How did people find the basic charge of oil droplets?

Now you You can only ask your smartphone to tell you the charge of one electron – the basic unit of charge. (Its magnitude is 1.6 x 10– 19 coulomb, the common unit of electric charge.) But in 1909, things weren’t quite so simple. At the time, physicists Robert Millikan and Harvey Fletcher discovered it using oil. Their “oil drop” experiment was not the first way to find this value, but it is probably the most famous, and it led to Received the Nobel Prize in 1923.

This historical experiment illustrates some important physics concepts, and it’s not too complicated, so let’s get to it!

The four forces

This experiment is all about oil drops — I mean, they’re in the name. But, really, it depends on understanding four different forces: gravitational force, electrical force, buoyancy force, and air resistance force. The idea is to use these four to measure the value of the electric charge on a single drop of oil.

Surely, you already know about the force of gravity. If I had to guess, I’d say you’re somewhere on Earth. This means that you are most likely experiencing the force of gravity as an interaction between your mass and the mass of the Earth. We can model this interaction by thinking of the Earth as creating a downward-facing gravitational field of magnitude 9.8 newtons per kilogram. Mass in this gravitational field will experience a force equal to the product of the object’s mass and the gravitational field. (Of course, this is just a model. If you move high above the ground, you will need a different model.)

Next is the wattage. This is an interaction between any two bodies that have an electric charge. Just as with the gravitational force, we can find the electric force by placing a single charge in an area with an electric field (NS) in units of newtons per coulomb. The electric force will then be due to the body’s charge (NS) and the electric field.

The two previous forces seem to complement each other. But the next two are a little different. It has to do with the interaction between the oil and the air that falls through it. You already understand the pull of air if you stick your hand out the window of a moving car. As the vehicle speeds up, this air pull on your hand increases as well.

For objects the size of your hand, the force of 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:

Illustration: Rhett Allen

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