It is relatively simple to measure the charge to mass ratio
of a
particle such as the electron by sending a beam of the particles through
crossed electric and magnetic fields (see, for example, experiment
1AN). 

However, to measure the charge is a little more difficult. 



Robert Millikan
(working with Harvey Fletcher) devised a method in which
tiny charged drops of oil, were observed as they moved through air, first
under the influence of gravity alone and then of gravity and an electric field. 



The diagram below is a very simplified representation of
Millikan’s apparatus. 







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 as they were
sprayed into the apparatus. 

Further ionization was caused by a beam of xrays. 

The drops were observed using a microscope. 



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. 



When many measurements had been done, all the charges
were found to be integral multiples of a basic unit of charge,
assumed to be the charge on one electron. 

The value (symbol e) is approximately 1.6×10^{19}C. 



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, as shown here. 



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



where E is the electric field strength 



where V is the voltage across the plates and d is the distance
between the plates 

Therefore, the charge on the drop is given by 





It is still necessary to measure the terminal speed of the drop
in order to find its radius from which the mass can be calculated
knowing the density of the oil. 
