Physics 241 Lab: Cathode Ray Tube
http://bohr.physics.arizona.edu/~leone/ua/ua_spring_2010/phys241lab.html
NAME:__________________________
Section 1:
1.1. A cathode ray tube works by ‘boiling’ electrons off a cathode heating element and accelerating
them with a large voltage difference. Then the high-speed electrons pass between a pair of charged
deflection plates so that the path of the electron is altered. Finally, the electrons strike a screen coated
with a fluorescent material and you see a scintillation take place (i.e. you see light emitted). All of this
is done in a vacuum so that the electron can travel through the CRT unhindered by collisions with air
molecules. Actually, there are two pairs of deflection plates: a pair of charged deflection plates for
vertical deflection and another pair of charged deflection plates for horizontal deflection. (See figure.)
Three-dimensional figure showing the operation of the CRT.
The dotted line shows the path traversed by an example electron.
1.2. In the cathode ray tube, an electron is initially at rest (approximately) and is accelerated by a
force produced by an electric field. However, in lab you will only know the positive change in voltage
Va (really “ΔVa”) of the plates through which the electron is accelerated. What simple formula using
Va, q and W can you write to relate the work done on the electron to the change in voltage of the
apparatus? Be careful, the charge of an electron is –e. (Be sure to check your answer with other
students or your TA!)
Your formula:
Now plug in q = -e into your formula (for an electron):
1.3. Now slightly extend this formula using the work-energy theorem. The work-energy theorem
states that the change in kinetic energy is equal to the work done on the object. Using this concept,
write a formula relating the change in the electron’s kinetic energy to the accelerating voltage Va of the
apparatus (use Va, e and ΔK). (Be sure to check your answer with other students or your TA!)
Your formula:
1.4. Write a formula that describes the final velocity of the electron if it starts from rest and you
know the work done on the electron (use vf, me, Va, and e). (Be sure to check your answer with other
students or your TA!)
Your formula:
1.5. Explain what the sign of the accelerating voltage difference Va must be in order for your
formula in #3 to make sense? Reconcile this with your knowledge of how negatively charged particles
respond to an electric field. Your explanation:
1.6. Now try out your formula using some numerical values. If the electron starts at the position
x=0 on the following graph, find out the speed of the electron once it has reached the area of constant
electric potential. (Remember that electrons flow upward in the voltage landscape.) You should use
the electron charge, e = 1.6x10-19 C, and the electron mass, me = 9.1x10-31 kg. Your calculations and
answer in SI units:
Section 2: Now you know how to find speed of the electrons after they are initially accelerated,
you will study how the electrons are deflected by the charged deflecting plates.
2.1. There are three electric fields affecting the trajectory of the electron. Ea accelerates the
electron initially to a high speed. Ed,v causes a deflection in the vertical direction and Ed,h causes a
deflection in the horizontal direction. In the CRT figure below, draw arrows correctly depicting
the direction and magnitudes of these fields. Do you best to draw Ed,v in the three-dimensional
picture.
2.2. Now examine a pair of charged deflection plates (see figure). The voltage difference between
the plates is Vd,y. Assume the plates are separated by a distance d. Assume Vd,y is positive
Find the magnitude and direction of the electric field between the plates Ey in terms of d and Vd,y
(ignore any edge effects). Your answer:
Determine the acceleration ay felt by an electron inside the space between the plates using e, me and
Ey. Your answer:
2.3. Now examine what happens when an electron enters the space between the vertical deflection
plates (see figure).
If the electron enters with a velocity in the x-direction of vo,x and travels the length of the plates w,
how long does it take for the electron to reach the other side, Δt? Write your answer for Δt using w
and vo,x. Your work and answer:
Explain why this time Δt is not affected by the acceleration in the y-direction caused by the deflection
plates? Your explanation:
2.4. As the electron traverses the space between the deflection plates, it is accelerated in the ydirection.
Using the kinematics equation Δy = ½ ay(Δt)2 to find vertical displacement Δy of the electron once it
has reached the other side of the deflection plates. Write your answer for Δy using w, vo,x, e, me and
Ey. Your work and answer in SI units:
Use the kinematics equation vf,y = ay(Δt) to determine the final y-velocity vf,y when the electron has
reached the other side of the deflection plates. Write your answer for vf,y using w, vo,x, e, me and Ey.
