The diagram below is a very simplified representation of Millikan’s apparatus.
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Small drops of oil were allowed to fall into a region between two metal plates, (the top plate had a hole in it).

Some of the drops became charged by friction. Further ionisation was caused by a beam of x rays.

Millikan measured the terminal speed of a drop as it fell through the air, with V = 0. From this he could calculate the radius of the drop (and hence its mass). He then applied a voltage, V, to the plates and measured the new terminal speed of the same drop.

The change in the terminal speed of the drop was used to calculate the magnitude of the charge on the drop.
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A simplified version of Millikan’s experiment can be done by finding the voltage needed to just hold an oil drop stationary between the two plates.

Consider a drop having a charge q and mass m.

If the drop is stationary, then the two forces acting on it have equal magnitudes.

where E is the field strength.

Now, E = V/d, where d is the distance between the plates,

In practice, it is still necessary to make a measurement of the terminal speed of the drop in order to find its radius and hence its mass.

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