PHYSICS SEMESTER ONE
AIR TRACK LAB
CHARGE TO MASS RATIO OF THE ELECTRON
Lab format: this lab is a remote lab activity
Relationship to theory: This activity involves the investigation of how the motion of an electron
is affected by the presence of a magnetic field.
Instructions for Instructors: This protocol is written under an open source CC BY license. You
may use the procedure as is or modify as necessary for your class. Be sure to let your students
know if they should complete optional exercises in this lab procedure as lab technicians will not
know if you want your students to complete optional exercise.
Remote Resources: Primary – Helmholtz Coil, Secondary - None.
Instructions for Students: Read the complete laboratory procedure before coming to lab. Under
the experimental sections, complete all pre-lab materials before logging on to the remote lab,
complete data collection sections during your on-line period, and answer questions in analysis
sections after your on-line period. Your instructor will let you know if you are required to complete
any optional exercises in this lab.
EQUIPMENT

Paper

Pencil/pen

Computer (access to remote laboratory)
PREPARING TO USE THE REMOTE WEB-BASED SCIENCE LAB (RWSL)
Click on this link to access the Installguide for the RWSL:
http://denverlabinfo.nanslo.org
Follow all the directions on this webpage to get your computer ready for connecting to
the remote lab.
INTRODUCTION TO THE REMOTE EQUIPMENT AND CONTROL PANEL
Watch this short tutorial video to see how to use the RWSL control panel:
http://denverlabinfo.nanslo.org/video/helmholtz_coil.html
There are appendices at the end of this document that you can refer to during your lab if
you need to remind yourself how to accomplish some of the tasks using the RWSL
control panel.
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PHYSICS SEMESTER ONE
AIR TRACK LAB
Contents
CHARGE TO MASS RATIO OF THE ELECTRON ............................................................... 1
Equipment ................................................................................................................... 1
Preparing to Use the Remote Web-based Science Lab (RWSL) ................................. 1
Introduction to the Remote Equipment and Control Panel ........................................... 1
Learning Objectives ..................................................................................................... 2
Background Information ............................................................................................... 3
References ............................................................................................................... 6
Experimental Procedure: ............................................................................................. 6
Pre-Lab Exercise ......................................................................................................... 7
Exercise 1: Qualitative Observations .......................................................................... 7
Exercise 2: e/m Measurement .................................................................................... 8
Exercise 3: Data Analysis (can be done off-line if necessary) ..................................... 8
Exercise 4 (Optional): Advanced Analysis ................................................................... 9
Appendix A: Using the Remote Lab Control Panel .................................................... 10
Appendix B: Controlling the Power Supplies ............................................................. 11
Appendix C: Using the Cameras ............................................................................... 13
Appendix D: Measuring the Electron Beam Diameter................................................ 14
LEARNING OBJECTIVES



Investigate how the motion of an electron is affected by the presence of a magnetic field.
Measure the ratio of the electron charge to the electron mass: e/m
o Control power supplies to optimize conditions for making measurements of e/m
o Calculate e/m from individual data points and average
o Graph the measurements to determine the value of e/m
o Compare the value of e/m from the graph to e/m calculated from individual data
o Compare the value of e/m from the graph to the accepted value of e/m
(OPTIONAL) Advanced Analysis
o Determine the effect of Earth’s magnetic field on the path of an electron.
o Relate the shape of an electron beam to its orientation in a magnetic field.
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BACKGROUND INFORMATION
(Adapted from materials created by the WASC project: http://rwsl.nic.bc.ca/)
Many of the equations that we use when using physic to study the natural world rely on
universal or physical constants. Many of these physical constants can be used to
identify specific atomic and subatomic particles. For instance the charge to mass ratio
of an electron is unique to only the electron. In fact the electron was the first atomic
practical identified In 1897 J.J. Thomson for which he won the Nobel prize. In this lab
you will be replicating his famous experiment. In this experiment, we will use a gas
Helmholtz coils
gas discharge tube
electron path
ruler
2
r
electron emitter
Pre-heater power supply
Accelerating voltage power supply
coil power supply
Figure 1 - Helmholtz Coils with Gas Discharge Tube showing Electron Path
discharge tube and a pair of Helmholtz coils, as illustrated in Figure 1, to examine the
motion of electrons in a magnetic field. The Helmholtz coils produce a nearly uniform
magnetic field over the entire gas discharge tube. The gas discharge tube produces a
stream of electrons that travel through a diffuse helium gas inside the tube. When
excited by collisions with electrons, the helium gas in the discharge tube emits light so
we can see the path of the electrons.
