Download GRAVITATIONAL FORCE ON THE ELECTRON – 1302Lab1Prob3

PROBLEM #3: GRAVITATIONAL FORCE
ON THE ELECTRON
You work in a research laboratory that is attempting to make a better electron
microscope. The project requires precise control of a beam of electrons. To study your
ability to manipulate electron motion, you decide to use a Cathode Ray Tube (CRT) (the
same device that is the basis of older, box-style TV sets. In the CRT, electrons are
emitted at one end of an evacuated glass tube (called the cathode) and are detected by
their interaction with a phosphorous screen on the other end (called the anode). Every
object near the Earth's surface is subject to the gravitational force. Your team-mates are
worried that the gravitational force will deflect the electron from the desired path, and
that this deflection will depend on whether the beam is vertical or horizontal (or at
some general angle of inclination). From your physics experience you also know that
the acceleration of all objects in free fall due to gravity is the same, independent of their
mass. You decide to compute how far the beam deviates from a straight-line trajectory
at different angles of inclination.
Instructions: Before lab, read the required reading from the textbook and the laboratory in its
entirety. In your lab notebook, respond to the warm up questions and derive a specific prediction
for the outcome of the lab. During lab, compare your warm up responses and prediction in your
group. Then, work through the exploration, measurement, analysis, and conclusion sections in
sequence, keeping a record of your findings in your lab notebook. It is often useful to use Excel to
perform data analysis, rather than doing it by hand. At the end of lab, disseminate any electronic
copies of your results to each member of your group.
Read: Tipler & Mosca Chapter 21 Section 21-6 and review Chapter 3 Sections 3-1 & 3-2.
EQUIPMENT
You have a Cathode Ray Tube (CRT), Cenco CRT
power supply, banana cables, DMM and shielded
banana cables. The fluorescent screen has a onehalf centimeter grid with millimeter hash marks in
so that you can measure the position of the beam
on the screen.

Read the section Cathode Ray Tube and Accessories in the Equipment appendix.
Read the appendices Significant Figures, Accuracy, Precision and Uncertainty, and
Review of Graphs to help you take data effectively.
If equipment is missing or broken, submit a problem report by sending an email to
[email protected]. Include the room number and brief description of the
problem.
GRAVITATIONAL FORCE ON THE ELECTRON – 1302Lab1Prob3
WARM UP
1. Draw a picture of the CRT in the horizontal position. Do not include the deflection
plates shown in the appendix diagrams since they will not be used in this lab. Draw
the electron's trajectory from the time it leaves the electron gun until it hits the screen.
Label each important kinematics quantity in the problem. Using a free body diagram,
label all forces on the electron during this time. Choose a convenient coordinate
system and put it on your drawing. Does the vertical component of the electron's
velocity change? Why or why not? Does the horizontal component of its velocity
change? Why or why not?
2. Calculate the velocity of the electron just after it leaves the electron gun.
Hint: The change in the electric potential energy of an electron moving across a pair of
acceleration plates is the voltage difference between the two plates times the electron's
charge. What basic physics principle can you use to calculate the electron’s velocity as
it exits the electron gun? What assumptions must you make to carry out this
calculation?
3. What physics principle(s) can you use to calculate how far the electron falls below a
straight-line trajectory due to the force of gravity? What quantities must you know to
make the calculation? Perform this calculation to find a symbolic and then a numerical
answer.
4. Does your solution make sense? You can check by estimating the time of flight of the
electron based on its initial velocity and the distance between its starting point and the
screen. In that amount of time, how far would a ball drop in free fall? If the solution
does not make sense, check your work for logic or algebra mistakes.
5. Repeat 1-4 for a CRT pointed directly upwards, finding first a symbolic and then a
numerical answer.
6. Finally, repeat 1-4 at an arbitrary inclination angle from the horizontal. State your
answer symbolically and then numerically (a number times a function of the
inclination angle, in this case).
