Electrophoresis is used to separate biological molecules of different dimensions

Question

Electrophoresis is used to separate biological molecules of different dimensions and electric charge (the molecules can have different charge depending on the pH of the solution). A particular molecule of radius R with charge q is in a viscous solution that has an E field across it. The field exerts an electric force on the molecule and the viscous solution exerts an opposing drag force Fdrag=DRv, where D is a constant drag coefficient that depends on the shape and other features of the molecule and the solution, and v is the molecule's speed in the solution. When the molecule gets up to speed, the electric force exerted on it by the field is equal in magnitude and opposite in direction to the drag force.

Find a distance that the molecule will travel during time interval t in situation when the electric force exerted on it by the field is equal in magnitude and opposite in direction to the drag force.

Express your answer in terms of the variables q , E , D , R , and t

Explanation / Answer

In the equilibrium, Fdrag = Fe

D*R*v = q*E

==> v = q*E/(D*R)

distance travelled in delta_t time, d = v*delta_t

= q*E*delta_t/(D*R)

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