The electron path can be used to determine the charge to mass (e/m) ratio of the
electron. Simply when a beam of electrons is travels through a constant magnetic field
in a perpendicular direction its orbit will be circular. The reason for this circular orbit is
the magnetic field imparting a force on the moving object. This is simply another
application of Newton’s laws of motion. Using this information we can derive equations
that allow us to calculate the e/m ratio of an electron. Specifically, when a charged
particle, of charge q, mass m and velocity v , enters a uniform magnetic field B , a force
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AIR TRACK LAB
FB on the charged particle is created by the magnetic field interacting with the moving
electron (Figure 2). This force is given by
FB  qv  B
(1)
The force direction is perpendicular to both the charged particle velocity and the
magnetic field.
r
v
FB
B
Figure 2 - Force on a moving charged
particle in a magnetic field (into the
page)
The magnitude of the force is
FB  qvB sin 
(2)
where  is the angle between velocity and the magnetic field.
In the case of an electron, charge e , moving perpendicular to the magnetic field
(θ = 90°), this simplifies to
FB  evB
(3)
The sign of the force is ignored here because we are only interested in the magnitude.
We will assume that all other forces on the electron are negligible. An object under a
net force that is perpendicular to its velocity will undergo circular motion with centripetal
acceleration
ac 
v2
r
(4)
In this case, the net force is FB  mac so, substituting terms,
evB  m
v2
r
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(5)
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PHYSICS SEMESTER ONE
AIR TRACK LAB
In this experiment, electrons pass through two parallel plates as they enter the gas
discharge tube. The potential difference between the plates is V. Assuming kinetic
energy of electrons before entering the plates is negligible, the kinetic energy of the
electrons after passing through the plates is
K  eV
(6)
or
1
2
mv 2  eV
(7)
We can rearrange equations (5) to isolate the velocity
v
erB
m
(8)
and substitute this into the kinetic energy equation (7) to get
2
1
2
 erB 
m
  eV
 m 
(9)
or, with a bit of work,
e
2V
 2 2
m r B
(10)
This shows that we can measure the ratio of the electron charge to the electron mass if
we know the potential difference used to accelerate the electrons, the magnetic field
strength, and the radius of the circular motion of the electron.
Depending on the magnetic field strength B and the accelerating potential V, the
electrons can travel anywhere within the discharge tube. The Helmholtz coils produce a
magnetic field that is constant to within 1%, and in the direction of the line joining the
centers of the two coils, over the entire discharge tube. According to the manufacturer
of the Helmholtz coil device we are using (NADA scientific), the magnitude of the
Helmholtz coil magnetic field within the discharge tube is
4𝜋
𝑁𝐼
𝐵 = (0.7155 ± 0.0001) (107 ) ( 𝑅 )
(11)
where I is the coil current, N is the number of coils, and R is the radius of the coils, both
of which are constants.
Now, we can combine equations 10 and 11 to get an equation that we can collect data
to satisfy in the experiment we’re about to do:
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𝑒
𝑚
=
2𝑉
𝑟2 𝐶 2𝐼2
(12)
Where C is the combination of all the constants from equation (11).
References
1. Laboratory Manual for Principles of Physics I and II, 5th Edition 2004, prepared by
Jason Diemer, North Island College.
2. Nakamura e/m Apparatus Manual. NADA Scientific, N99-B10-7350
EXPERIMENTAL PROCEDURE:
Read and understand these instructions BEFORE starting the actual lab procedure and collecting
data. Feel free to “play around” a little bit and explore the capabilities of the equipment before
you start the actual procedure. If you want to see the Helmholtz coils and discharge bulb, ask
the Lab Technicians to remove the cover for you before you start the experiment. They will
have to replace the cover before you begin the experimental procedure, however.
Summary of Experimental Procedure:
You will control the settings of an experimental apparatus similar to that depicted in Figure 1 to
collect data with which you can solve for the charge/mass ratio of the electron using equation
(10). The goal is to find a combination of voltage and current that will produce the best value of
e/m.
1. The electron emitter in the gas discharge tube must be heated for it to work optimally.
The control won’t allow the application of the acceleration potential until the emitter is
sufficiently heated, so turn the heater on first.