Your work and answer:
Section 3: This section is not a problem, but you must read through it in lab. This is where all the
analysis you have done from the previous section is synthesized together to derive the cathode ray tube
equation. You will need to understand the following work in order to write your lab report. The
derivation will use the following figure to find Dy.
3.1. READ THE FOLLOWING SENTENCE TWICE! Our goal here is to derive a final equation
that relates Dy to the only things we can control in the lab Va and Vd,y (as well as the things we can’t
control: the geometric parameters of the CRT d, w and L). Note that capital V will always represent a
voltage while a lower case v will always represent a velocity. In the derivation ignore directional
1
2
negative signs for simplicity, and also we need to use me v o,x
= e " Va (usually to substitute for vo,x).
2
First we need to find Δy: (You will need to justify each step below in your report.)
1
2
"y = ay ("t )
2
!
2
1 $ e # E y '$ w '
= &
)
)&
2 % me (% v o,x (
'
$ $ Vd ,y ' '$
)
& e&
) )&
1 & % d ( )& w 2 )
=
2 & me )& $ 2e # Va ' )
))
&
)& &
%
(% % me ( (
!
=
2
1 e # Vd ,y # w # me
4 d # me # e # Va
=
w 2 Vd ,y
4d Va
Next we need to find Δy’: (You will need to justify each step below in your report.)
"y'= v f ,y "t'
# L &
= ( ay "t )%
(
$ v o,x '
# e ) E w &# L &
=%
)
(%
(
$ me v o,x '$ v o,x '
# # Vd ,y &
&
% e%
(
(
$ d ' w (# L &
%
=
)
%
(
% me
v o,x ($ v o,x '
%
(
$
'
w ) L ) e ) Vd ,y
=
2
d ) me v o,x
w ) L ) e ) Vd ,y
2d ) e ) Va
w ) L Vd ,y
=
)
2d Va
Finally this gives our equation for the total deflection on the oscilloscope screen Dy:
# w 2 w " L & Vd ,y
. However, we cannot open up the CRT to measure d, w or L so we might as
Dy = %
+
("
2d ' Va
$ 4d
!
V
well replace all these geometric factors with a single unknown geometric constant kg,y: Dy = kg,y d ,y .
Va
THIS IS OUR FINAL CRT DEFLECTION EQUATION. Note that by symmetry we get the same
V
derivation for the total deflection in the horizontal z-direction: Dz = kg,z d ,z . THEREFORE, THERE
Va
!
IS A CRT DEFLECTION EQUATION FOR EACH DEFLECTION DIRECTION EACH WITH ITS
OWN GEOMETRIC CONSTANT.
=
!
!
Section 4: Now you need to answer some questions about the CRT deflection equations.
V
4.1. Given the CRT deflection equation in the vertical direction Dy = kg,y d ,y , what you would see
Va
on the CRT screen if the deflection voltage was increased. Explain why this would happen using a
physical argument (i.e. not using math). Your answer and explanation:
!
Vd ,y
, what you would see
Va
on the CRT screen if the accelerating voltage was increased. Explain why this would happen using a
physical argument (i.e. not using math). Your answer and explanation:
4.2.
Given the CRT deflection equation in the vertical direction Dy = kg,y
!
4.3.
You will now experimentally test the horizontal CRT deflection equation Dz = kg,z
Vd ,z
by
Va
adjusting Vd,z and observing Dz.
Use tape on screen to mark position of electron beam when there is NO DEFLECTION (Vd,z set to
! constant for the rest of
zero to find the ‘origin’ of the CRT). Be sure to record Va and keep this value
this section. (Va is the sum of VB and VC on the CRT power module and should be set as high as
possible while the scintillation dot is still in focus). Record your constant accelerating voltage Va:
Adjust Vd,z on the horizontal plates and mark Dz on the tape for several values of Vd,z (make a data
table with at least 5 data points). Record your data table of Vd,z and Dz:
Create graph of Dz vs Vd,z by hand. Graph Dz vs Vd,z on graph paper. Your data should give you a
straight line.
k
Vd ,z
, the slope will equal g,z so multiply by
Va
Va
Va to obtain kg,z. Record your result for kg,z here in SI units:
Measure the slope of the line of best fit. Since Dz = kg,z
!
!
Vd ,y
that you
Va
have derived by adjusting Vd,y and observing Dy. This is because the geometry of the deflecting plates
is different in the z-direction from the y-direction.
