# 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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