NANSLO REMOTE LAB ACTIVITY

 

SUBJECT SEMESTER: XXXXXXXXXXXXXXXXXXXXX

TYPE OF LAB:  XXXXXXXXXXXXXXXXXXXX

 

 

 

 

 

TITLE OF LAB:  Electron Charge Mass (Helmholtz Coil)

 

Electron Charge Mass (Helmholtz Coil) NANSLO Lab Activity in Word format last updated April 23, 2014.

 

Lab format: This lab is a remote lab activity.

 

Relationship to theory:  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 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.

 

Remote Resources:  Primary - Helmholtz Coil Apparatus; Secondary - High-voltage power supplies.

 

LEARNING OBJECTIVES:

 

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 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-the-atom.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 C and the mass is 9.109390 x 10^-31 kg.

 

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 effect 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:

 

where m is the mass and v is the velocity.  The kinetic energy is also equal to:

 

where e is the charge of the electron and V is the accelerating potential. Setting equations (1) and (2) equal to each other:

 

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:

 

This force must also be equal to the centripetal force since the motion of the electrons is circular:

 

Setting equations (3) and (4) equal to each other:

and then solving for e/m:

 

Looking back at equation (3), we can rearrange to solve for the velocity in terms of the mass, the charge, and the accelerating potential:

 

Putting equation (8) into equation (7) gets:

 

If both sides were squared:

 

Dividing both sides by e/m gets:

 

For the Helmholtz coil used in this experiment, the magnetic field can be determined using this equation:

 

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:

 

where C represents all of the constants from equation (12).  Now putting equation (13) into equation (11) gets:

 

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. 

 

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:
• N:  130 turns of wire
• 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)
  
  

 

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
   
   
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.
1. Measure the outside edge of the glowing plasma ring produced by the electrons.
2. 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.
3. 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.
4. 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. 
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    in terms of the other variables.  We will treat   as the dependent variable that depends on independent variable I ².  For each of your accelerating potential values, plot    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 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:
11. Solve for e/m using the values for each data point in equation (14).
12. Average the value of e/m from all six data points.
13. Calculate e/m from the slope of the best fit line of those six data points.
14. 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.
15. 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:
    
        Using metric units, show that equation (14) results in units of Coulomb/kg.

 

 

PREPARING TO USE THE REMOTE WEB-BASED SCIENCE LAB (RWSL)

 

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

 

You must install software on your computer before accessing a NANSLO lab activity for the first time. Use this link to access instructions on how to install this software based on the NANSLO lab listed below that you will use to access your lab activity – www.wiche.edu/nanslo/lab-tutorials.

 

1. NANSLO Colorado Node -- all Colorado colleges.
2. NANSLO Montana Node -- Great Falls College Montana State University, Flathead Valley Community College, Lake Area Technical Institute, and Laramie County Community College.
3. NANSLO British Columbia Node -- Kodiak College.

 

Using the Helmhotz Coil for a NANSLO Lab Activity

 

We've provided you with three ways to learn how to use the Helmholtz Coil apparatus for this NANSLO lab activity:

 

1. Read these instructions.
2. View this short video.
   
   
   
   
3. Print off these instructions to read later (PDF version of the instructions.)
   
   NOTE:   The conference number in this video tutorial is an example.  See “Communicating with Your Lab Partners” below to determine the toll free number and pin to use for your NANSLO lab activity.

 

Helmhotz Coil Apparatus RWSL Lab Interface Instructions

 

The Remote Web-based Science Lab (RWSL) Helmholz Coil apparatus is used for this lab activity.  Using a web interface as shown below, you can control this equipment just as if you were sitting in front of it. 

 

The equipment control software shown below is written using the LabVIEW software from National Instruments. The user interface is presented as a LabVIEW control panel which will be referred to as the lab interface for the remainder of the document.

 

Figure 1:  Lab interface for Helmholtz Coil Apparatus

 

Communicating with your Lab Partners

 

As soon as you have accessed this lab interface, call into the toll free conference number shown on the control panel to communicate with your lab partners and with the Lab Technicians.  Use the PIN code noted to join your lab partners.  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.

 

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 2:  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 3:  Right click and select "Release Control of VI" to give others a chance to perform the activity.

 

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 4:  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 5:  Indicating that the Helmholtz Coils is being heated.

 

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 6:  Select the "DC Power Output" buttons that now appear under the
Helmholtz Coil and Accelerating Voltage areas of the lab interface.

 

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 7:  Adjusting the current and voltage on the Helmholtz Coil Apparatus.

 

Helmholtz Coild 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 8:  Image View Window image displayed is based on Camera Preset selected.

 

 

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 9 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.   Figure 9:  Camera Preset Positions

For each camera preset view, additional camera options are available when Camera 1 is being used (see Figure 10.) 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 10:  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 11 below, Camera 2 is selected.  Notice that the electron ring looks far away. 

 

Figure 11:  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.

 

To get a closeup view and make measurements, select Camera Preset Position 2.  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 12: Camera 2, Preset 2 showing closeup of coils for measurement purposes

 

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 13:  Illustration of how to measure diameter of the beam.

 

 

 

For more information about NANSLO, visit www.wiche.edu/nanslo.

 

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Creative Commons Attribution 3.0 United States License 3  

 

 

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