LPC Physics
Determination of the Electron Charge-to-Mass Ratio, “e/m”
Determination of the Electron Charge-to-Mass Ratio,
"e/m"
Figure 1. the apparatus used in the e/m experiment
Purpose:
To study the behavior of electrons in electromagnetic fields, and to determine the ratio
e/m (the "specific electronic charge").
Equipment:
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Teltron 525 Deflection e/m Tube
Teltron 502 Helmholtz Coils
Teltron 501 Universal Stand
Pasco 8000 Low Voltage DC Power Source ( 12.0 VDC )
Teltron 813 High Voltage Power Source (0 - 5000 Vdc & 6.3 Vac)
Digital Multimeter (DMM)
Decade Resistance Box
Electrical Patch Cords (w/ Banana Plugs)
Insulating Corks
Theory:
In this experiment we will use a cathode ray gun as a source of electrons. The electrons
are accelerated to a velocity, v, by the potential difference (anode voltage), Va. The
speeding electrons then enter the bulb of the Teltron tube where electric and magnetic
fields can be applied to the electron beam. If Va is fixed, the electron velocity is also
fixed.
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LPC Physics
Determination of the Electron Charge-to-Mass Ratio, “e/m”
When a current I, passes through the Helmholtz coils, a fairly uniform magnetic field is
generated in the bulb:
B = αI
(I in amperes, B in Tesla)
where
α = 4.23 × 10 −3
The coils are arranged so that B is perpendicular to v and so the path of the electrons is
circular, with radius of curvature r:
mv 2
FB = qv × B = ma =
r
Eq. 1
and hence
e
v
=
m rB
Eq. 2
Therefore, if we know I and r we can determine e/m if we know the velocity v.
There are two methods to determine the velocity. One method is to consider the
relationship between the accelerating voltage, V, and the kinetic energy: K = 12 mv 2
qV = 12 mv 2
Eq. 3
Setting q = e and substituting into Eq. 2, gives:
e
2V
= 2 2 2
m Rα I
Eq. 4
Thus by experimental measurement of V, R, and I the charge to mass ratio can be
determined.
To determine v in Eq. 2 another way, we will apply an electric field, E, and a magnetic
field B ′ such that FE = − FB ' . Thus a = 0 and v = constant. Note that we want the
same Va as before in order to measure the same velocity, v. This method can be thought
of as the "crossed electric and magnetic fields method."
To understand this method, consider the that the electrons will move in a straight line if
FE = FB '
eE = evB ′
and hence
v=
E
B′
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Eq. 5
LPC Physics
Determination of the Electron Charge-to-Mass Ratio, “e/m”
By combining Equations 2 and 5, and measuring r, B, E and B' , the ratio e/m can be
determined.
E '
V
e
v
E
d
B
= =
=
='
m rB RB RBB R (α I )(α I ' )
e
V
eq 6.
=
m R (α 2 II ' )d
Where d is the distance between the two plates inside the Teltron tube.
Experiment:
CAUTIONS & WARNINGS before you begin:
It is VERY IMPORTANT that you read the following:
The potential difference Va that accelerates the electrons is on the order of 3000 V. This is dangerous
and caution must be observed.
Therefore, in all procedures in this lab, YOU MUST:
A. Keep calm and think before you reach for something.
B. Always dial down the voltage using the lever and turn to OFF the switch on the
back of the kilovolt power supply while making any changes in the circuit or, if
you are not at that moment making an observation!
A
+2500 V
Z
0.303 V
6.3VAC
Pasco
-2500 V
100K Ω
10K Ω
1K Ω
Decade Resistance Box
100 Ω
10 Ω
1Ω
+5V
-5V +12V -12V
Figure 2. Teltron e/m Tube, Teltron Coils, Teltron Power Supplies .
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LPC Physics
Determination of the Electron Charge-to-Mass Ratio, “e/m”
Part A: Measuring the Electron Beam Radius
In this section of the laboratory, you will accelerate the electrons using an AC source to
“boil” electrons off the Teletron tube cathode. Then a high voltage power supply will be
applied to accelerate the electrons past a pair of horizontal deflecting plates. An Electric
field will be applied across these plates (also controlled with the high voltage power
supply). A Magnetic field will be established in the Helmoltz coils (using an entirely
different circuit and low voltage power supply). Finally, the Electric and magnetic fields
will be varied and measured, along with the resulting deflection and radius of the electron
beam.
Figure 3. Basic Circuit Diagram for Experimental Apparatus
1. Assemble the Deflection e/m Tube, Helmholtz Coils, Universal Stand, Power
Supplies, DMM, and Decade Box as shown in Figure 2 and Figure 3. It is important
to line up the Helmholtz magnetic coils perpendicular to the Earth’s magnetic field in
order to reinforce the magnetism’s effort to straighten out the electron beam.
2. Figure 3 is a schematic diagram of this set-up. Connect the Low Voltage Power
Supply, the Decade Resistance Box and the DMM to the Helmholtz Coils. This set
up provides DC current through the Helmholtz Coils to establish the magnetic field.
