The Determination of the Charge on the Electron (Millikan) - Turning Points - A2 Physics - AQA

In the exam you are expected to know about:

• determination of Q

• Condition for holding a charged oil droplet, of charge Q, stationary between oppositely charged parallel plates;

• (QV)/d = mg

• Motion of a falling oil droplet with and without an electric field;

• terminal speed, Stokes’ Law for the viscous force on an oil droplet used to calculate the droplet radius

• F = 6phrv

• Quantisation of electric charge.

Robert Millikan used a simple experiment that served to confirm the unit electronic charge as 1.6 × 10^-19 C.    He sprayed oil drops into a space between two charged plates. Each tiny oil droplet was charged up by friction as it left the sprayer.  The theory was simple; the attractive electrostatic force between the droplet and the positively charged plate would balance out the weight of the droplet.  His apparatus was like this:

He would select a particular oil drop and hold it stationary by altering the voltage between the two plates. 

The forces on the stationary drop are like this:

We know that:

• the electric force = electric field × charge (F = Eq)

• the electric field strength in a uniform field, E = V/d

We can see that if the forces are balanced;

This method leaves us with a problem, calculating the mass of a single, tiny oil drop is too difficult to directly do accurately.  Millikan used the following method to calculate the mass; he turned off the plates and watched the oil drop.  Very quickly the oil drop reached terminal speed.

So we can write:

mg = drag force

The drag force can be worked out indirectly using Stoke's Law, which describes the force acting on a sphere falling at terminal speed through a …