Electric Deflection of Electrons - Arts & Sciences

Electric Deflection of Electrons

3. Electric Deflection of Electrons

Objective: In this unit you will work with a cathode ray tube or CRT. The point of the lab activity
is to study the way electrons respond to electric forces. The measurement objective is to find the
charge to mass ratio e/m for an electron.

The learning objectives are the following:

1. To know how to apply Newton’s to moving charges, for which the force and
potential energy are electrical in nature.

2. To know how electric force relates to charge and electric field, and how potential
energy relates to charge and electric potential (or voltage).

3. To be able to use energy conservation to explain the operation of an electron gun.
4. To know how to relate electric field between parallel plates to the voltage

difference between the plates and the spacing between them.
5. Finally, to be able to calculate and also to measure the electric deflection of

electrons in a CRT as a function of acceleration voltage, deflection voltage, and
geometry of the tube.

(All these concepts are described in your textbook .)

Reading assignment:
Before you come to the lab study the sections on motion of charged particles in uniform electric
field and review projectile motion, conservation of mechanical energy. Read the following
sections. (Section numbers may be slightly different depending on the edition of your textbook:
Check the section titles.)

Knight, Jones and Field (162): 20.5 Applications of Electric Field, 21.1 Electric Potential Energy
and Electric Potential

Serway and Vuille (212): 3.4 Projectile motion, 15.4 The Electric Field, 15.5 Electric Field Lines,
15.6 Conductors in Electrostatic Equilibrium , 16.1 Potential difference

Serway and Jewett (252): 23.7 Motion of Charged Particles in a Uniform Electric Field

Pre-Lab Exercises: Do the following exercises before you come to lab. Bring them with you so
your TA can check them off when you enter the lab. Later, you will hand them in with your report.

1. Let’s suppose for simplicity that the gravitational field strength is g = 10 30m
m/s2. A projectile is shot horizontally from a height of 30 meters, quite a
ways up, with initial speed vo = 10 m/s. It strikes the side of a tower after
traveling a horizontal distance of 20 meters. Show your work.

(a) at what height y above the ground does the projectile strike the tower? 20m

(b) what are the vertical and horizontal components vx, vy of its velocity when it hits the tower?
(Hint: time of flight)

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*© William A Schwalm 2012 3-1

Electric Deflection of Electrons
2. Suppose that in an electron gun, electrons are emitted from a hot filament at point f and are
accelerated by an electric field to an opening at o, as shown. The charge on an electron is (– e)
where e = 1.6 x 10-19 C.
(a) If the voltage (same as electric potential) at point f is – 280 Volts, what is the potential energy

of an electron at f ?

fo

(b) The electrons come off the filament with very low velocity, hence with very little kinetic energy.
So what is the total energy of an electron at f ?

(c) After the electrons exit the gun at o the voltage is zero. Thus, what is the potential energy of
an electron at o?

(d) Given that the mass of an electron is m = 9.11x 10-31 kg, how fast must an electron be going
when it exits the gun?

3. Consider two parallel, horizontal metal plates a distance d = 2.0 cm apart. The upper plate is
at +25 volts and the lower one is at 0 Volts. Let’s assume that except near the edges, the electric
field between the plates is constant in both magnitude and direction. From your reading,
(a) What is the direction of the electric field between the plates?

(b) What is the magnitude of the electric field?

(c) What would be the magnitude and the direction the electric force acting on an electron
moving in between the plates?

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Electric Deflection of Electrons

4. (Theory of electric deflection) A schematic representation of a CRT is as follows. (In the
special case show, there is no deflection voltage so the beam is straight.)

Electron gun Deflection plates Screen
V=0

C – B+ Electron beam
C+= B –

The figure above shows a beam of electrons leaving the electron gun and traveling straight
through the deflection plates, because both plates are grounded, hence there is no electric field
between them. Let d be the vertical distance between the plates, and let the horizontal length of

the deflection plates be  . Then let L be the distance from the center of the deflection plates to

the screen, and D the deflection, or distance on the screen from central line up to the spot where
the beam strikes. (See the figure on page 4.) The next objective is to express D in terms of the

accelerating voltage Vo (which is VB+VC of the electron gun) the voltage V applied to the
deflection plates, the distance L to the screen and the distance d between plates. From
conservation of energy, an electron at rest at the filament has only potential energy (- e)(-VB)
= e VB.

Use conservation of energy to find the speed at which the electrons exit the gun at point o. You
should find

v  2eVo ,
m

where Vo=VB+VC is the total voltage drop across the electron gun. But show the details of your
calculation.

