We all know that the electron is a fundamental particle carrying the smallest unit of electric charge. How did people find out what is the value of this charge?
Millikan did a clever experiment using an oil drop that could absorb positively charged molecular ions. A molecular ion with a positive charge is a molecule from which one or more electrons have been taken away. The idea is very simple, if you take away one electron, the value of the positive charge will be equivalent to that of the negative charge on one electron. An oil drop may absorb one or more such ions, thus carry charges equal in magnitude to that of either one or two or three, etc., electrons. If we apply an electric field, the charged ion will move aligned with the field. It is by studying the motion of the oil drop, we can find the amount of charge carried. If we do several such experiments and find the common denominator of the charges observed, it must be charge of an electron.
So, how did Millikan do it? He used an interesting idea. An oil drop if allowed to fall freely in air will be accelerated by gravity. However, the viscous drag on the falling drop will do a balancing act (as long as the drop is very small, typically of a micrometer radius), and soon it reaches a constant terminal velocity, say vdown If the electric field is applied in the opposite direction, i. e., vertically upwards, the drop is now subject to two forces - gravity (mg) puling it downwards and the field (qE) pushing it upwards. The net force qE-mg is balanced by the viscous drag of air and a terminal velocity upwards, say vup is reached. Comparing the two velocities, together with a knowledge of the mass, m, and the field, E, the charge can be calculated.
We will carry out this experiment virtually and learn how it works.