 # Oil-Drop Experiment Requires a Wolfram Notebook System

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This Demonstration simulates Millikan's well-known oil-drop experiment. By means of a thin nozzle, atomized oil drops are sprayed between two parallel horizontal metal surfaces that form the plates of a capacitor. The drops are ionized using an external x-ray source; statistically, the most likely event is the capture of an electron by the oil drop. However, a drop can also wind up with no charge, a double negative charge or a positive charge. You can see the charges by checking the "show/hide particle charges" box.

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If no electric field is present, only gravity acts and all the particles move down at the same speed. The particles are assumed to all have the same mass, which can be calculated from the oil density. Millikan found their volumes using an optical microscope.

If you select the electric field, coulombic electrostatic forces are introduced. You can choose either polarity. The field direction is marked by the + and - symbols on the right. The horizontal lines help you to visualize the motions of the oil drops. [1, 2]

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Contributed by: D. Meliga and S.Z. Lavagnino (December 2017)
Open content licensed under CC BY-NC-SA

## Details

The equation of motion of an oil drop immersed in a fluid in the presence of a gravitational field and an electric field is given by ,

where is the mass calculated through the oil density of the drop, is the electronic charge, is gravitational acceleration, is the drag force due to air friction (in the case of low velocities, it depends linearly on velocity ), is the electric field force (negative when the field is upward, positive when the field is downward), and is the buoyancy force. Solving the differential equation yields that the drop reaches a drift velocity , where and is the initial velocity.

To a good approximation, the drift velocity is reached after a time ; this Demonstration assumes that drift velocity has already been reached.

The measurement of allowed Millikan to calculate the elementary electron charge, about coulombs .

Snapshot 1: only the gravitational field is present; all drops move downward at the same velocity

Snapshot 2: added to the gravitational field, an upward electric field dominates for particles with a positive charge

Snapshot 3: the upward electric field also dominates for particles with a negative charge

References

 A. Redfield and F. Friedman. The Millikan Experiment [Video]. (Dec 13, 2017) www.youtube.com/watch?v=JuXtk3bC2iM.

 Wikipedia. "Oil Drop Experiment." (Dec 13, 2017) en.wikipedia.org/wiki/Oil_drop_experiment.

 Encyclopaedia Britannica. "Millikan Oil-Drop Experiment." (Dec 13, 2017) www.britannica.com/science/Millikan-oil-drop-experiment.

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