MILLIKAN OIL DROP
Ken Cheney
4/8/2006
PICTURES:
http://www.paccd.cc.ca.us/physics/teachers/cheney/lab%20manuals/WEB%20Image%20
Folders/Millikan%20oil-drop%20WEB/index.htm
ABSTRACT
The charge on an electron will be measured by observing the rising and falling of oil
drops (or latex spheres) in an electric field.
HISTORY
The charge to mass ratio of an electron is relatively easy to measure using electric and
magnetic fields. However to measure either the charge or mass separately is very
difficult and was first done by Millikan. As we will demonstrate, unfortunately, the
measurement is still quite difficult!
EQUIPMENT NOTE
We have three generations of Millikan Oil Drop apparatus from various manufactures, all
different in the details!
My discussion here will be fairly general.
When I do give specifics they will refer to our latest generation, from Cenco/UCHIDA
TM-15.
OUTLINE OF EXPERIMENT
Very small oil drops are produced by spraying air over oil (or premade latex spheres are
used) into a “drift chamber”.
The oil drops fall but reach terminal velocity very quickly because of their large area to
mass ratio.
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The terminal velocity is measured using a microscope with a graduated scale and a
stopwatch.
If the drop is charged it can then be moved upward (or forced down) using the electric
field produced by metal plates above and below the experimental chamber. The upward
and downward terminal velocities are also measured.
DRIFT CHAMBER: TOP VIEW
Light
“Oil
Drops”
“Oil Drop”
Drift
Chamber
- Plates
Interior
Scale
Microscope
From the properties of air, oil, and the apparatus the charge on the oil drop can be
calculated.
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Since the “oil drop” could have several electron charges (probably only 1-5) the
experiment is repeated a number of times to find out the minimum charge (one hopes the
electron charge) that will go into each observed charge an integer number of times.
THEORY
FREELY FALLING
If the falling (or rising) drop is spherical the air drag at low velocities can be calculated
by Stoke’s Law:
In 1851, George Gabriel Stokes derived an expression for the frictional force
exerted on spherical objects with very small Reynolds numbers (e.g., very
small particles) in a viscous fluid by solving the generally unsolvable
Navier-Stokes equations:
F  6 r vg
(1.1)
where:
F is the frictional force
r is the Stokes radius of the particle
latex spheres r = 5.5 10-7 m according to Cenco
v g is the particles speed falling with only gravity and viscosity acting on it
 is the fluid (air) viscosity = 1.8479 10-5 + 0.00275 10-5 (T-72 degrees
F) N s/m2 (1/degrees F) The SI units of viscosity are Ns/m2, Poise are
cgs units of dyne s/cm2 . My temperature compensation for near 72
degrees F, from tables. For a calculator see:
http://www.lmnoeng.com/Flow/GasViscosity.htm
But
effective   (1 
b 1
)
pr
is the Effective viscosity, notice it depends on the radius
of the object. For best results use this correction.
b = 6.17 10-6 m cm of Hg
p = barometric pressure in cm of Hg
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(1.2)
If the particles are falling in the viscous fluid (air) due to their own weight,
then we can derive their settling velocity by equating this frictional force
with the gravitational force – the buoyant force:
Fg  weight - boyant force
=Volume x object density x g - Volume x fluid density x g
4
4
=(  r 3 ) p g  (  r 3 ) f g
3
3
2
2 r g ( p   f )
vg 
9
effictive
where:
4
V is the volume of the “oil drop”,  r 3
3
g is the acceleration of gravity,
 p is the density of the particles; oil drops or latex spheres
 f is the density of the fluid; air in this case
(1.3)
(1.4)
This analysis is mostly from http://en.wikipedia.org/wiki/Stokes'_law, I
added a little of my own and some ideas from Jones and Cenco.
We can measure or look up everything here except r, this give us r and, knowing the
density of the fluid the mass of the “oil drop”
RISING WITH AN ELECTRIC FIELD
Now we turn on an electric field to produce an upward force on the “oil drop”.
The drop again very quickly reaches a constant upward velocity of v  .
ELECTRIC FIELD PLATES: SIDE VIEW
Ve
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Oil Drop
E field
4
d
Forces up = Forces down
Electrical Force + Buoyant Force = Weight + Frictional Force
qE   f Vg  mg  6 reffictivev 
Equation Up
(1.5)
Now we know everything except q, which must be an integer number of electron charges.
