the other end, over and over many times a second. The electrons in between

shift over with a speed of 0.00255 cm/s. However, the speed of the "push" is

close to the speed of light, so that the electron on the far end of the wire

pops out very soon after the electron on the other end is pushed in. I think

your question brings up the additional question of what exactly electricity is.

Is it the electrons, or the movement of electrons?]

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