3. The electrical lead from the Decade Box should connect to the DMM’s “Amps” jack,
and the DMM’s “Common/Ground” jack should connect to the “A” terminal of the
first coil. Set the DMM function to Amps on the 10 A range.
4. Connect the 6.3 VAC terminals on the High Voltage Power Supply to the 4 mm
sockets in the plastics cap at the end of the tube’s gun. This connection provides
power to the anode filament. The filament current “boils” off electrons providing a
source of electrons for the gun.
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LPC Physics
Determination of the Electron Charge-to-Mass Ratio, “e/m”
5. Connect the positive “+” terminal of the High Voltage Power Supply to the 4 mm
plugs mounted on the side of the gun’s neck. This connection to the anode of the gun
provides the accelerating potential Va.
6. Also connect the positive “+” terminal of the High Voltage Power Supply to the 4
mm plugs connected to the deflection plates. Note that the plates are at the same
potential and hence there is no E-field.
7. Connect the Power Supply’s negative “-” terminal to the gun socket marked “-” to
provide a common return path
8. Place insulating corks on all exposed plugs and check the circuit.
9. Turn on the Low Voltage Power Supply and adjust the Decade Resistance Box for a
DMM reading of about 300 mA. Record the coil current, I.
10. Turn on the High Voltage Power Supply and slowly increase Va to 2500 V by reading
the top scale of the supply’s meter.
11. Note the deflection of the electron on the luminescent screen. In order to determine r,
the radius of curvature of the electron path, record X and Y for three points fairly far
out on the curve.
12. Decrease the voltage to zero and turn off the High Voltage Power Supply.
Procedure: Crossed Electric and Magnetic Fields
In this section of the lab you will first determine the electron velocity by providing
“crossed” electric and magnetic fields of the proper magnitude to allow the electron to
move through without deflection. In this case, the electric field is provided across the
horizontal deflection plates within the Teletron tube. The Magnetic field is provided by
the Helmoltz coils. Finally, the high voltage power supply applies the accelerating
voltage, which in turn determines the electron velocity. A schematic diagram of the
connections for both the Helmholtz coils and the Teletron tube is shown in figure 4
below:
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LPC Physics
Determination of the Electron Charge-to-Mass Ratio, “e/m”
Figure 4: Crossed Electric and Magnetic Fields (FB = FE Configuration)
1. To measure the velocity v of the electron, set up the circuit as shown in Figure 4.
This circuit differs from the previous set up in that the bottom deflection plate in
connected to the positive “+” terminal of the High Voltage Power supply and the top
deflection plate is connected to the negative “-” terminal of the HV Power Supply.
Note that an electrostatic field is set up across the deflection plates.
2. Turn on the High Voltage Power Supply and gradually increase Va to 2500. (Hence,
the velocity, v, is the same as before.)
3. Change the coil current, I, (and hence B) by changing the decade resistance until the
path of the electrons is as straight as possible. Record the new current, I.
4. Decrease Va to zero and turn off the High Voltage power supply and the Low Voltage
Power Supply.
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LPC Physics
Determination of the Electron Charge-to-Mass Ratio, “e/m”
Analysis:
1. To determine the radius of curvature, r, consider the equation of a circle located as
shown:
r
y
x
0,0
The equation of such a circle is
x2 + y2
x + (y − r) = r ⇔ r =
2y
However, this assumes that the x-coordinates are measured from the origin.
Before substituting your x- and y- values into this equation, add +0.5 cm to the x-values.
Calculate r for each pair. Calculate r average.
2
2
2
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LPC Physics
Determination of the Electron Charge-to-Mass Ratio, “e/m”
2. Use the results of Part A, and Eq. 4 to determine e/m .
3. Now you will make use of the "crossed electric and magnetic fields" method. First,
substitute Eq. 5 into Eq. 2 to derive an expression for e/m in terms of the values from
Part B. Substitute for B, B ′ , and E in terms of I, I' , Va and d using
B = αI and
Va
where d is the separation of the plates.
d
4. Calculate e/m using the observed values I, I' , Va , d, and r and equation 6, and
compare to the accepted value.
E=
5. The main goal in this experiment is to measure a well-known physical quantity and
compare your results with those of previous experiments (resulting in the values
posted in physics texts).
Results:
Write at least one paragraph describing the following:
• what you expected to learn about the lab (i.e. what was the reason for conducting the
experiment?)
• your results, and what you learned from them
• How did your results compare to the accepted value?
• Is the accepted value within your uncertainty range for both methods? If not,
which method worked better? Why?
• What errors and problems, both systematic and random prevented a better value?
• If you could improve the design and equipment to improve the accuracy and precision
for this measurement, how would you do so?
• Think of at least one other experiment might you perform to verify these results
• Think of at least one new question or problem that could be answered with the
physics you have learned in this laboratory, or be extrapolated from the ideas in this
laboratory.
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