IMPORTANT hints: (1) Try using a reference frame where x is always along and y is
always perpendicular to electron’s initial trajectory. (2) If your equations become
complicated, make useful approximations by considering how large any term that
contains the electron’s velocity is to other terms in a given equations. (3) Does your
arbitrary angle answer comport with the strictly horizontal and strictly vertical cases?
GRAVITATIONAL FORCE ON THE ELECTRON – 1302Lab1Prob3
PREDICTION
Determine the physics task from the problem statement, and then in one or a few
sentences, equations, drawings, and/or graphs, make a clear and concise prediction that
solves the task. (Hint: How can you make a qualitative prediction with as much detail
as possible?)
EXPLORATION
WARNING: You will be working with equipment that generates large electric
voltages. Improper use can cause painful burns. The power must be turned off and
you must wait at least one minute before any wires are disconnected from or
connected to the power supply. Never touch the conducting metal of any wire.
Follow the directions in the appendix for connecting the power supply to the CRT.
Check to see that the connections from the power supply to the high voltage and the
filament heater are correct, before you turn the power supply on. You should have a
difference of ~250-500 Volts of electric potential between the cathode and anode. After a
moment, you should see a spot that you can adjust with the knob labeled “Focus”.
Note the details of all the connections in your lab notebook. (If your connections are
correct and the spot still does not appear, inform your lab instructor.)
Discuss the following in your group and note your responses in your lab notebook.
 Do you expect the gravitational deflection to vary as a function of the angle of the
CRT with the horizontal? Try different orientations in the horizontal plane to see if
you can observe any difference. Does the observed behavior of the electron deflection
agree with your prediction?
 For what orientation of the CRT is it impossible for the gravitational force to deflect
the electron? This is the location of the beam spot when there is no gravitational effect
on the motion of the electrons and should be used as the origin (and NOT the arbitrary
origin on grid).
 Do you observe any deflection of the electron beam? How can you determine if this
deflection is or is not caused by the gravitational force? If it is not, how can you
minimize such effects on your measurements?
 Devise a measurement scheme to record the angle of the CRT and the position of the
beam spot and record you measurement plan. (In general, a measurement plan
minimally consists of three labeled columns of numbers with units: (1) the
independent variable that you vary (you should pre-determine at which values of the
independent variable you will perform your measurements; also, what is the
independent variable in this experiment?), (2) the predicted values of the dependent
variable (i.e., use your prediction equation to compute what measurement you expect
GRAVITATIONAL FORCE ON THE ELECTRON – 1302Lab1Prob3
to observe at each value of the independent variable; what is the dependent variable
for this experiment), and (3) the actual, measured values of the independent variable.
Try doing this in Excel, as the computational power of using a computer program will
make doing labs easier as the labs themselves become more difficult.)
MEASUREMENT
Following your measurement scheme, measure the position of the beam spot at an
orientation of the CRT for which you expect the gravitational deflection to be zero and
then at the orientation for which you expect the gravitational deflection to be
maximum. Finally, make measurements at several different intermediate angles of
inclination.
Note: Be sure to record your measurements with the appropriate number of significant figures
and with your estimated uncertainty Otherwise, the data is virtually meaningless. If necessary,
read the suggested appendix material.
ANALYSIS
Use your data to determine the magnitude of the deflection of the electron. Make a
graph of the position of the electron beam spot as a function of the angle that the CRT
makes with the horizontal for both your predicted and measured deflection values.
If you observe a deflection, how can you tell if it is caused by the gravitational force? If
the deflection is not caused by gravity, what might be its cause? How will you decide?
CONCLUSION
Did you observe any deflection of the electron beam? Was it in the direction you
expected due to the gravitational force? Did you observe any aberrant behavior? What
could account for this? How did you conduct the experiment to minimize any aberrant
behavior?
Can you measure the effect of the Earth's gravitational force on the motion of the
electrons in the CRT? Why or why not?
Based on your results, do you think you need to take gravitational deflection into
account when using the CRT? Why or why not?
Overall, was your prediction successful? Why or why not?