We get the electric field from the applied voltage and the separation of the plates above
and below the “oil drop”.
Ve  Ed
(1.6)
Where;
is the charge on the “oil drop”
is the electric field strength
is the applied voltage
is the separation between the plates above and below the “oil drop”, 5
10-3m according to Cenco
v
is the upward velocity of the “oil drop”

v
is the downward velocity of the “oil drop” when the
electric field is pushing the charge down. Use absolute value, >0.
q
E
Ve
d
“FALLING WITH AN ELECTRIC FIELD”
The electric field can be applied to push the “oil drop” down, then:
Forces Up = Forces Down
Friction Force + Buoyant Force = Electrical Force + Weight
6 reffictive v  +  f Vg = qE +
mg
Equation “down”
(1.7)
Using the absolute velocity of the drop gives the upward force here.
Subtracting Equation “down” from Equation “up” gives:
qE  3 reffective (v  v )
Equation “Charge”
(1.8)
Remember to use the effective viscosity.
The advantage of using the electric field both up and down is that Equation “Charge”
doesn’t involve any densities, and is pretty simple!
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WARNING!! 
This all sounds simple and straightforward but “The devil is in the details” which is why
Millikan earned a Nobel Prize and we may go crazy!
EXPERIMENTAL PROBLEMS
The “oil drops” are so small that a microscope must be used to see them and to measure
their velocity. A scale is built into the microscope.
MICROSCOPE FOCUS AND LIGHT
There must be LOTS of light at the spot where the microscope is focused.
It must be dark behind the “oil drops”.
The microscope must be focused at the center of the drift volume.
To insure both of these hold a piece of wire at the center of the drift volume and move the
light and microscope until you can see a bright, sharp image of the wire with a dark
background.
SCALE
Check that the interior scale of the microscope is reading accurately. A microscope is
meant to magnify and may magnify different amounts depending on the settings, focus
etc.. Put a small external scale (perhaps from a verneer calipers) at the focus of the
microscope and use the built in interior scale to read the external scale. The scales
probably won’t agree so adjust your readings to compensated for the optical distortion.
WIND
Be sure your “drift volume” is isolated from wind as well as possible!
However if the volume is sealed too well “oil drops” may not be able to enter!
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JUST A LITTLE “OIL”
You only need a “few good drops”! Give a puff with the “oil” source and wait for some
drops to appear.
In some designs you will block the small entrance hole if you use very much oil!
DIGITAL VOLTMETER
Use a digital voltmeter to get accurate voltage readings.
VISCOSITY
Use the corrected “Effective viscosity” not the average, book, viscosity.
SEPARATION OF PLATES
This is a small distance, any errors can lead to big percent errors. Cenco may not be
exactly right!
USE OF ASPIRATOR
Be sure the tube etc. are VERY clean, Alcohol!
Be sure to put your finger over the hole in the aspirator, otherwise no “oil drops”
may appear.
ROUGH PROCEDURE
 Align the light and microscope.
 Check the magnification of the internal scale.
 Turn on the voltage, 300v perhaps.
 Loosen the plates so air can escape.
 Put your finger over the hole in the aspirator.
 Give a small puff of air and “oil drops”.
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 Find a rising “oil drop”
 Time the “oil drop” over as large a rise as possible.
 Turn off the voltage, or reverse it as desired, and time the fall of the ‘oil drop”.
 Repeat as many times as possible.
 Continue with more oil drops.
CONSTANTS
Don’t forget to get:
 The separation (d) of the electrodes in the drift volume.
 The correction factor for the scale in the microscope.
 The density of your “oil” or latex spheres.
 The diameter of the latex spheres.
ANALYSIS
 Find the charge for each “oil drop”.
 Make a histogram of charge verses number of occurrences of that charge.
 Find the maximum electron charge that will go into all your charges an integer
number of times. Don’t expect integers greater than five or so.
 Find the usual average, standard deviation of the mean, percent error, error
sources, etc.
REFERENCES
The Cenco manual.
Ray C. Jones, “The Millikan oil-drop experiment: Making it worthwhile”, American
Journal of Physics 63 (11), November 1995 – many suggestions to improve this as a
student experiment.
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