Drift velocity
In physics a drift velocity is the average velocity attained by particles, such as electrons, in a material due to an electric field. It can also be referred to as axial drift velocity. In general, an electron in a conductor will propagate randomly at the Fermi velocity (due to thermal energy of the conductor), resulting in an average velocity of zero. Applying an electric field adds to this random motion a small net flow in one direction; this is the drift.
Drift velocity is proportional to current. In a resistive material it is also proportional to the magnitude of an external electric field. Thus Ohm's law can be explained in terms of drift velocity. The law's most elementary expression is:
where u is drift velocity, μ is the material's electron mobility, and E is the electric field. In the MKS system these quantities' units are m/s, m^{2}/(V·s), and V/m, respectively.
Experimental measure
The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by:^{[1]}
where u is the drift velocity of electrons, j is the current density flowing through the material, n is the charge-carrier number density, and q is the charge on the charge-carrier.
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:
where
is the charge density (SI unit: coulombs per cubic metre).
In terms of the basic properties of the right-cylindrical current-carrying metallic ohmic conductor, where the charge-carriers are electrons, this expression can be rewritten as^{[citation needed]}:
where
- 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
Numerical example
Electricity is most commonly conducted in a copper wire. Copper has a density of , and an 8.94 g/cm^{3}atomic weight of , so there are 63.546 g/mol685.5 mol/m^{3}. In one 140mole of any element there are ×10^{23} atoms ( 6.02Avogadro's constant). Therefore, in of copper there are about 1 m^{3}×10^{28} atoms ( 8.5×10^{23} × 6.02685.5 mol/m^{3} 140). Copper has one free electron per atom, so n is equal to ×10^{28} 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} m^{2} ( 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:
Dimensional analysis:
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 .^{[2]} 1570 km/s
See also
References
External links
- Ohm's Law: Microscopic View at Hyperphysics