Hangyu Liu(Roger)

The Quantization of Charge

What is quantization of charge?Millikan oil drop experiment and equipment

setupThe data collection and analysisThe conclusion

Outline

In general, the quantization of charge is the principle that the charge of any object is an integer multiple of the elementary charge.

What is Quantization of Charge?

For example:

0e, 1e, -1e Yes

0.5e, ½e, -0.9e No

In 1909, R. Millikan reported a reliable method for measuring ionic charge. The main process is to observe the motion of small oil droplets under the influence of an electric field.

It involves three types of motion:gravity fall motion (g);electric field aided downward motion (d);electric field aided upward motion (u).

Millikan Oil Drop Experiment

The Equipment Setup

•Webcam•Viewing Scope•Atomizer•Droplet Viewing Chamber•LED Light Source•Platform•Plate Charging Switch

•Stopwatch•Gadwin PrtSc

Constant Velocity

The Data Collection

Type Top Plate

Voltage

Y1

(minor lines)

Y2

(minor lines)

T1 T2

g / 10.0 5.1 00:30.00 00:48.77

d - 9.1 4.0 1:30.04 1:35.72

u + 6.1 10.9 1:57.25 1:58.49

The black lines: gravity fall motion (g)The red lines:electric field aided downward motion (d)The blue lines:electric field aided upward motion (u).

The Data Analysis

Figure: free body diagrams of all three cases.

Thus, for gravity fall measurements (f):

Fg=mg=4/3*πr3ρg

Fd=6πηeff rv

ηeff=η*[1/(1+b/pr)] due to Stokes’ law

Fd=Fg, 4/3*πr3ρg=6πηeff rv, we can find

For electric field aided upward motion (u):FE =Fd + Fg ,

q=(Fd+Fg) /E=[6πηeffrv+4/3* πr3ρg]*s/VFor electric field aided downward motion (d):FE =Fd - Fg ,

q=(Fd-Fg) /E=[6πηeffrv-4/3* πr3ρg]*s/V

The definitions of symbols used:q - charge carried by the droplets – separation of the platesρ – density of oilg – acceleration of gravityηeff - viscosity of air

r – the radius of dropv – the velocity of dropV – potential difference across the plates inb – constant, equal to 8.13* 10-8N/m

In general, in order to figure out the uncertainty of data, we could measure the same thing for several times.

While in this particular case, we have an upward motion and a downward motion for a same charge, so we just need to get the different values for the same charge and calculate the average difference between them as the uncertainty.

The Uncertainty of Data

The Conclusion

By adjusting the scaling, I found out the value of charge is (1.29+ 0.04)* 10-19 , which is smaller than the expected value 1.6* 10-19 . However, we clearly see the evidence of quantization of charge, so it might be experimental error which I can not figure out.

0 10 20 30 40 50 600123456789

101112

The Quantization of Charge

Series1

Measurements

Cha

rger

s (u

nits

of

e)

0 10 20 30 40 50 600

2

4

6

8

10

12

The Quantization of Charge

Series1

Measurements

Charg

ers

(unit

s of

e)