Part 1 - Get a Lab Appointment and Install Software:
Set up an Account on the Scheduler (FIRST TIME USING NANSLO):
Find the email from your instructor with the URL (link) to sign up at the scheduler.
Set up your scheduling system account and schedule your lab appointment.
NOTE: You cannot make an appointment until two weeks prior to the start date of this lab assignment.
You can get your username and password from your email to schedule within this time frame.
Install the Citrix software: – go to http://receiver.citrix.com and click
download > accept > run > install (FIRST TIME USING NANSLO).
You only have to do this ONCE. Do NOT open it after installing. It will work automatically when you go
to your lab. (more info at
http://www.wiche.edu/info/nanslo/creative_science/Installing_Citrix_Receiver_Program.pdf)
Scheduling Additional Lab Appointments:
Get your scheduler account username and password from your email.
Go to the URL (link) given to you by your instructor and set up your appointment.
(more info at http://www.wiche.edu/nanslo/creative-science-solutions/students-scheduling-labs)
Changing Your Scheduled Lab Appointment:
Get your scheduler account username and password from your email. Go to http://scheduler.nanslo.org
and select the “I am a student” button. Log in to go to the student dashboard and modify your
appointment time. (more info at http://www.wiche.edu/nanslo/creative-science-solutions/studentsscheduling-labs)
Part 2 – Before Lab Day:
Read your lab experiment background and procedure below, pages 1-21.
Submit your completed Pre-Lab Questions (page 6) per your faculty’s instructions.
Watch the Helmholtz Coil Control Panel Video Tutorial
http://www.wiche.edu/nanslo/lab-tutorials#helmholtz
Part 3 – Lab Day
Log in to your lab session – 2 options:
1)Retrieve your email from the scheduler with your appointment info or
2) Log in to the student dashboard and join your session by going to http://scheduler.nanslo.org
NOTE: You cannot log in to your session before the date and start time of your appointment. Use
Internet Explorer or Firefox.
Click on the yellow button on the bottom of the screen and follow the instructions to talk to your lab
partners and the lab tech.
Remote Lab Activity
SUBJECT SEMESTER: ____________
TITLE OF LAB: Electron Charge Mass (Helmholtz Coil)
Lab format: This lab is a remote lab activity.
Relationship to theory (if appropriate): In this lab you will learn about the interaction between
electrons and electric and magnetic fields.
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 exercises.
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 online period, and answer questions
in analysis sections after your online period. Your instructor will let you know if you are
required to complete any optional exercises in this lab.
Remote Resources: Primary – Helmholtz Coil Apparatus; Secondary – High-voltage power
supplies.
CONTENTS FOR THIS NANSLO LAB ACTIVITY:
Learning Objectives........................................................................................................ 2
Background Information ............................................................................................... 2-4
Calculating the Charge to Mass Ratio ........................................................................... 4-6
Pre-lab Questions........................................................................................................... 7
Equipment ..................................................................................................................... 7
Preparing for this NANSLO Lab Activity ........................................................................ 7-8
Experimental Procedure ............................................................................................... 8-9
Exercise 1: Qualitative Observation ............................................................................. 9
Exercise 2: e/m Measurement ..................................................................................... 9-10
Data Analysis (Can be Done Off Line if Necessary) ....................................................... 10
(Optional) Advanced Analysis ....................................................................................... 10
Helmholtz Coil Apparatus NANSLO Control Panel Instructions .................................... 11-19
Creative Commons Licensing ........................................................................................ 20
U.S. Department of Labor Information ......................................................................... 20
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LEARNING OBJECTIVES:
After completing this laboratory experiment, you should be able to do the following things:
1. Perform a modified version of JJ Thomson’s historic cathode ray experiment with
Helmholtz coils.
2. Evaluate the effect of a magnetic field on a beam of electrons.
3. Determine the charge to mass ratio of an electron.
BACKGROUND INFORMATION:
The screen of the smartphone, the light bulb in the lamp, and countless other modern luxuries
and necessities depend on electricity. Electricity is generated by the flow of electrical charge
which is carried by electrons. Electrons are subatomic particles that are not only integral for
the generation of electricity but for many chemical and physical properties of molecules and
elements.
Before the research and experiments of the late 19th century confirmed what we know today
about the atom and electronics, the composition of electric current or the fact that electrons
were negative was not yet known. Among the researchers, like Milikan and Rutherford, who
provided evidence for the structure of the atom, was J. J. Thomson. Here is a historical timeline
to put some of the relevant discoveries in perspective:
1803: Dalton proposes the Atomic Theory stating that all matter is composed of tiny
particles called atoms and that atoms are indivisible.
