posted by JOTHEY .
In the early 1900s, Robert Millikan used small charged droplets of oil, suspended in an electric field, to make the first quantitative measurements of the electron’s charge. A 0.67-um-diameter droplet of oil, having a charge of +e, is suspended in midair between two horizontal plates of a parallel-plate capacitor. The upward electric force on the droplet is exactly balanced by the downward force of gravity. The oil has a density of 860 kg/m^3, and the capacitor plates are 4.0 mm apart.
What must the potential difference between the plates be to hold the droplet in equilibrium?
Actually, in the Millikan experiment, there can be one or several charges per drop. What was observed was that the charges were a small multiple of e.
In your case, go along with the assumption that the charge is +e and equate the electric force
e V/d to the particle's weight. d is the plate separation. Solve for V.
Ignore the small effect of buoyancy, the error will be less than 1%. Millikan had to take it into account