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Concept
Drift velocity
Summary
In physics, drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, 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, drift velocity has units of m/s, electron mobility, m2/(V·s), and electric field, V/m.
When a potential difference is applied across a conductor, free electrons gain velocity in the direction, opposite to the electric field between successive collisions (and lose velocity when traveling in the direction of the field), thus acquiring a velocity component in that direction in addition to its random thermal velocity. As a result, there is a definite small drift velocity of electrons, which is superimposed on the random motion of free electrons. Due to this drift velocity, there is a net flow of electrons opposite to the direction of the field.
The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by:
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).
Official source
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