This problem illustrates the ideas behind the Millikan oil drop experiment-the first measurement of the electron charge. Millikan examined a fine spray of spherical oil droplets falling through air; the drops had picked up an electric charge as they were sprayed through an atomizer. He measured the terminal speed vt of a drop when there was no electric field and then the electric field E that kept the drop motionless between the plates of a capacitor (plate spacing d).
(a) With no electric field, the forces acting on the oil droplet were the gravitational force, the buoyant force, and viscous drag. The droplets used were so tiny (a radius of about 1μm) that they rapidly reached terminal velocity. Find the radius R of a drop in terms of vt, g, the densities of the oil and of air r oil and r air, and the viscosity of air h.
(b) Find the charge q of a drop in terms of g, E, d, R, g, r oil, and r air.