Determination of the elementary electric charge according to Millikan and proof of charge quantisation

With his famous oil-drop method, R. A. Millikan succeeded in demonstrating the quantum nature of minute amounts of electricity in 1910. He caused charged oil droplets to be suspended in the vertical electric field of a plate capacitor and, on the basis of the radius r and the electric field E, determined the charge q of a suspended droplet:

He discovered that q only occurs as a whole multiple of an electron charge e.

In experiment C1.1.3.5, the electric field

is calculated from the voltage U on the plate condenser at which the oil droplet is observed floating straight. To determine the radius, the constant sinking velocity v₁ of the droplet is then measured with the electric field switched off. From the equilibrium between the force of gravity and Stokes’ drag, it follows that