Drift velocity

Inphysics,drift velocityis theaverage velocityattained by charged particles, such aselectrons,in a material due to anelectric field.In general, an electron in aconductorwill propagate randomly at theFermi 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 tocurrent.In aresistivematerial, it is also proportional to the magnitude of an external electric field. ThusOhm's lawcan be explained in terms of drift velocity. The law's most elementary expression is:

u=\mu E,

where $u$ is drift velocity, $μ$ is the material'selectron mobility,and $E$ is theelectric field.In theMKS 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 drift speed of electrons is generally in the order of 10⁻³meters per second whereas the thermal speed is on the order of 10⁶meters per second.

Experimental measure

The formula for evaluating the drift velocity of charge carriers in a material of constantcross-sectionalarea is given by:^[1]

u={j \over nq},

where $u$ is the drift velocity of electrons, $j$ is thecurrent densityflowing through the material, $n$ is the charge-carriernumber density,and $q$ is thechargeon the charge-carrier.

This can also be written as:

j=nqu

But the current density and drift velocity, j and u, are in fact vectors, so this relationship is often written as:

\mathbf {J} =\rho \mathbf {u} \,

where

\rho =nq

is thecharge density(SI unit: coulombs percubic metre).

In terms of the basic properties of the right-cylindrical current-carryingmetallic ohmic conductor,where the charge-carriers areelectrons,this expression can be rewritten as:^{[citation needed]}

u={m\;\sigma \Delta V \over \rho ef\ell },

where

$u$ is again the drift velocity of the electrons, inm⋅s⁻¹
$m$ is themolecular massof the metal, inkg
$σ$ is theelectric conductivityof the medium at the temperature considered, inS/m.
$Δ V$ is thevoltageapplied across the conductor, inV
$ρ$ is thedensity(massper unitvolume) of the conductor, inkg⋅m⁻³
$e$ is theelementary charge,inC
$f$ is the number offree electronsperatom
$ℓ$ is thelengthof the conductor, inm

Numerical example

Electricity is most commonly conducted through copper wires.Copperhas a density of8.94 g/cm³and anatomic weightof63.546 g/mol,so there are140685.5 mol/m³.In onemoleof any element, there are6.022×10²³atoms (theAvogadro number). Therefore, in1 m³of copper, there are about8.5×10²⁸atoms (6.022×10²³×140685.5 mol/m³). Copper has one free electron per atom, so $n$ is equal to8.5×10²⁸electrons per cubic metre.

Assume a current $I$ = 1 ampere,and a wire of2 mmdiameter (radius =0.001 m). This wire has a cross sectional area $A$ of π × (0.001 m)²=3.14×10⁻⁶m²=3.14 mm².Theelementary chargeof anelectronis $e$ =−1.6×10⁻¹⁹C.The drift velocity therefore can be calculated: ${\begin{aligned}u&={I \over nAe}\\&={\frac {1{\text{C}}/{\text{s}}}{\left(8.5\times 10^{28}{\text{m}}^{-3}\right)\left(3.14\times 10^{-6}{\text{m}}^{2}\right)\left(1.6\times 10^{-19}{\text{C}}\right)}}\\&=2.3\times 10^{-5}{\text{m}}/{\text{s}}\end{aligned}}$

Dimensional analysis: $u={\dfrac {\text{A}}{{\dfrac {\text{electron}}{{\text{m}}^{3}}}{\cdot }{\text{m}}^{2}\cdot {\dfrac {\text{C}}{\text{electron}}}}}={\dfrac {\dfrac {\text{C}}{\text{s}}}{{\dfrac {1}{\text{m}}}{\cdot }{\text{C}}}}={\dfrac {\text{m}}{\text{s}}}$

Therefore, in this wire, the electrons are flowing at the rate of23 μm/s.At 60Hz alternating current, this means that, within half a cycle (1/120th sec.), on average the electrons drift less than 0.2 μm. In context, at one ampere around3×10¹⁶electrons will flow across the contact point twice per cycle. But out of around1×10²²movable electrons per meter of wire, this is an insignificant fraction.

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 around1570 km/s.^[2]

References

^Griffiths, David (1999).Introduction to Electrodynamics(3 ed.). Upper Saddle River, NJ: Prentice-Hall. p.289.ISBN 9780138053260.
^http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.htmlOhm's Law, Microscopic View, retrieved 2015-11-16

External links

Ohm's Law: Microscopic Viewat Hyperphysics

[1] Griffiths, David (1999).Introduction to Electrodynamics(3 ed.). Upper Saddle River, NJ: Prentice-Hall. p.289.ISBN 9780138053260.

[2] ttp://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.htmlOhm's Law, Microscopic View, retrieved 2015-11-16

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Drift velocity

Contents

Experimental measure

Numerical example

See also

References

External links