In 1909, Robert Millikan and Harvey Fletcher conducted an experiment to determine the charge of an electron. This breakthrough in Physics became known as the oil drop experiment and Robert Millikan won the Nobel Prize in Physics for it in 1923. The experiment has now become a staple in physics education for students. 

Previous to the oil drop experiment they knew charge was held in a sub-atomic particle called an electron but in this experiment Milikan measured the elementary electric charge to an unprecedented accuracy and thereby confirmed the quantum nature of charge. 

The apparatus used consists of a chamber which has two metal plates that are seperated by a ring of insulating material.. A fine mist of oil droplets are sprayed into a chamber above the plates. The oil drops became electrically charged through friction with the nozzle as they were sprayed. A hole in the upper plate facilitates entry of oil drops from the spray chamber above. A potential difference is applied across the plates (one plate becomes positivelycharged and the other plate becomes negatively charged) producing an electric field. 

The oil drops in this experiment are subject to three different forces: viscous, gravitational and electrical.  When there is no electric field present, the drop under observation falls slowly, subject to the downward pull of gravity and the upward force due to the viscous resistance of the air to the motion of the oil drop. However when the electric field is produced the electrons are attracted to the positive plate which is often the top plate. The bigger the oil drop the more mass it hads increasing the gravitational force on it. Therefore, depending on the strength of the eelctric field, the smaller oil drops may start to move upwards towards the plate, larger ones may still fall down but at a slower velocity and some drops inbetween may stop moving at all. 

A microcope allows students to see the oil drops inside the chamber and the student may also change the strength of the electric field. Students measure the velocity of the oil before and after the electric field is turned on, or measure the ekectric field strength required to get a drop to stay stationary (electric field attraction equals the pull of gravity). Using this the size of the oil drop and the charge of the drops. A good breakdown of the equations used to determine this can be found in this guide. 

You can try this lab out yourself with these simulations / online labs: 

Milikans Oil Drop Lab

The Milikan Oil Drop Experiment

Milikans Oil Drop Experiment