2. Once you have turned on the pre-heater power supply, there will be a 100-second time
delay before you can turn on the accelerating voltage power supply.
3. You will be able to control the amperage sent to the Helmholtz coils and the
accelerating voltage for the electron beam.
4. The discharge from the gas in the tube is rather faint, so the camera views the discharge
tube through a darkened cardboard tube.
5. Once established, the electron ring will look like this:
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AIR TRACK LAB
6. Once you establish a ring of electrons in the discharge tube, you will use the scale on the
control panel to measure the diameter of the electron ring.
a. Measure the outside edge of the glowing plasma ring produced by the electrons.
b. There is a glass rod inside the discharge bulb with a cm scale on it, but it is
difficult to see, so use the scale with moveable slider that is on the control panel.
c. Use a square piece of paper or something similar to line up with the top edge of
the control panel on your computer screen and the outside edge of the left side
of the plasma ring.
d. Move the slider on the scale under the video panel to coincide with the edge of
your piece of paper. This will be the diameter of the electron beam.
7. Ensure that each of your lab partners gets a chance to collect at least one set of data.
PRE-LAB EXERCISE
1. The accepted value of the charge/mass ratio of an electron is 1.758820088 x 1011
Coulomb/kg (National Institute of Standards and Technology:
http://physics.nist.gov/cgi-bin/cuu/Value?esme). How close do you think your result
from this experiment will be to that value?
2. What are the sources of uncertainty (error) in this experiment? How will they impact
your result?
3. Here are values you will need for your calculations. Calculate the value of C from
equation (12), and estimate the total uncertainty contributed by these values:
a. N: 130 turns of wire
b. R: 0.0150 +/- 0.0005 meters
4. Electrons are sub-microscopic, so how are you able to see them in this experiment?
EXERCISE 1: QUALITATIVE OBSERVATIONS
5. Set the electron acceleration potential difference to something between 250 and 400 V,
and raise the Helmholtz coil current in steps. What happens to the electron beam?
Does this make sense with respect to equation (10)?
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6. Set the Helmholtz coil current to between 1.0 and 2.0 A, and raise the electron
acceleration potential difference in steps. What happens to the electron beam? Does
this make sense with respect to equation (10)?
EXERCISE 2: E/M MEASUREMENT
7. Set the accelerating potential difference to between 200 and 500 V. Record this value
and estimate its uncertainty.
8. Adjust the Helmholtz coil current so the electron beam forms a circular path within the
discharge tube. Measure the outside diameter of the electron beam. Record your
measurements along with the coil current and the associated estimated uncertainties.
9. Repeat step 8 for six different Helmholtz coil currents.
10. Let another student take control of the control panel, change the accelerating potential
difference by at least 50 V, and repeat steps 8 and 9 for another set of radius
measurements.
11. Other students should repeat step 10 for at least two more sets of data at different
accelerating potential voltages between 200 and 500 V.
12. Make sure that each student in the group collects at least one set of data.
13. Make sure that each student records all the data sets that are collected. You will have
at least 4 sets of data; one each for the 4 different accelerating potential settings.
14. Turn off the discharge tube accelerating voltage, then the Helmholtz coil power supply,
in that order.
EXERCISE 3: DATA ANALYSIS (CAN BE DONE OFF-LINE)
Rewrite equation (12) with
1
𝑟2
in terms of the other variables. We will treat
1
𝑟2
as the
dependent variable that depends on the independent variable I2. For each of your accelerating
potential values use a spreadsheet application to create a graph of the date, plot
1
𝑟2
on the
vertical axis versus I2 on the horizontal axis. Use your spreadsheet application to calculate a
best fit line (insert a Trendline in Excel) for each set of data.
15. If
1
𝑟2
is the y-variable, and I2 is the x-variable, what is the resulting expression for the
slope of the best fit line?
16. How are the slopes of the best fit lines related to the ratio of e/m?
17. For the 4 accelerating potential data sets you collected in exercise 2 :
a. Solve for e/m using equation (12) and the values for each data point
b. Average the value of e/m from all 6 data points at each accelerating potential.
c. Calculate e/m from the slope of the best fit line of those 6 data points.
d. Do this for all the data sets that you have collected. You will end up with at least
4 averages and 4 slopes.
e. Compare the values from d to the accepted value of e/m. Which value is closest
to the accepted value? Does this make sense? Explain.
