How did people with oil droplets find the underlying charge?

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You now it can probably just ask your smartphone to tell you the charge of one electron – the basic unit of charge. (It has a magnitude of 1.6 x 10–19 coulombs, a common unit for electric charge.) But in 1909 things were not so simple. Then physicists Robert Millikan and Harvey Fletcher figured it out using oil. Their “oil drip” experiment was not the first method to find this value, but it is perhaps the most famous and led to Millikan winner of the Nobel Prize in 1923.

This historical experiment illustrates some important physical concepts and isn’t too terribly complicated, so let’s move on to them!

Four forces

This experiment deals with oil droplets – I mean, it’s in the name. But, really, it depends on understanding four different forces: gravitational forces, electric forces, buoyancy forces and air resistance forces. The idea is to use these four to measure the value of the electric charge on one drop of oil.

You probably already know about gravitational force. If I had to guess, I’d say you’re somewhere on the surface of the Earth. This means that you are probably experiencing gravitational force as an interaction between your mass and the mass of the Earth. We can model this interaction by looking at the Earth as the creation of a downward-directed gravitational field-vector with a magnitude of 9.8 Newtons per kilogram. The 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 just a model. If you’re moving too high above the Earth, you’ll need a different model.)

The next is the electric force. This is the interaction between any two objects that have an electric charge. Just as with gravitational force, an electric force can be found by placing a single charge in an area with an electric field (E) in newton units per coulomb. The electric force will then be the product of the charge of the object (q) and electric field.

The previous two forces seem to complement each other. But the next two are a little different. They have to do with the interaction between the oil and the air through which it decays. You already understand the force of air resistance if you have ever reached out your hand through a moving car window. As you increase the speed of the car, so does the force of air resistance on your arm.

For objects the size of your hand, the force of air resistance is proportional to the square of the speed of the hand. However, if a very small spherical object (such as a drop of oil) moves through the air, we can model this force with the following equation:

Illustration: Rhett Allain

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