Electrophoresis (Electro: electric, Phoresis (greek word): to carry) is the migration of charged molecules or particles under the influence of an external electric field. Electrophoresis-based methods are extensively used in laboratories for the analysis, separation and purification of biomolecules such as nucleic acid and proteins in laboratories. These methods use electric energy to drag biomolecules in a liquid conductive medium, often through a porous matrix that results in separation of molecules by their size, structure, or electrical charge.

The electric force on a charged particle that causes molecule to accelerate and migrate can be defined by law of electrostatics:

F electric force = qE

F electric force : Electric force on charged particle 
q: Net charge on a molecule
E: Strength of electric field

The migration of molecules is opposed by frictional force that limits its velocity

F frictional force = fV

F frictional force = Frictional force
V = Velocity (rate of migration) of the of charged molecule
f = frictional coefficient which depends on the properties of the medium (e.g., viscosity) in which molecule is migrating

Molecule attain a constant speed (no more acceleration)
when F frictional force = F electric force

The most common electrophoresis-based methods in laboratories are agarose gel electrophoresis and polyacrylamide gel electrophoresis. Agarose gel electrophoresis is mostly used for the analysis of nucleic acids whereas polyacrylamide gel electrophoresis is extensively used for protein analysis as well as analysis of small size (low molecular weight) nucleic acids. 

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