Robert Millikan received the Nobel Prize in 1923 for the spectacularly designed ‘oil drop experiment’. A fine mist of oil was sprayed from an atomizer. Most of the droplets get negatively charged as they picked up a small, unknown number of electrons as they passed through its nozzle. Some of the drops then fell through a hole in the top plate and drifted into the region between two parallel plates between which a variable electric field had been established. Lit from the side by an intense light, these drops glistened when the region was viewed through a telescope. Once a drop was located, the voltage was varied thus controlling the electric field, E, to slow down the drop’s descent. When the drop reached terminal velocity (weight downwards mg = electrostatic force upwards EQ) it was tracked through the remainder of its fall and a ratio of mass per unit charge was recorded.
Drops either drifted upwards or downwards at a steady speed, or remained at rest in the electric field. A simpler version located a stationary drop at a particular voltage thus doing away with the need for complicated viscosity equations as it fell.
from mg = QE = QV/d, assuming the drops are of equal mass…Millikan himself used viscosity determinations to establish the drop radius. Knowing the density of the oil, he could find the mass of the drop. For our purposes, let’s assume a constant mass.
Voltage between the plates for a particular stationary droplet is therefore inversely proportional to the charge on the droplet.
Millikan found that the voltages required went up or down in predictably sized jumps, consistent with a quantised charge on the electron. The whole deal is a bit more formal than this, but you get the idea….
Look at this applet