1869: Mendeleev publishes a periodic table listing the elements according to chemical
and physical properties.
1897: JJ Thomson conducts the Cathode Ray experiment.
1909: Milikan conducts the Oil drop experiment definitively calculating the charge on a
single electron.
1911: Rutherford conducts the Gold Foil experiment providing evidence for the
existence of the nucleus of the atom and concluding that atoms are mostly empty
space.
Prior to Thomson's experiment, atoms were thought to be indivisible and the existence of
electric charge was not yet confirmed. In Thomson's experiment, as well as in Milikan's and
Rutherford's experiments, information about the atom and the subatomic particles is gathered
from the interaction of matter with electric fields.
When a glass tube with conducting plates on either end is filled with gas and an electric
potential difference is imposed across the plates, a current will pass through the gas. This
suggests that the gas has broken down into something that is carrying the charge between the
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plates. When the tube is evacuated of gas and an electric potential difference is again imposed
across the plates, there is still some current that flows through the glass. This suggests that the
presence of gas molecules is not necessary for the current to flow but rather the current is
originating from the metal conducting plates. Specifically, the current appears to start from the
cathode, the plate with a negative potential, and travel to the anode, the plate with the positive
potential. These rays are called cathode rays and are what is carrying negative charge.
Figure 1: Thomson's Cathode Ray experiment in a glass tube with electric and
magnetic fields perpendicular to each other and the beam of electrons.
This image has Creative Commons Attribution. See
http://2012books.lardbucket.org/books/principles-of-general-chemistry-v1.0/s05-05-theatom.html.
Thomson conducted his experiment on cathode rays in an evacuated glass tube and produced
a beam of cathode rays from the cathode to the anode as expected. In his setup, he had the
beams continue passed the anode through a hole in order to study what would happen to these
cathode rays in the presence of a magnetic field and an electric field. He set up an electric field
with a positive and a negative plate and noticed that the beam of cathode rays deflected away
from the negative plate to the positive plate. This suggested that the cathode rays were in fact
negatively charged. Additionally, a magnetic field was set up perpendicular to both the beam
of cathode rays and the electric field. By varying the strength of both the magnetic field and
the electric field, the deflection of the rays varied. Thomson was able to use the degree of
deflection and the strengths of the magnetic and electric fields to calculate the charge to mass
ratio of the rays. These rays were in fact electrons. The ratio of the charge to mass is
1.7588196 𝑥 1011 C/kg where C is Coulombs and the mass is in kilograms. Less than a decade
later, Milikan was able to calculate the actual charge of the electron using the ratio that
Thomson determined. The actual charge of an electron is 1.6021773 𝑥 10−19 and the mass is
9.109390 𝑥 10−31 kg.
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In this experiment, you will perform a modified version of this experiment using Helmholtz
coils. The principles remain the same. A beam of electrons will be deflected by changes in the
magnetic and electric field and you will measure the amount of deflection. The path of the
electrons will appear different however because this is using a Helmholtz coil which will
produce a circular motion and therefore the path of the electrons will be circular. You will be
able to see the path of the electrons (a faint green line) because there is a small amount of inert
gas that undergoes excitation upon coming in contact with the electron beam.
Figure 2: Helmholtz coil apparatus with
glass bulb in the center.
Figure 3: The Helmholtz coil apparatus with
a box over it so that the beam of electrons is
made more visible
CALCULATING THE CHARGE TO MASS RATIO:
In this experiment, electrons are emitted similar to Thomson’s original experiment and are
accelerated by a known potential difference 𝑽. The beam of electrons then experience the
magnetic field produced by the Helmholtz coil which then deflects the beam on a circular path.
During this experiment, you will be able to control the accelerating potential and the current in
the coils which will affect how much the electrons are deflected. By measuring the radius of
the circular beam, and using the accelerating potential and current, you will be able to calculate
the charge to mass ratio of an electron.
The kinetic energy of the beam of electrons, as with all matter, can be calculated by:
(1)
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𝐾𝐸 = 12𝑚𝑣 2
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where 𝒎 is the mass and 𝒗 is the velocity. The kinetic energy is also equal to:
(2)
𝐾𝐸 = 𝑒𝑉
where 𝒆 is the charge of the electron and 𝑽 is the accelerating potential. Setting equations (1)
and (2) equal to each other:
(3)
𝑚𝑣 2 = 𝑒𝑉
1
2
If we were to use the equation above to calculate the charge to mass ratio of the electron, the
velocity of the electron beam would need to be known. The velocity is not one of the variables
measured in this lab, however, the accelerating potential and the current can be used to
calculate the force of the electrons.
