Calculation of Drift Velocity Vd:
Since an electron carries a charge of 1.6 x 10^-19 Coulombs, and one Ampere is a current of one Coulomb per second, the number of electrons passing any cross-section of the wire is 1/(1.6x10^-19) or about 6.3x10^18 electrons per second. This must equal the drift velocity Vd of the electrons times the number of mobile electrons Nl per unit length. Since copper has a valence of one, and fundamental experiments have shown that these valence electrons behave just like free electrons, Nl is just the density of copper atoms (8.45x10^22 / cm^3) times the cross sectional area A of the wire. Therefore,
Vd = 6.3x10^18 / (NlxA)The time for an electron to traverse the one meter length of the wire is therefore about 12 hours. The drift velocity of electrons is very small due to the carrier scattering with the atomic vibrations ("phonons") at room temperature. In fact, it is just this scattering behavior that is responsible for the linear relation between electric field and current density in a conductor, or in more familiar terms, Ohm's Law. Note that the electromagnetic field, and hence any voltage changes, associated with the electrical current propagates down the wire at a speed close to the speed of light (3x10^10 cm/sec).
or Vd = 0.0024 cm/sec
M. Gallant 01/05/97
M. Gallant 10/20/2007
Physics, D. Halliday and R. Resnick, part II, 1962 Wiley, pp 770-773.
Introduction to Solid State Physics, C. Kittel, 4th Edn. 1971 Wiley, pp 39, 248, 257.