Numerical Example
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:
Analysed dimensionally:
= / ( × × )
- = / ( × × × )
- = / ( × × )
- = /
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
Read more about this topic: Drift Velocity
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