Oil-drop experiment

The purpose of Robert Millikan's oil-drop experiment (1909) was to measure the electric charge of the electron. He did this by carefully balancing the gravitational and electric forces on tiny charged droplets of oil suspended between two metal electrodes. Knowing the electric field, the charge on the droplet could be determined. Repeating the experiment for many droplets, it was found that the values measured were always multiples of the same number. This was taken to be the charge on a single electron: 1.602 × 10−19 coulombs (SI unit for electric charge).

In 1923, Millikan won the Nobel Prize for physics in part because of this experiment. This experiment has since been repeated by generations of physics students, although it is rather expensive and difficult to do properly.

A version of the oil drop experiment has subsequently been used to search for free quarks (which, if they exist, would have a charge of 1/3 e), without success. Current theories of quarks predict that they are tightly bound and will not exist in a free form.

 Contents

Experimental procedure

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Simplified_Millikan_oil_drop.PNG
Image:Simplified Millikan oil drop.PNG

The apparatus

The diagram shows a simplified version of Millikan's set up. A uniform electric field is provided by a pair of horizontal parallel plates with a high potential difference between them. A charged drop of oil is allowed to drift in between them. By varying the potential, the drop can be made to rise, descend or stay steady. The plates are held apart by a ring of insulating material (not shown in the diagram). There are two holes cut into the ring. A bright light source is shone through one of the holes, and focused on region where the oil drops drift between the plates. A low-powered microscope is inserted through the other hole. The oil drops reflect the light and look like bright points on a dark field of view through the microscope. The microscope has a graduated scale in the eyepiece which allows for the velocity of the drop to be measured by timing how long it takes to travel from one division to another.

The oil used is the type that is usually used in vacuum apparatus. This is because this type of oil has an extremely low vapour pressure. Ordinary oil would evaporate away under the heat of the light source and so the mass of the oil drop would not remain constant over the course of the experiment. Some oil drops will pick up a charge through friction with the nozzle as they are sprayed, but more can be charged by allowing an ionising radiation source ( such as an x ray tube) to ionise the air in the chamber.

Method

Initially the oil drops are allowed to fall between the plates without the electric field turned on. They very quickly reach a terminal velocity because of friction with the air in the chamber. The field is then turned on and, if it is large enough, some of the drops (the charged ones) will start to rise. (This is because the upwards electric force FE is greater for them than the downwards gravitational force W). A likely looking drop is selected and kept in the middle of the field of view by alternately switching off the voltage until all the other drops have fallen. The experiment is then continued with this one drop.

The drop is allowed to fall and its terminal velocity v1 in the absence of an electric field is calculated. The drag force acting on the drop can then be worked out using Stokes law:

[itex]F = 6\pi r \eta v_1 \,[itex]
where v1 is the terminal velocity (i.e. velocity in the absence of an electric field) of the falling drop, η is the viscosity of the air, and r is the radius of the drop.

The weight W is the volume V multiplied by the density ρ. However what is needed is the apparent weight. The apparent weight in air is the true weight minus the upthrust (which equals the weight of air displaced by the oil drop). For a perfectly spherical droplet the apparent weight can be written as:

[itex]W = \frac{4}{3} \pi r^3 g(\rho - \rho_{air}) \,[itex]

Now at terminal velocity the oil drop is not accelerating. So the total force acting on it must be zero. So the two forces F and W must cancel one another out.
[itex]F = W[itex] implies:

[itex]r^2 = \frac{9 \eta v_1}{2 g (\rho - \rho _{air})} \,[itex]

Once r is calculated, W can easily be worked out.

Now the field is turned back on.

[itex]F_E = q E \,[itex]

where q is the charge on the oil drop and E is the electric field between the plates. For parallel plates

[itex]E = \frac{V}{d} \,[itex]

where V is the potential difference and d is the distance between the plates.

One conceivable way to work out q would be to adjust the p.d. until the oil drop remained steady. Then we could equate FE with W. But in practice this is extremely difficult to do precisely. A more practical approach is to turn the p.d. up slightly so that the oil drop rises with a new terminal velocity v2. Then

[itex]q E - W = 6\pi r \eta v _2 \,[itex]
[itex]= \frac{W v_2}{v_1} \,[itex]

• Karlsson, Magnus, "Millikan's oildrop experiment (http://www.edu.falkenberg.se/gymnasieskolan/fysik/elektron/millikaneng.html)". (Simplified version)
• Graphical simulation of the experiment - examples of the difficulties
• Thomsen, Marshall, "Good to the Last Drop (http://www.physics.emich.edu/mthomsen/sege.htm)". Millikan Stories as "Canned" Pedagogy. Eastern Michigan University.
• CSR/TSGC Team, "Quark search experiment (http://www.tsgc.utexas.edu/floatn/1997/teams/UT-austin.html)". The University of Texas at Austin.

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