Right now you can probably just ask your smartphone to tell you the charge of a single electron, the fundamental unit of charge. (It has a magnitude of 1.6 x 10–19 coulombs, the common unit of electric charge.) But in 1909, things weren’t that simple. At the time, physicists Robert Millikan and Harvey Fletcher discovered it using petroleum. Their “oil drop” experiment was not the first method to find this value, but it is perhaps the most famous, and it led to Millikan receive the Nobel Prize in 1923.
This historical experiment illustrates some important physics concepts, and it’s not too complicated, so let’s review them!
The four forces
This experiment deals with oil drops – I mean, it’s right there in the name. But, in reality, it depends on understanding four different forces: the gravitational force, the electric force, the buoyancy force and a force of air resistance. The idea is to use these four to measure the value of the electric charge on a single drop of oil.
You surely already know the gravitational force. If I had to guess, I would say you are somewhere on the surface of the Earth. This means that you are probably feeling a gravitational force as an interaction between your mass and the mass of the Earth. We can model this interaction by viewing the Earth as creating a gravitational field, a downward pointing vector with a magnitude of 9.8 newtons per kilogram. A mass in this gravitational field will experience a force equal to the product of the mass of the object and the gravitational field. (Of course, this is only a model. If you move too high above the Earth, you will need a different model.)
The next is electric force. It is an interaction between two objects that have an electric charge. Just like with gravitational force, we can find electric force by putting a single charge in a region with an electric field (E) in units of newtons per coulomb. The electric force will then be the product of the object’s charge (q) and the electric field.
The two previous forces seem to complement each other. But the next two are a bit different. They have to do with the interaction between oil and the air it falls into. You already understand the force of air drag if you’ve ever put your hand out the window of a moving car. As you increase the speed of the car, this drag force of the air on your hand also increases.
For objects the size of your hand, the force of the air drag is proportional to the square of the speed of the hand. However, if you have a very small spherical object (like an oil drop) moving through the air, we can model this force with the following equation: