The drift velocity is the average velocity that a particle, such as an electron, attains due to an electric field. It can also be referred to as axial drift velocity since particles defined are assumed to be moving along a plane. In general, an electron will ‘rattle around’ randomly in a conductor at the Fermi velocity. An applied electric field will give this random motion a small net velocity in one direction.
Because current is proportional to drift velocity, which is, in turn, proportional to the magnitude of an external electric field, Ohm's law can be explained in terms of drift velocity.
Drift velocity is expressed in the following equations:
where v is the drift velocity of electrons, I is the current flowing through the material, n is the charge-carrier density, A is the area of cross-section of the material and q is the charge on the charge-carrier.
- v is again the drift velocity of the electrons, in m·s−1;
- M is the molar mass of the metal, in kg·mol−1;
- V is the voltage applied across the conductor, in V;
- NA is Avogadro’s number, in mol−1;
- d is the density (mass per unit volume) of the conductor, in kg·m−3;
- e is the fundamental electric charge, in C;
- ρ0 is the resistivity of the conductor at 0°C, in Ω·m;
- α0 is the temperature coefficent of resistivity of the conductor at 0°C, in K−1;
- T is the temperature of the conductor, in °C,
- ℓ is the length of the conductor, in m; and
- f is the number of free electrons released by each atom.
Electricity is most commonly conducted in a copper wire. Copper has a density of 8.94 g/cm³, and an atomic weight of 63.546 g/mol, so there are 140685.5 mol/m³. In 1 mole of any element there are 6.02×1023 atoms (Avogadro's constant). Therefore in 1m³ of copper there are about 8.5×1028 atoms (6.02×1023 × 140685.5 mol/m³). Copper has one free electron per atom, so n is equal to 8.5×1028 electrons per m³.
Assume a current I = 3 amperes, and a wire of 1 mm diameter (radius in meters = 0.0005m). This wire has a cross sectional area of 7.85×10−7 m2 (A = π×0.00052). The charge of 1 electron is q=−1.6×10−19 Coulombs. The drift velocity therefore can be calculated:
[v] = [amperes] / ( [electron/m3] × [m2] × [coulombs/electron] )
- = [coulombs] / ( [seconds] × [electron/m3] × [m2] × [coulombs/electron] )
- = [coulombs] / ( [seconds] × [meters-1] × [coulombs] )
- = [meters] / [second]
Therefore in this wire the electrons are flowing at the rate of −0.00029 m/s, or very nearly −1.0 m/hour.
By comparison, the Fermi velocity of these electrons (which, at room temperature, can be thought of as their approximate velocity in the absence of electric current) is around 1570 km/s.
In the case of alternating current, the direction of electron drift switches with the frequency of the current. In the example above, if the current were to alternate with the frequency of F = 60 Hz, drift velocity would likewise vary in a sine-wave pattern, and electrons would fluctuate about their initial positions with the amplitude of:
- Griffiths, David (1999). Introduction to Electrodynamics (3 ed.). Upper Saddle River, NJ: Prentice-Hall. p. 289.
- http://230nsc1.phy-astr.gsu.edu/hbase/electric/ohmmic.html Ohm's Law, Microscopic View, retrieved Feb 14, 2009
- Ohm's Law: Microscopic View at Hyperphysics