The Helmholtz coil that the electrons travel through has a magnetic field, B, that affects the
circular path of the electrons and the force exerted by the electrons:
(4)
𝐹 = 𝑒𝑣𝐵
This force must also be equal to the centripetal force since the motion of the electrons is
circular:
(5)
𝐹=
𝑚𝑣 2
𝑟
Setting equations (3) and (4) equal to each other:
(6)
𝑒𝑣𝐵 =
𝑚𝑣 2
𝑟
and then solving for e/m:
(7)
𝑒
𝑚
=
𝑣2
𝑟𝐵
Looking back at equation (3), we can rearrange to solve for the velocity in terms of the mass,
the charge, and the accelerating potential:
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(8)
𝑣=√
2𝑒𝑉
𝑚
Putting equation (8) into equation (7) gets:
(9)
𝑒
=
𝑚
1
𝑟𝐵
√
2𝑒𝑉
𝑚
If both sides were squared:
(10)
𝑒2
𝑚2
=
1
𝑟 2 𝐵2 𝑚
Dividing both sides by
(11)
𝑒
𝑚
=
2𝑒𝑉
𝑒
𝑚
gets:
2𝑉
𝑟 2 𝐵2
For the Helmholtz coil used in this experiment, the magnetic field can be determined using this
equation:
(12) 𝐵 = (0.7155 ± 0.0001) (
4𝜋
107
𝑁𝐼
)(𝑅)
where 𝑁 is the number of coils and 𝑹 is the radius of the coils. Those two variables are held
constant throughout the experiment, because the experimental apparatus is not altered at all
during the experiment. 𝑰 is the coil current which will be controlled by the experimenter.
Since only the current changes in this experiment, it is helpful to consider equation (12) as the
product of all of the constants and the current, I. Equation (12) may then be written:
(13)
𝐵 = 𝐶𝑥𝐼
where C represents all of the constants from equation (12). Now putting equation (13) into
equation (11) gets:
(14) )
𝑒
𝑚
=
2𝑉
𝑟 2𝐵2𝐼2
From this experiment, we will have collected all the necessary data to use equation (14) in order
to calculate the charge to mass ratio of an electron.
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PRE-LAB QUESTIONS:
1. In equation (14), what variables will you record in this experiment and what variables
are kept constant throughout the experiment? Which of those variables do you think
will contribute the most to error?
2. Calculate the value of C in equation (14) using the following:
o 𝑁: 130 turns of wire
o 𝑅: 0.0150 +/- 0.0005 meters
3. What is the uncertainty in question 2 above.
4. How is the electron beam visible?
5. What would be different about this experiment in terms of your data analysis if you
were to use a cathode ray tube like JJ Thomson did as opposed to this Helmholtz coil?
6. Could you imagine doing an experiment like this on any other subatomic particles? Why
or why not?
EQUIPMENT:



Paper
Pencil/pen
Computer (access to remote laboratory)
PREPARING FOR THIS NANSLO LAB ACTIVITY:
Read and understand the information below before you proceed with the lab!
Scheduling an Appointment Using the NANSLO Scheduling System
Your instructor has reserved a block of time through the NANSLO Scheduling System for you to complete
this activity. For more information on how to set up a time to access this NANSLO lab activity, see
www.wiche.edu/nanslo/scheduling-software.
Students Accessing a NANSLO Lab Activity for the First Time
For those accessing a NANSLO laboratory for the first time, you may need to install software on
your computer to access the NANSLO lab activity. Use this link for detailed instructions on
steps to complete prior to accessing your assigned NANSLO lab activity –
www.wiche.edu/nanslo/lab-tutorials.
Video Tutorial for RWSL: A short video demonstrating how to use the Remote Web-based
Science Lab (RWSL) control panel for the air track can be viewed at
http://www.wiche.edu/nanslo/lab-tutorials#helmholtz
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NOTE: Disregard the conference number in this video tutorial.
AS SOON AS YOU CONNECT TO THE RWSL CONTROL PANEL: Click on the yellow button at the
bottom of the screen (you may need to scroll down to see it). Follow the directions on the pop
up window to join the voice conference and talk to your group and the Lab Technician.
EXPERIMENTAL PROCEDURE:
Once you have logged on to the remote lab system, you will perform the following laboratory
procedures. See Preparing for the Electron Charge Mass (Helmhotz Coil) NANSLO Lab Activity
below.
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.
