Download MAGNETIC FORCE ON A MOVING CHARGE – 1302Lab5Prob8

PROBLEM #8: MAGNETIC FORCE ON A MOVING CHARGE
You are working with a team to design a better electron microscope. To precisely
control the beam of electrons, your research team decides to try a magnetic field. For
your study of electron control you decide to use a Cathode Ray Tube (CRT) with a
magnetic field perpendicular to its axis. From your work with Helmholtz coils in the
earlier problem, Measuring the Magnetic Field in Two Parallel Coils, you know that
the magnetic field between these parallel coils is fairly uniform, so you decide to use
them for your test. Before you can evaluate the sensitivity of the electron microscope
design, you need to determine how the magnitude of a constant magnetic field affects
the position of the beam spot.
Instructions: Before lab, read the laboratory in its entirety as well as the required reading in the
textbook. 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.
Read: Tipler & Mosca Chapter 26.2 Chapter 27 Section 1.
Review Deflection of an Electron Beam by an Electric Field
EQUIPMENT
You have a cathode ray tube (CRT), digital multimeter (DMM), compass, meterstick,
Helmholtz coils, banana cables, Hall probe and computer data acquisition system. The
magnetic field is provided by connecting the Helmholtz coils to a power supply and
placing the CRT between the coils.
Read the sections Cathode Ray Tube (CRT) and Accessories, The Magnetic Field Sensor (Hall
Probe) & The Digital Multimeter in the Equipment appendix.
Read the section Measuring Constant Magnetic Field in the Software appendix.
If equipment is missing or broken, submit a problem report by sending an email to
labhelp@physics.umn.edu. Include the room number and brief description of the
problem.
WARM UP
1. Draw a picture of the CRT in the Helmholtz coils. Since you will not be using electric
fields, do not include the deflection plates in your sketch. Be sure you have all the
other components in your sketch. Draw a coordinate axis on this sketch and show
the magnetic field direction and the region occupied by the magnetic field. Draw the
electron trajectory through all regions of the CRT together with its velocity and
MAGNETIC FORCE ON A MOVING CHARGE – 1302Lab5Prob8
acceleration. Draw the electron trajectory if there were no magnetic field. The
difference between where these two trajectories hit the CRT screen is the deflection.
2. What path does an electron follow while traveling through a constant magnetic field?
The magnetic force is always perpendicular to the electron’s velocity. Are there any
forces other than the magnetic force that need to be considered?
3. Determine the velocity of the electrons as they leave the electron gun in the CRT.
(See your notes from the earlier problem Deflection of an Electron Beam by an
Electric Field)
4. Determine the position, direction, and velocity of an electron entering the region of
constant magnetic field. Determine the position, direction, and velocity of an
electron as it leaves the region of constant magnetic field. What type of curve is the
electron’s trajectory in that region?
5. Determine the path of the electron as it travels after it leaves the magnetic field region
until it strikes the screen. Use geometry to determine how far from the center the
electron strikes the screen.
PREDICTION
Write an equation for the deflection of an electron as a function of the strength of a
constant magnetic field and the velocity of the electron when the direction of the
magnetic field is such as to give maximum deflection. Use this equation to graph the
deflection as a function of magnetic field strength for a typical electron velocity in the
CRT.
EXPLORATION
Review your notes from your exploration in the problem Magnets and Moving Charge.
WARNING: You will be working with equipment that generates large electric
voltages. Improper use can cause painful burns. To avoid danger, the power
should be turned OFF and you should 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.
Connect the CRT according to the directions in the Equipment appendix and review the
problem Deflection of an electron beam by an Electric Field in your lab journal. If
known, select the accelerating voltage that gave the largest deflection for the smallest
electric field. Record the location of the non-deflected beam spot using the selected
accelerating voltage.
MAGNETIC FORCE ON A MOVING CHARGE – 1302Lab5Prob8
NOTE: In this experiment we are interested in understanding the effects of ONLY a magnetic
field and NOT an electric field. Do not use the deflection plates.
You should have between 250 and 500 volts between the cathode and anode (Note:
cathode is negative and anode is positive). After a moment, you should see a spot that you
can adjust with the knob labeled “Focus”. If your connections are correct and the spot
still does not appear, inform your lab instructor.
The voltages listed on the CRT power supplies are approximate, you should check and
measure ALL voltages AND currents with a DMM. Read the Equipment appendix if
you need to review using a DMM.
Devise a measuring scheme to record the position of the beam spot. Record your zero
deflection position and do not move the CRT once you have started taking
measurements.
Review the magnetic field map from the Helmholtz Coils. Does it matter what direction
the currents flows in the two Helmholtz coils? Should it be in the same direction or
opposite directions? Ensure to send currents in the coils accordingly.
Set up your Hall probe as explained in the Equipment and Software appendices. Before
you push any buttons on the computer, locate the magnetic field strength window. You
will notice that even when the probe is held away from obvious sources of magnetic
fields, such as your bar magnets, you see a non-zero reading. From its behavior
determine if this is caused by a real magnetic field or is an electronics artifact or both?
If you notice an ambient field, can you determine its cause?
Go through the Hall probe calibration procedure outlined in the appendix, or in the
Magnetlab Guide Box in the upper right corner of the application. Be sure the sensor
amplification switch on the Hall probe is set to 6.4mT range. The MagnetLab
application requires the probe to be set to the 6.4mT range to work correctly. Does
the Hall probe ever read a zero field?
How will you orient the CRT with respect to the coils? Would the deflection be the
same if the magnetic field were reversed? Try it. How will you determine the length of
the CRT within the magnetic field? Is the field uniform throughout the flight of the
electrons?
Write down a measurement plan.
MAGNETIC FORCE ON A MOVING CHARGE – 1302Lab5Prob8
MEASUREMENT
Use the Hall Probe to Measure the magnetic field between the Helmholtz coils.
Use the Hall probe to measure the magnitude and direction of the magnetic field
between the coils. Measure the field near the coils. Be sure your Hall Probe is
calibrated and has the correct orientation to accurately measure the magnetic field.
Measure the position of the beam spot for each selected magnetic field. Make at least
two measurements for averaging.
The voltages listed on the CRT power supplies are approximate, you should check and
measure ALL voltages AND currents with a DMM. Read the Equipment appendix if
you need to review using a DMM.
ANALYSIS
Graph your measurements of the deflection of the electron beam for the different values
of the magnetic field at a fixed electron speed and compare to your prediction.
Repeat for deflection as a function of electron speed for a fixed magnetic field.
CONCLUSION
How does the deflection of the electron beam depend on the magnetic field? Did your
data agree with your prediction? If not, why? What are the limitations on the accuracy
of your measurements and analysis?
How does the deflection of the electron beam depend on the electron speed? Did your
data agree with your prediction? If not, why? What are the limitations on the accuracy
of your measurements and analysis?
Is controlling the deflection of an electron beam easier with a magnetic field or an
electric field? Write down what you mean by easier.