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| The '''drift velocity''' is the average [[velocity]] that a particle, such as an [[electron]], attains due to an [[electric field]]. It can also be referred to as axial drift velocity since particles defined are assumed to be moving along a plane. In general, an electron will ‘rattle around’ in a [[Electrical conductor|conductor]] at the [[Fermi velocity]] randomly. An applied electric field will give this random motion a small net velocity in one direction.
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| In a [[semiconductor]], the two main carrier scattering mechanisms are [[ionized impurity scattering]] and [[lattice scattering]].
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| Because current is proportional to drift velocity, which is, in turn, proportional to the magnitude of an external electric field, [[Ohm's law]] can be explained in terms of drift velocity.
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| Drift velocity is expressed in the following equations:
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| <math>J = \rho v_{\it avg}</math>
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| <math>v_{\it avg} = \mu E</math>
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| where <math>J</math> is the [[current density]], <math>\rho</math> is [[charge density]] (in units [[Coulomb|C]]/m<sup>3</sup>), and <math>v_{\it avg}</math> is the drift velocity, and where <math>\mu</math> is the [[electron mobility]] (in units (m^2)/[[volt|V]]*s) and <math>E</math> is the [[electric field]] (in units V/m).
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| ==Mathematical formula==
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| The formula for evaluating the drift velocity of charge carriers in a material of constant [[cross-section (geometry)|cross-section]]al area is given by:<ref>{{cite book|last=Griffiths|first=David|title=Introduction to Electrodynamics|year=1999|publisher=Prentice-Hall|location=Upper Saddle River, NJ|page=289|edition=3}}</ref>
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| <math>v={I \over nAq}</math>
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| where {{math|''v''}} is the drift velocity of electrons, {{math|''I''}} is the current flowing through the material, {{math|''n''}} is the charge-carrier density, {{math|''A''}} is the [[area]] of [[cross section (geometry)|cross-section]] of the material and {{math|''q''}} is the [[electric charge|charge]] on the charge-carrier.
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| In terms of the basic properties of the right-[[cylindrical]] [[electrical current|current]]-carrying [[metal]]lic [[electrical conductor|conductor]], where the charge-carriers are [[electrons]], this expression can be rewritten as {{Citation needed|date=June 2013}}:
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| <math>v={MV \over d N_A \ell e f \rho_0 (1+\alpha_0 T)}</math>
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| where,
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| *{{math|''v''}} is again the drift velocity of the electrons, in {{math|''[[metre|m]]·[[second|s]]''}}<sup>−1</sup>;
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| *{{math|''M''}} is the [[molar mass]] of the metal, in {{math|''[[kg]]·[[mole (unit)|mol]]''}}<sup>−1</sup>;
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| *{{math|''V''}} is the [[voltage]] applied across the conductor, in [[volt|{{math|''V''}}]];
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| *{{math|''N''<sub>A</sub>}} is [[Avogadro’s number]], in {{math|''[[mole (unit)|mol]]''}}<sup>−1</sup>;
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| *{{math|''d''}} is the [[density]] ([[mass]] per unit [[volume]]) of the conductor, in {{math|''[[kg]]·[[metre|m]]''}}<sup>−3</sup>;
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| *{{math|''e''}} is the [[Elementary charge|fundamental electric charge]], in [[coulomb (unit)|{{math|''C''}}]];
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| *{{math|''ρ''<sub>0</sub>}} is the [[resistivity]] of the conductor at 0{{math|''°C}}, in ''{{math|[[ohm (unit)|''Ω]]·[[metre|''m'']]}}'';
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| *{{math|''α''<sub>0</sub>}} is the [[temperature coefficient#Temperature coefficient of electrical resistance|temperature coefficent of resistivity]] of the conductor at 0{{math|''°C''}}, in [[kelvin (unit)|{{math|''K''}}]]<sup>−1</sup>;
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| *{{math|''T''}} is the [[temperature]] of the conductor, in {{math|''[[degree Celcius|°C]]''}},
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| *{{math|''{{unicode|ℓ}}''}} is the [[length]] of the conductor, in {{math|''[[metre|m]]''}}; and
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| *{{math|''f''}} is the number of [[free electrons]] released by each [[atom]].
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| == Numerical example ==
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| 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 (unit)|mole]] of any element there are 6.02×10<sup>23</sup> atoms ([[Avogadro's constant]]). Therefore in 1m³ of copper there are about 8.5×10<sup>28</sup> atoms (6.02×10<sup>23</sup> × 140685.5 mol/m³). Copper has one free electron per atom, so ''n'' is equal to 8.5×10<sup>28</sup> electrons per m³.
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| 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<sup>−7</sup> m<sup>2</sup> (''A'' = π×0.0005<sup>2</sup>). The charge of 1 [[electron]] is ''q''=−1.6×10<sup>−19</sup> Coulombs. The drift velocity therefore can be calculated:
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| <math>v={I \over nAq}</math>
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| <math>v= {3 \over \big({{8.5 \times 10^{28}} \big) \times \big({7.85\times 10^{-7}} \big) \times \big({-1.6 \times 10^{-19}} \big)}}</math> | |
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| <math>v={-0.00028} \text { m/s}\,\!</math>
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| Analysed dimensionally:
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| [v] = [amperes] / ( [electron/m<sup>3</sup>] × [m<sup>2</sup>] × [coulombs/electron] )
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| := [coulombs] / ( [seconds] × [electron/m<sup>3</sup>] × [m<sup>2</sup>] × [coulombs/electron] )
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| := [coulombs] / ( [seconds] × [meters<sup>-1</sup>] × [coulombs] )
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| := [meters] / [second] | |
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| Therefore in this wire the electrons are flowing at the rate of −0.00029 m/s, or very nearly −1.0 m/hour.
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| 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.<ref>http://230nsc1.phy-astr.gsu.edu/hbase/electric/ohmmic.html Ohm's Law, Microscopic View, retrieved Feb 14, 2009</ref>
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| 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:
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| <math>A = (1/2F) (2\sqrt{2}/\pi)|v| = 2.1\times10^{-6} \text{m}</math>
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| ==See also==
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| *[[Electron mobility]]
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| *[[Speed of electricity]]
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| *[[Drift chamber]]
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| *[[Guiding center]]
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| ==References==
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| <references/>
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| <!-- Other Project Links -->
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| ==External links==
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| * [http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html Ohm's Law: Microscopic View] at Hyperphysics
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| {{DEFAULTSORT:Drift Velocity}}
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| [[Category:Condensed matter physics]]
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