Procedure Summary
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 code 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:
Figure 4: Electron Ring on Helmholtz Coil
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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. 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 edges 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.
EXERCISE 1: Qualitative Observations
1. Set the electron acceleration potential difference to 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 (11)?
2. 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 (11)?
EXERCISE 2:
𝒆
𝒎
Measurement
3. Set the accelerating potential difference to between 200 and 500 V. Record this value
and estimate its uncertainty.
4. 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. The beams on the
outside have kinetic energies closest to that due to the acceleration potential
difference. Record your measurements along with the coil current and the associated
uncertainties.
5. Repeat step 4 for four more different Helmholtz coil currents. Try to have at least 0.2
mm difference between each of the radius measurements.
6. Let another student take control of the control panel, change the accelerating potential
difference by at least 50 V, and repeat steps 4 and 5 for another set of radius
measurements.
7. Other students should repeat step 6 for at least two more sets of data at different
voltages between 200 and 500 V.
8. Make sure that each student in the group collects at least one set of data.
9. Make sure that all students have all the collected data for later use. You will have at
least 4 sets of data.
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10. FIRST, turn off the discharge tube accelerating voltage. SECOND, turn off the Helmholtz
coil power supply. Make sure you follow this order.
DATA ANALYSIS (CAN BE DONE OFF LINE IF NECESSARY)
Rewrite equation (14) with
1
𝑟2
in terms of the other variables. We will treat
1
𝑟2
as the dependent
variable that depends on independent variable I 2. For each of your accelerating potential values, plot
1
𝑟2
on the vertical axis versus I 2 on the horizontal axis. Draw a best fit line (insert a trendline in Excel)
for each set of data.
11. If
1
𝑟2
is the y-variable, and 𝐼 2 is the x-variable, what is the resulting expression for the slope of
the best fit line?
12. How are the slopes of the best fit lines related to the ratio of e/m?
13. For the data sets at each value of accelerating potential:
a.
b.
c.
d.
Solve for e/m using the values for each data point in equation (14).
Average the value of e/m from all six data points.
Calculate e/m from the slope of the best fit line of those six data points.
Compare the values from b and c to the accepted value of e/m. Which value is
closer to the accepted value? Does this make sense? Explain.
e. Which accelerating voltage potential setting produced the most accurate value of
e/m? Does this make sense based on the background material? Explain.
(OPTIONAL) ADVANCED ANALYSIS
14. In the analysis of this experiment, we ignored the magnetic field due to the Earth. Use
the internet to estimate the Earth’s magnetic field strength at the lab site (Denver, CO.)
Estimate how much this affects a typical radius measurement.
15. Describe the electron beam shape that would result if we rotate the gas discharge tube
so the beam is emitted with some component of its velocity vector in the same direction
as the magnetic field (instead of perpendicular to it).
16. Describe the electron beam if it is emitted in the same direction as the magnetic field.
17. In metric units, an Amp is a Coulomb/second and a Volt is expressed as:
𝑘𝑔 ∗ 𝑚2
𝐴𝑚𝑝 ∗ 𝑠 3
Using metric units, show that equation (14) results in units of Coulomb/kg.
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Helmholtz Coil Apparatus NANSLO Control Panel Instructions
The Remote Web-based Science Lab (RWSL) Helmholtz Coil apparatus is controlled remotely by
using a web interface as shown below. This NANSLO control panel allows you to control every
function of the spectrometer just as if you were sitting in front of it.
Figure 5: Lab interface for Helmholtz Coil Apparatus
Communicating with your Lab Partners
As soon as you have accessed this lab interface, click on the “Voice Conference” yellow button
(you may need to scroll down to see it) to view instructions for communicating with your lab
partners and with the Lab Technicians. Only one person can be in control of the equipment at
any one time so talking together on a conference line helps to coordinate control of the
equipment and creates a more collaborative environment for you and your lab partners.
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Gaining Control of the Helmholtz Coil Apparatus
Right click anywhere in the grey area of the lab interface and choose “Request Control of VI”
from the dialogue box that appears when multiple students are using the Helmholtz Coil
apparatus at the same time. After you request control, you may have to wait a short time
before you actually receive control and are able to use the features on this lab interface.
Figure 6: Right click and select "Request Control of VI" to gain control of the lab interface.
Releasing Control of the Helmholtz Coil Apparatus
To release control of the Helmholtz Coil apparatus so that another student can use it, right click
anywhere in the grey area of the lab interface and choose "Release Control of VI" from the
dialogue box that appears.
Figure 7: Right click and select "Release Control of VI" to give others a
chance to perform the activity.
