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# Millikan’s Oil Drop Experiment

This is the original equipment used by Robert Millikan and Harvey Fletcher in 1909 to measure the electric charge on a single electron.  The work was done at the University of Chicago.

### Millikan’s Oil Drop Experiment

One important application of the uniform electric field between two charged parallel plates was the determination of the charge on a single electron by Robert Millikan (1868 – 1953).

The sketch below shows a diagram of the Millikan oil drop experiment Two parallel charged plates are placed with the positively charged plate above and the negatively charged plate below.  The positively charged plate has a pinhole opening in its center.  An atomizer is used to spray drops of oil into the apparatus.  The friction of the oil passing through the narrow opening puts charges on many of the oil drops.  As the oil drops fall, one or more pass through the pinhole opening and enter the area between the plates.  The charge on the plates is adjustable.

A separate experiment with uncharged plates was used to determine the terminal velocity of the oil drops and from the terminal velocity, the weight of the oil drops could be established.  When an oil drop fell through the pinhole with the plates charged, the electric field between the plates could be adjusted to exactly stop the fall of the oil drop.  When the fall of the oil drop was stopped, the electric force pushing up on the drop was exactly equal to the weight of the drop pushing down.

Example Problem:  An oil drop weighs $1.9 \times 10^{-14} \ N$ .  It is suspended in an electric field whose intensity is $4.0 \times 10^4 \ N/C$ .  Since the oil drop is suspended, the gravitational force, $1.9 \times 10^{-4} \ N$ , is equal to the electrical force, $F_E = Eq$ .

Solution: $q=\frac{weight}{E}=\frac{1.9 \times 10^{-14} \ N}{4.0 \times 10^4 \ N/C}=4.8 \times 10^{-19} \ C$

So the charge on the suspended oil drop was $4.8 \times 10^{-19} \ C$ .  When the oil is sprayed through the atomizer, some oil drops are negatively charged but we don’t know how many extra electrons the drops acquire.  Therefore, this charge on the oil drop could be the result of having one extra electron or having five extra electrons.

In order to determine the charge on one electron, the oil drop experiment was carried out many times and the charge on many oil drops was determined.  The smallest charge on any oil drop was found to be  $1.6 \times 10^{-19} \ C$ and all the other charges on oil drops were found to be whole number multiples of $1.6 \times 10^{-19} \ C$ .  In the example problem above, we would conclude that the oil drop held three extra electrons.

#### Summary

• One application of the uniform electric field between two charged parallel plates was the determination of the charge on a single electron by Robert Millikan.
• An atomizer is used to spray drops of oil into the apparatus.
• The friction of the oil passing through the narrow opening puts charges on many of the oil drops.
• As the oil drops fall, one or more pass through the pinhole opening and enter the area between the plates.
• The charge on the plates is adjusted to stop the fall of one oil drop.
• When the oil drop is stopped, its weight mg downward equals the electrical force, $Eq$ , upward.

#### Practice

The following video covers Millikin's oil drop experiment. Use this resource to answer the following questions.

1. What was the purpose of the x-rays passing through the instrument?
2. At which university was Millikin's oil drop experiment conducted?

#### Review

1. Give reasons for each drop requiring a different voltage to balance.
2. Why do some oil drops not react to adjustments in voltage?
3. Why do some drops fall faster instead of slower when you increase the voltage?
4. In another universe,  where the unit for charge is the mork, a physicist performed the Millikan oil drop experiment and measured the following charges on a series of oil drops.
 Trial Charge Trial Charge 1 $2.62 \times 10^{-13}$ mork 4 $5.24 \times 10^{-13}$ mork 2 $3.93 \times 10^{-13}$   mork 5 $6.55 \times 10^{-13}$ mork 3 $1.31 \times 10^{-13}$ mork

Which of the following is the best choice for the charge on an electron in morks?

1. $2.62 \times 10^{-13}$ mork
2. $6.55 \times 10^{-13}$ mork
3. $1.31 \times 10^{-13}$ mork
4. $1.6 \times 10^{-19}$ mork
5. None of these.
5. An oil drop weighs  $1.9 \times 10^{-15} \ N$  and it suspended in an electric field of  $6.0 \times 10^3 \ N/C$ .
a. What is the charge on the drop?
b. How many excess electrons does it carry?