Chapter 18, Problem 61GP

* BIO Electrophoresis 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 $\stackrel{\to }{E}$ field across it. The field exerts an electric force on the molecule and the viscous solution exerts an opposing drag force $F_{\text{drag}}=DRv,$ 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. Experiments show that once the molecule reaches terminal velocity, the distance $\Delta x$ traveled by the molecule during time interval $\Delta t$ is determined by the expression $\Delta x=\frac{qE\Delta t}{DR}$. Describe the assumptions that were made when deriving this equation, and show the derivation.