4.4.
You will now experimentally test the vertical CRT deflection equation Dy = kg,y
Use tape on screen to mark position of electron beam when there is !
NO DEFLECTION (Vd,y set to
zero to find the ‘origin’ of the CRT). Be sure to record Va and keep this value constant for the rest of
this section. (Va is the sum of VB and VC on the CRT power module and should be set as high as
possible while the scintillation dot is still in focus). Record your constant accelerating voltage:
Adjust Vd,y on the horizontal plates and mark Dy on the tape for several values of Vd,y (make a data
table with at least 5 data points). Record your data table of Vd,y and Dy:
Create graph of Dy vs Vd,y by hand. Graph Dy vs Vd,y on graph paper. Your data should give you a
straight line.
Vd ,y
k
, the slope will equal g,y so multiply by
Va
Va
Va to obtain kg,y. Record your result for kg,y here in SI units:
Measure the slope of the line of best fit. Since Dy = kg,y
! CRT deflection equation
You will now experimentally!test in another way the horizontal
V
Dz = kg,z d ,z by adjusting Va and observing Dz.
Va
4.5.
!
Set Va to about ½ to ¾ its maximum value and adjust Vd,z to the largest value possible that still enables
you to see the scintillation dot (it may be fuzzy, but you should measure deflections using the center of
the dot). Be sure to record Vd,z and to keep this value constant for the remainder of this section.
Record your constant deflecting voltage Vd,z:
Adjust Va to larger and larger values and record the corresponding horizontal screen displacement Dz
for several values of Va (make a data table with at least 5 data points). Record your data table of Va
and Dz:
Linearize your data by making a graph of Dz vs 1/Va by hand. Graph Dz vs 1/Va on graph paper.
Your data should give you a straight line.
Vd ,z
, the slope will equal kg,zVd ,z so divide by
Va
Vd,z to obtain kg,z. Record your result for kg,z here in SI units.
Measure the slope of the line of best fit. Since Dz = kg,z
!
!
r
r r
Section 5: The magnetic force is given by FM = qv " B , but usually the speed of the charged particle
is too slow to be able to visually see the effects of the magnetic force. However, electrons in CRTs
move so fast, you can actually see them being deflected by a magnetic field. In fact, this is how oldfashioned “television” first worked. You must correctly predict whether the scintillation dot will be
deflected horizontally or vertically!when a magnetic field is created nearby the CRT. Then check your
prediction. For this you will need to remember
whatr the cross product means in the Lorenz force
r
r
equation (better ask around if you don’t ), FM = qv " B and how to use the right-hand rule.
Circle your predictions then check them experimentally:
!
Report Guidelines:
• Title – A catchy title worth zero points so make it fun.
• Goals – Write a 3-4 sentence paragraph stating the experimental goals of the lab. [~1-point]
• Concepts & Equations – [~6-points] Be sure to write a separate paragraph to explain each of
the following concepts.
• Describe (without math) using text and diagrams how a cathode ray tube works.
• Examine the vertical CRT deflection equation. Explain how the deflection equation
works (how to think about this equation). What happens to the deflection distance
when Vd,y is increased and WHY? What happens to the deflection distance when Va is
increased and WHY?
• Derive the deflection equation. Explain every step of the derivation from section 3.
This is the largest part of this weeks report and will be worth a large percentage of
the report grade. It should take at least a full page. You may leave spaces and
write equations by hand, use equation editor or any other tool, but all the
equations must be embedded into your report. Making notes of where to leave
spaces in your report and keeping track of the equations that go into those spaces
and later adding them by hand is probably easiest.
• Procedure & Results – Write a 2-4 sentence paragraph for each section of the lab describing
what you did and what you found. Save any interpretation of your results for the conclusion.
[~4-points]
• Conclusion – Write at least three paragraphs where you analyze and interpret the results you
observed or measured based upon your previous discussion of concepts and equations. It is all
right to sound repetitive since it is important to get your scientific points across to your reader.
Do NOT write personal statements or feelings about the learning process (keep it scientific).
[~4-points]
• Graphs – All graphs must be neatly hand-drawn during class, fill an entire sheet of graph
paper, include a title, labeled axes, units on the axes, and the calculated line of best fit if
applicable. [~5-points]
o The three graphs from section 4.
• Worksheet – thoroughly completed in class and signed by your TA. [~5-points.]