Now you can proceed just as you would to solve a projectile motion problem, using the
kinematics of constant acceleration. Assuming the velocity in the x direction remains constant, it
is easy to see how long it takes for electrons to pass through the space between the two vertical
deflection plates. Thus you can find two things (a) the vertical distance away from the axis and
also (b) the x and y components of the velocity at the point where the electrons exit the region
between the plates. You should find that at the point where the electrons leave that region,

y1  eV t12 , and vy  e V t1
2md m d

respectively, where of course t1 is how long it takes to traverse the plates. However, once again
you need to show the details of your calculation.

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Electric Deflection of Electrons

Continuing on, show that the deflection of the spot on the screen  LV
measured from the central axis would be D where D

2 d Vo
.

It is important to notice that when the smoke has cleared the net distance D on the screen is
proportional to the voltage V applied to the deflection plates.

Vo  VB  VC V (positive)

D



C – B+ L
C+= B –

Exploring the equipment: The figure above shows measurements and the deflection process.
Because of the high voltage, your laboratory instructor or TA will help you wire up the CRT. You
ought to check the wiring of your apparatus with the diagram provided below to see that it agrees.
If anything in the apparatus wiring appears to differ from the diagram, let your TA know
immediately. Also, while performing the experiment, keep your hands away from the wires and

connections. The voltages at C, C  B and H are higher than you usually encounter in the

laboratory and can give uncomfortable shocks, if you get too close to an exposed (that is, un-
insulated) connection. This is not very dangerous, just uncomfortable.

The following is a wiring diagram for the power supply.

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Electric Deflection of Electrons

This switch toggles both meters
between the two different voltage
sources. Each time you press it
switches.

Voltage Current (mA) 6.V On
Off
50 volts adjust 500 volts adjust This dial
must stay at
DC 6 volts (heater

filament)

AC

-50 V +500 V

C– C+ 0 = B– B+ HH

Green
Blue
Red
Brown
Yellow
Yellow

Pigtail to CRT

Follow the description of how the tube is wired and check the diagram against your apparatus as
you go along.

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Electric Deflection of Electrons

20 Volts DC

+ from wall
receptacle

Wires from back of CRT
enter the pigtail and go to
the HV power supply.

red Vertical
blue deflection
yellow
yellow TV lead wires

brown CRT

green Horizontal
deflection
both grounded

TV lead wires

Pigtail to power supply

All ground connections are made to the same point, which is connected to the ground prong on
the plug of the low voltage power supply. (See below.) Notice that the CRT you are using
actually has two sets of deflection plates, one each for horizontal vertical deflection. It is
important that both the unused horizontal deflection plates and one of the vertical deflection
plates are grounded. Otherwise they develop a charge and electrons never get to the screen. In
a later experiment, a low-voltage supply lets you apply a voltage across the vertical deflection
plates. (Notice: Rather than an independent low-voltage DC power supply you may need to use
external voltage source via a wall receptacle and adjustable resistor. If so, your TA will explain.)

Problem

Your team is assigned to study the effect of having deflection plates that are not parallel on the
electron deflection formula derived above. One problem you see in the actual device is that, for
practical reasons, the plates are bent off at an angle so the electrons don’t strike them. (This also
compensates for the fringe field.) So, (a) there is no well defined length , (b) thus there is also
no definite L, and finally (c) there is no well defined separation d between the plates. Your team
is assigned to find out if you can replace the quantity L / d in the formula derived above for D by

some effective length a and thereby apply more or less the same formula to the modified device.

Perhaps:

D  aV .
2Vo

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Electric Deflection of Electrons

Exploration: As you explore the equipment, there are several tricky points, so you will need to
study the manual (provided in the room). We replace parts of the manual here for your
convenience.

Power to the experiment should be turned on in the following way. All of steps 1 through 5 refer
to the high-voltage power supply. There is also a low-voltage supply referred to in step 6 below.

1. First be sure that the CRT power from the power supply is off and disconnected and that the
deflection plate power from the wall receptacle is disconnected. Be absolutely sure the selector
dial on the AC panel is set at 6. Volts. (It should be taped.)

2. Examine the TV lead wires coming from the CRT assembly. These connect to the deflection
plates. The pair for causing horizontal deflection of the beam is unused and both sides will
remain grounded for this experiment. However, note that the TV lead wires coming from each
pair of deflection plates terminates in a double banana plug which has a resistor across it. This is
so that, as soon as the power is disconnected, the plates can discharge through the resistor,
eliminating a stray voltage build up.

3. Next be sure both the dials, the “500-volt” one for the B and the “50-volt” one for the C voltage,
are turned down—full counter clockwise. Flip the main power on-off switch at the right of the
high-voltage power supply panel to on. Wait a minute or so as the filament in the CRT warms up.
You will see it glowing.

