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Considering the oil-drop-Experiment: Which of the following 2 techniques is more accurate:

  1. Measuring rise and fall times.
  2. Using (measuring) voltage while levitating and measuring fall times.

I'd say 1 because in 2 you are having problems levitating the drop because of brownian motion, which makes the oil-drop move and therefore makes it hard to find it being stationary. In 1 you simply have the error you get from measuring time.

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  • $\begingroup$ In the first case wouldn't you would also have error due to Brownian motion? $\endgroup$
    – BallisticThomist39
    Commented Apr 1, 2021 at 21:24
  • $\begingroup$ Yes but it is harder to manipulate the voltage so that you have a stationary particle. In 1 (compared to the speed at which the particle is moving) the brownian motion can be neglected. $\endgroup$
    – manuel459
    Commented Apr 1, 2021 at 21:31
  • $\begingroup$ Unless a voltage is applied, you wont have a clue what the charge is on the droplet. So, #1 alone doesn't work $\endgroup$
    – S. McGrew
    Commented Apr 1, 2021 at 21:52
  • $\begingroup$ I understand. But it somehow comes down to the fact that one must establish levitation quite precisely, which then makes the voltage more important than in #1. $\endgroup$
    – manuel459
    Commented Apr 1, 2021 at 21:57
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    $\begingroup$ You might find this article of interest? and another article of interest? $\endgroup$
    – Farcher
    Commented Apr 1, 2021 at 22:24

1 Answer 1

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In my opinion (1) is the better technique. It avoids having to know the exact viscosity of the air, questions about the Reynolds number of the flow etc - all the things that make drag such a difficult subject.

Further, you get "infinitely long time" to take a good measurement - you can iteratively adjust your voltage until the drops float "just so", and since the drops end up stationary you can measure their size very accurately (for example, by using diffreaction with a laser ... something Millikan didn't have the luxury to have).

Whenever you do an experimental determination of a quantity it is good to consider the sources of error, and how they propagate. In the case of the stationary drop, the quantities that go into your final answer are:

  • mass of droplet (->size, density)
  • electric field (->voltage, plate separation)
  • local gravitational field

If you have a falling drop, you additionally worry about:

  • drag (-> density of air, temperature of air, composition of air e.g. humidity)
  • changes in electric field with position between plates

Note - in Millikan's original experiment, he did use the fall velocity (at E=0) as a means of determining the radius of the drop; but he used the voltage needed to create a stationary (or slowly rising) drop to estimate the charge of the electron.

In general, "zero" is a good thing to measure - it usually requires less calibration.

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