Consider two fragments of DNA of radius r1 = 31 nm and r2 = 38 nm when they are coiled up as they move through a gel. An electrophoresis analysis (see figure below) is carried out to separate these two fragments. Suppose the drag factor C in the equation Fdrag = -Crv is C = 5.0 10-5 kg/(m · s), and assume each fragment has a charge q = -14e.
(a) If the electric field has a magnitude of 1.5 N/C, what is the speed of each fragment in the gel?
(b) How long will it take the smaller fragment to move a distance 1 cm (a typical distance used in DNA fingerprinting)?