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Heating the Helmholtz Coils
As mentioned in the Procedure Summary above, the electron emitter in the gas discharge tube must be
heated for it to work optimally. The control code won’t allow the application of the acceleration
potential until the emitter is sufficiently heated so turn the heater on first. To do this, click on the "DC
Power Output" button in the "Pre-Heater DC Power Supply" area of the lab interface.
Figure 8: Select the "DC Power Output" button to preheat the Helmholtz Coil.
In this closeup of the Pre-Heater DC power Supply area, while heating, you will see the message shown
here and a blue progress bar will move from left to right.
Figure 9: Indicating that the Helmholtz Coils is being heated.
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Turning on the Helmholtz Coil and Accelerating Voltage DC Power Supply
When the electrode is ready, the message shown in Figure 5 will disappear and the "DC Power
Out" button will appear in the "Accelerating Voltage Power Supply" portion of the lab
interface. It is now safe to click on the "DC Power Output" button in the "Helmholtz Coil DC
Power Supply" area of the lab interface as well as the "DC Power Output" button now available
in the "Accelerating Voltage DC Power Supply" area.
Figure 10: Select the "DC Power Output" buttons that now appear under the
Helmholtz Coil and Accelerating Voltage areas of the lab interface.
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Adjusting the Current and Voltage
Use the "Current" dial or the up/down arrows to the left of the box in the "Helmholtz Coil DC
Power Supply" area to adjust the current and use the "Voltage" dial or the up/down arrows to
the left of the box in the "Accelerating Voltage DC Power Supply" area to adjust the voltage in
the Helmholtz coil.
Figure 11: Adjusting the current and voltage on the Helmholtz Coil Apparatus.
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Helmholtz Coil Image View Window
There are two digital cameras set up for this lab activity. The Image View Window displays the
real-time video feed from the digital camera currently selected (Camera 1 is displayed in this
Image View Window.) The instructions below provide more detail on using Camera 1 and
Camera 2.
Figure 12: Image View Window image displayed is based on Camera Preset selected.
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Using the Cameras to View the Helmholtz Coil Apparatus and the Helmholtz Coils
There are two digital cameras set up for the Helmholtz Coil lab. First, we'll describe the options
when "Camera Selection" 1 is available.
Camera Selection = 1
This camera allows you to see what is going on in the lab and on the Helmholtz Coil apparatus itself.
Figure 13 below provides a description of
each Camera Preset available when
Camera 1 is being used. You can also
access this list via the lab interface by
hovering over the preset buttons.
For each camera preset view, additional camera
options are available when Camera 1 is being used
(see Figure 14.)
Use the up and down arrows to tilt the camera up
or down.
Use the right and left arrows to pan right or left.
Use the left "Zoom OUT" arrow and right "Zoom
IN" arrow to zoom out and in.
Figure 13: Camera Preset Positions
Figure 14: Pan-Tilt-Zoom Camera Control
Camera Selection = 2
Make sure Camera 2 is selected to view the Helmholtz coils and discharge tube that are
located inside the box. Camera 2 looks down a tube attached to the device and is used to view
the electron beam inside the discharge tube. When you send amperage to the Helmholtz coils
and voltage to the electron emitter inside the discharge tube, you will form a ring of
electronics. In Figure 15 below, Camera 2 is selected. Notice that the electron ring looks far
away.
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Figure 15: Camera 2 is selected and the camera (shown in the upper right image) is displaying
the Helmholtz coils and discharge tube inside the box (shown in the lower right image) using
Camera Present Position 1.
Select Camera Preset Position 2 to get a close up view and make measurements. DO NOT
change the position of the camera with any of the camera controls while you are making
measurements. Preset 2 is set so that the scale at the bottom of the video window is set
correctly.
Figure 16: Camera 2, Preset 2 showing close up of coils for measurement purposes
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To make a measurement, please a piece of paper or something similar against your computer
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.
Figure 17: Illustration of how to measure diameter of the beam.
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For more information about NANSLO, visit www.wiche.edu/nanslo.
All material produced subject to:
Creative Commons Attribution 3.0 United States License 3
This product was funded by a grant awarded by the U.S.
Department of Labor’s Employment and Training Administration.
The product was created by the grantee and does not necessarily
reflect the official position of the U.S. Department of Labor. The
Department of Labor makes no guarantees, warranties, or
assurances of any kind, express or implied, with respect to such
information, including any information on linked sites and
including, but not limited to, accuracy of the information or its
completeness, timeliness, usefulness, adequacy, continued
availability, or ownership.
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