Electron Drift Velocity in Conductor

A copper wire of length 1 meter and diameter 2 millimeters carries a DC current of 1 Ampere. How long does it take a given electron to migrate from one end to the other end of the wire?

This basic physics problem demonstrates clearly the difference between drift velocity and instantaneous velocity of electrons in a typical conductor. While the instantaneous speed of electrons in copper at room temperature is about 1.6 x 10^8 cm/sec (and in random directions), the drift velocity of the electrons which determines the measured macroscopic circuit current is much smaller.

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) 


     or    Vd = 0.0024 cm/sec
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).

M. Gallant 01/05/97


Now calculate the voltage drop across the same 1 meter length of wire carrying 1 Ampere of current. Assume that copper has a resistivity at room temperature of 1.7 X 10^-8 ohm-meter. If the electrons were not hindered by the collisions with the atoms, what drift velocity would the electrons attain in the 1 meter length with this voltage drop?
M. Gallant 10/20/2007

References:

The Theory of the Properties of Metals and Alloys, N. Mott and H. Jones, 1936 Oxford, pp 88, 315.

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.

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