The drift velocity is the average velocity that a particle, such as an electron, attains in a material due to an electric field. It can also be referred to as axial drift velocity. In general, an electron will propagate randomly in a conductor at the Fermi velocity. An applied electric field will give this random motion a small net flow velocity in one direction.
Because current is proportional to drift velocity, which in a resistive material is, in turn, proportional to the magnitude of an external electric field, Ohm's law can be explained in terms of drift velocity.
The most elementary expression of Ohm's law is:
This can also be written as:
But the current density and drift velocity, j and u, are in fact vectors, so this relationship is often written as:
- u is again the drift velocity of the electrons, in m⋅s−1
- m is the molecular mass of the metal, in kg
- σ is the electric conductivity of the medium at the temperature considered, in S/m.
- ΔV is the voltage applied across the conductor, in V
- ρ is the density (mass per unit volume) of the conductor, in kg⋅m−3
- e is the elementary charge, in C
- f is the number of free electrons per atom
- ℓ is the length of the conductor, in m
Electricity is most commonly conducted in a copper wire. Copper has a density of , and an 8.94 g/cm3atomic weight of , so there are 63.546 g/mol685.5 mol/m3. In one 140mole of any element there are ×1023 atoms ( 6.02Avogadro's constant). Therefore, in of copper there are about 1 m3×1028 atoms ( 8.5×1023 × 6.02685.5 mol/m3140). Copper has one free electron per atom, so n is equal to ×1028 electrons per cubic metre. 8.5
Assume a current I = 1 ampere, and a wire of diameter (radius = 2 mm). This wire has a cross sectional area of 0.001 m×10−6 m2 ( 3.14A = π × ()2 0.001 m). The charge of one electron is q = ×10−19 C−1.6. The drift velocity therefore can be calculated:
Therefore, in this wire the electrons are flowing at the rate of . At 60 Hz alternating current, this means that within half a cycle the electrons drift less than 0.2 μm. In other words, electrons flowing across the contact point in a switch will never actually leave the switch. 23 μm/s
By comparison, the Fermi flow 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
- Griffiths, David (1999). Introduction to Electrodynamics (3 ed.). Upper Saddle River, NJ: Prentice-Hall. p. 289.
- http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html Ohm's Law, Microscopic View, retrieved 2015-11-16
- Ohm's Law: Microscopic View at Hyperphysics