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AIR TRACK LAB
f. Which accelerating voltage potential setting produced the most accurate value
of e/m? Does this make sense based on the background material? Explain.
EXERCISE 4 (OPTIONAL): ADVANCED ANALYSIS
18. Using the t-test, analyze the averages from each of the acceleration potential voltage
settings to see if they can be combined together to produce a grand average across all
the voltage settings. If the averages can be combined, then average the results from the
graphical approach as well. Which grand average is closest to the accepted value of
e/m?
19. In the analysis of this experiment, we ignored the magnetic field due to the Earth. Use
the Internet to find an estimate of Earth’s magnetic field strength at the lab site
(Denver, CO). Use this information to estimate how this affects a typical radius
measurement. Estimate both the direction and magnitude of the affect.
20. Describe the electron beam shape that would result if we rotate the gas discharge tube
so the beam is emitted so that some component of its velocity vector is in the same
direction as the magnetic field (instead of perpendicular to it).
21. Describe the electron beam if it is emitted in the same direction as the magnetic field.
𝑘𝑔∙𝑚2
22. In metric units, an Amp is a Coulomb/second, and a Volt is expressed as:
𝐴𝑚𝑝∙𝑠3
Using metric units, show that equation (12) results in units of Coulomb/kg.
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APPENDIX A: USING THE REMOTE LAB CONTROL PANEL
When you login to the RWSL and start the Helmholtz Coil app, you will see this control panel:
Figure 3 - Control Panel for Helmholtz Experiment
On the left side of the panel are the controls for the power supplies, and on the right side are
the camera controls.
At the bottom of the screen are instructions for joining the voice conference that will allow you
to talk with any other students who are doing the same experiment and also to the Lab
Technicians who are there in the lab to assist you.
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APPENDIX B: CONTROLLING THE POWER SUPPLIES
Figure 4 - Pre-Heating the Electrode
When you click on the “DC Power Out” button for the Pre-Heater Power Supply, you will
see the message shown in the above screenshot and a blue progress bar will move
from left to right.
When the electrode is ready, the message will disappear and the DC Power Out button
for the Accelerating Voltage Power Supply will appear. It is now safe to turn on the
accelerating voltage (Figure 5).
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Figure 5 - Pre-Heating is Complete
Click the DC Power Out buttons for both the Coil power supply and the Accelerating
Voltage. Use the dials to set the current and voltage, use the “up down” arrows, or just
type directly into the number boxes.
Up/Down Arrows
Figure 6 - Setting Current and Voltage
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APPENDIX C: USING THE CAMERAS
The right side of the control panel allows you to see what’s going on in the lab. Use the
Pan-Tilt-Zoom controls to move the selected camera and see different parts of the
apparatus.
Camera 2
Figure 7 - Camera Controls
Hovering over the Preset buttons will cause a text box to pop up that tells you what
each button will show you.
This activity has two cameras connected to it. You can see Camera 2 at the right side
of the screen. It is the one you will use to view the electron beam inside the discharge
tube.
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AIR TRACK LAB
APPENDIX D: MEASURING THE ELECTRON BEAM DIAMETER
The Helmholtz coils and discharge tube are located inside the box on the right side of
the apparatus. Camera 2 is looking down a tube directly at the device.
Coils and discharge
tube are in here.
Tube for Camera 2
Figure 8 - Helmholtz Coil Case
When you send amperage to the Helmholtz coils and voltage to the electron emitter
inside the discharge tube, you will form a ring of electrons. Switch to Camera 2 to view
this (Figure 9).
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AIR TRACK LAB
Click here for Preset 2
Figure 9 - Looking down the tube with Camera 2
Notice that the electron ring looks far away. To get a close-up view and make
measurements, select Preset 2. See the next figure for the close-up view.
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Measurement
Scale with
moveable slider
Figure 10 - Close-up View of Electron Beam
Do NOT change the position of the camera with any of the camera controls while you
are making measurements. Preset 2 is set exactly so that the scale at the bottom of the
video window is set correctly.
To make a measurement, place a piece of paper or something similar against the
screen and line it up with the outside of the electron beam. Move the slider over to
where it meets the edge of the paper, and that will be the diameter of the beam.
See the next figure for an approximation of this.
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AIR TRACK LAB
A piece of
paper lined
up with the
edge of the
video frame
and the edge
of the
electron
beam.
Slider moved to the
edge of the paper
Diameter of the
electron beam
Figure 11 - Measuring the Beam Diameter
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