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Millikanís Experiment to Measure the Charge on one Electron
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 Millikanís 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 x-rays.  
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◊10-19C.  
   
A simplified version of Millikanís 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.  
 
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