4. Remember not to get your hands close to any bare wires or connections, or you may get a
shock. (Not dangerous, just unpleasant.) Here is how to measure the VB and VC voltages. It’s a
little tricky. There are two voltages and two meters. However, one meter measures voltage and
the other measures current. The meter toggle switch (see the figure) toggles back and forth
between the B (high voltage) and C (low voltage). These are both provided by the high-voltage
power supply. In each case you have a voltage and a current reading. Be sure to be looking at
the B position when you’re turning the “500-volt” dial and the C position when you’re turning the
“50-volt” dial.

5. Turn the B dial up, thus increasing VB until a green lighted area appears on the screen of the
CRT. Then increase to somewhat beyond this point. This may be close to the top of its range, or
near its maximum possible value. (VB should not exceed 425 Volts, however. So if you get no
green area seek help.) Then turn up the voltage VC up until the green region “inverts,” or turns
inside out and focuses down to a broad spot on the screen. The voltage VC is used to focus an
electrostatic lens, here. We need not know exactly how this works, only that the net accelerating
voltage for the electron gun winds up as Vo = VB+VC . Now turn the voltage VB back down
somewhat until the spot is focused to as small a diameter as possible. The focused spot will
usually not be in the middle of the screen. This is due to the original intended use of the tube and
a number of effects, such as the earth’s magnetic field. The spot’s not being centered will not
cause any trouble, just so long as the CRT is not moved in the course of making measurements.

Now the power is on and the spot is focused. (Some CRTs focus better than others.)

6. The deflection plates are the plates that can provide a transverse electric field to deflect or turn
the electrons. Applying a voltage difference between them will cause a deflection. This voltage
difference is gotten from the separate, low-voltage power supply. Connect the negative output to
ground.

The TV plug from the deflection plates should then be connected one side to the  and the other
to the  of the power supply. When operating, be sure to turn the current adjust up a little bit first

to permit some current to flow, then turn up the voltage adjust a little bit at a time as needed.

Now it is important to fiddle around. You have to try making adjustments and taking some
measurements until you have a fair idea of how the meters and the toggle switch work.

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Electric Deflection of Electrons

Measurement Plan: Your group needs work out a measurement plan. The idea will be to study
the deflection D as a function of acceleration voltage Vo and deflection voltage V and to see if the
formula can be made to work with the suggested modification. Take a few minutes with your
group to develop a plan. You will be reporting this plan to the class and then turning it in with
your report. The plan needs to include what data you will have to take, why you need it,
considering the theory, how you will take the data, and finally how you will analyze the data to
solve the problem assigned. For instance, you probably want to make some graphs (of what
versus what?) Be prepared to discuss this with your instructor if called upon to do so.

The following are some remaining technical points:

7. If you want to collect data to graph D versus V at fixed Vo for instance, you will have to know
how to measure D on the screen. You should make sure you find out what the units are before
proceeding. How would you determine this?

8. The specifications for the CRT say that L should be about 14.3 cm. However a complication
arises as noted above in that the deflection plates are not flat. (This becomes obvious if you
study the tube itself or look at the apparatus data or at the technical drawings provided in the lab.)

They have a flared shape convenient for picture tube applications. That makes both d and 

rather hard to define. What you are trying to do, by using your data is to replace the undefined
lengths by a single adjustable constant (as noted above). And then the practical question your
employer has is this: Will this type of simple approach work? Do we need a more complicated
formula?

9. Your plan might include constructing graphs of D versus V, for two or more different values of
the accelerating voltage Vo. For each of these, you should choose first a value VB sufficient to
make a spot on the screen, and then adjust VC and VB so as to focus properly. Then record the
sum of these two as Vo.

Do the results give straight lines in each case? Are the slopes different when the
accelerating voltages differ? Are these results consistent with what you would predict from the
kinematical analysis?

Before leaving the lab, take time to go over with your team mates the learning objectives listed at
the start and figure out how the work you did relates to these objectives. Your notes on this
discussion should be included in the report you hand in.

Plan: Record your measurement plan here, including all the usual things, such as what you need
to measure, what data to take, what the team members do, how you will analyze the data, and so
on. If you plan to graph something you need to explain what to graph and how the graph will be
analyzed to get what you need. Keep in mind that you need to keep track of the expected sizes
of the errors.

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Electric Deflection of Electrons
Implementation: Carry out your plan, making changes as necessary. Record the data here as
well as any relevant notes and observations you might need to have later.

Analysis: Analyze your data as described in the plan. Explain clearly where appropriate so that
your supervisor can follow what you have done. The graphs you construct can be shared by your
group members, but each lab report needs a copy of each graph.

Conclusion: Write a brief paragraph four your employer summarizing the problem, what you have
done to solve it, what the results were, what the error estimate is and how you estimated the
error. Then give a solution for the original problem. It has to be clear to your supervisor what
your team has done.

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Post discussion: Write a brief summary of comments made by your group members (see above)
and also during the post lab classroom discussion on the objectives.

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