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:''For other uses, see '''[[electric vehicle]]'''.''
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:''For the electrical mobility of an [[electron]] or [[electron hole|hole]] in [[solid-state physics]], see '''[[Electron mobility]]'''.''
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'''Electrical mobility''' is the ability of charged particles (such as [[electron]]s or [[proton]]s) to move through a medium in response to an [[electric field]] that is pulling them. The separation of ions according to their mobility in gas phase is called [[Ion mobility spectrometry]], in liquid phase it is called [[electrophoresis]].
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==Theory==
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When a [[charged particle]] in a [[gas]] or [[liquid]] is acted upon by a uniform [[electric field]], it will be accelerated until it reaches a constant [[drift velocity]] according to the formula:
: <math>\,v_d = \mu E</math>
 
where
* <math>\, v_d</math> is the drift velocity (m/s)
* <math>\, E</math> is the magnitude of the applied electric field (V/m)
* <math>\, \mu</math> is the mobility (m<sup>2</sup>/(Vs))
 
In other words, the electrical mobility of the particle is defined as the ratio of the drift velocity to the magnitude of the electric field:
: <math>\,\mu = \frac{v_d}{E}</math>
 
Electrical mobility is proportional to the net [[electric charge|charge]] of the particle. This was the basis for [[Robert Millikan]]'s demonstration that electrical charges occur in discrete units, whose magnitude is the charge of the [[electron]].
 
Electrical mobility of spherical particles much larger than the mean free path of the molecules of the medium is inversely proportional to the [[diameter]] of the particles; for spherical particles much smaller than the mean free path, the electrical mobility is inversely proportional to the square of the particle diameter.
 
==Mobility in gas phase==
Mobility is defined for any species in the gas phase, encountered mostly in [[Plasma (physics)|plasma]] physics and is defined as:
 
:<math>\mu = \frac{q}{m\, \nu_m}</math>  
 
where
 
*<math>\, q</math> is the charge of the species,
*<math>\, \nu_m</math> is the momentum transfer collision frequency, and
*<math>\, m</math> is the mass.
 
Mobility is related to the species' '''diffusion coefficient''' <math>\, D</math> through an exact (thermodynamically required) equation known as the [[Einstein_relation_(kinetic_theory)|Einstein relation]]:
 
:<math>\mu = \frac{q}{k\, T}D</math>,
 
where
 
*<math>\, k</math> is the [[Boltzmann constant]],  
*<math>\, T</math> is the [[gas]] temperature, and
*<math>\, D</math> is a measured quantity that can be estimated. If one defines the [[mean free path]] in terms of [[momentum transfer]], then one gets:
 
:<math>D = \frac{\pi}{8}\lambda^2 \nu_m</math>.
 
But both the ''momentum transfer mean free path'' and the ''momentum transfer collision frequency'' are difficult to calculate. Many other mean free paths can be defined. In the gas phase, <math>\, \lambda</math> is often defined as the diffusional mean free path, by assuming a simple approximate relation is exact:
 
:<math>D = \frac{1}{2}\lambda \,v</math>,
 
when <math>\, v</math> is the [[root mean square]] speed of the gas molecules:
 
:<math>v = \sqrt {{3\, k\, T}\over{m}}</math>
 
where <math>\, m</math> is the mass of the diffusing species. This approximate equation becomes exact when used to define the diffusional mean free path.
 
==Applications==
Electrical mobility is the basis for [[electrostatic precipitation]], used to remove particles from exhaust gases on an industrial scale. The particles are given a charge by exposing them to ions from an [[electrical discharge]] in the presence of a strong field.  The particles acquire an electrical mobility and are driven by the field to a collecting electrode.
 
Instruments exist which select particles with a narrow range of electrical mobility, or particles with electrical mobility larger than a predefined value.<ref>{{cite journal | author=E. O. Knutson and K. T. Whitby | title=Aerosol classification by electric mobility: Apparatus, theory, and applications | journal=J. Aerosol Sci. | year=1975 | volume=6 | pages=443–451 | doi=10.1016/0021-8502(75)90060-9 | issue=6}}</ref>  The former are generally referred to as "differential mobility analyzers". The selected mobility is often identified with the diameter of a singly charged spherical particle, thus the "electrical-mobility diameter" becomes a characteristic of the particle, regardless of whether it is actually spherical.
 
==References==
{{Reflist}}
 
[[Category:Physical quantities]]
[[Category:Electrophoresis]]
[[Category:Mass spectrometry]]

Revision as of 10:43, 1 March 2014

UGG Promo Code September 2014

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