Experiment 8: Determination of the charge to mass ratio of an electron
Since a moving charged particle will follow a curved path in a magnetic field, it is possible
to determine some physical properties of those particles. In particular, with the appropriate
interaction of electric and magnetic fields, the ratio of charge to mass can be determined (See
text for a description of a velocity selector, and a mass spectrometer for the description of these
interactions). A description of the Pasco apparatus follows:
The beam of electrons in the tube is produced by an electron gun composed of a filament
surrounded by an anode containing a single slit. See Fig. 1 for a picture of the apparatus.
Electrons emitted from the heated filament by a potential difference. When electrons of
sufficiently high kinetic energy they collide with helium atoms, a low pressure helium gas being
present in the tube, a fraction of the atoms will be ionized. On recombination of these ions
with stray electrons the helium spectrum is emitted with its characteristic color. Since
recombination with emission of light occurs very near the point where ionization took place, the
path of the beam of electrons is visible as the electrons travel through the helium gas.
Figure 1. A picture of the e/m apparatus with the
various power supplies, meters wired so the
apparatus is ready to take data. The hood that covers
the apparatus is removed.
Figures 2. Block wiring diagram provided by the
manufacturer for the apparatus pictured in Figure 1
Figure 3. A picture of the tube with hood so the beam is visible.
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The magnetic field of the Helmholtz Coils causes the stream of electrons to move in a circular path the radius of which decreases as the magnetic field increases.
Each coil of the pair of Helmholtz Coils has 130 turns of copper wire and a separation and
a mean radius of 15 cm. A lighted mirrored scale behind the tube allows measurement of the
radius of the beam.
Theory: A charged particle moving in a uniform magnetic field experiences a radial force
which has a magnitude of
F = ev B =
m
v2
r
1
where e and m are the charge and mass of the electron, v is the velocity of the particle, and r is
the radius of the beam.
The electron is originally accelerated in the electron gun by the potential difference V between the cathode (filament) and anode. Thus the electron has a kinetic energy
1
2
mv2 =eV
2
Combining the two equations, and solving for e/m yields
2V
e
m = B2 r 2
3
The magnetic field generated by the Helmholtz Coils is given by
B =
8μ o NI
4
5 5a
where o is the magnetic permeability of free space, N is the number of turns of one coil, I is
the current through the coils, and a is the mean radius of the coil. (PLEASE NOTE: All units
in the above equations are SI units.)
Combining equations (3) and (4) yields
e
m =
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 125a2  V

2
2 2 2
 32μ o N  I r
5
2
PROCEDURE:
1. Be sure the switch on the e/m apparatus is switched to e/m MEASURE.
2. Turn the current know for the Helmholtz coils to the OFF position.
3. Connect your power supplies and meters to the front panel of the e/m apparatus as shown
in Figures 1 and 2.
4. Adjust the power supplies to the following values:
CAUTION: The voltage to the heater of the electron gun should NEVER exceed 6.3 volts.
High voltages will burn out the filament and destroy the e/m tube.
ELECTRON GUN HEATER:
6.3 VAC
ACCELERATING ELECTRODES
175 to 275 VDC (see below)
HELMHOLTZ COILS
8.5 VDC
5. Choose a voltage for the accelerating electrode (you will eventually choose a second value).
6. Slowly turn the current adjust knob for the Helmholtz coils clockwise. Watch the ammeter
and take care that the current does not exceed 2 A.
7. Wait several minutes for the cathode to heat up. When it does, you will see the electron
beam emerge from the electron gun and it will be curved by the field from the Helmholtz
coils. Check that the electron beam is parallel to the Helmholtz coils. If it is not, turn the
tube until it is. Don’t take the tube out of its socket. As you rotate the tube, the socket will
turn.
8. Record the current through the Helmholtz coils and the accelerating voltage.
9. Carefully measure the radius of the electron beam. Look through the tube at the electron
beam. To avoid parallax errors, move your head until you align the beam with its reflection
that you see in the mirrored scale. Read the scale on both the left and right side and then
average your results to get the best value for the radius. Have your partner do the same
thing and average the two results.
10. Change the radius of the beam by adjusting the current in the Helmholtz coils so the radius
changes by about 0.2 cm. Repeat steps 9 and 10.
11. Continue as in step 10 for a total of 5 different radii for one accelerating voltage.
12. Change the accelerating voltage, and repeat the above procedure for another 5 radii.
13. When finished shut off the power supplies.
ANALYSIS:
Solve equation 5 for
1
.
I2
Using a spread sheet program, and using r2 as the independent variable (x-axis
variables) and
1
as the dependent variable (y-axis variables), plot the data and determine the
I2
best straight line fit for one of the accelerating voltage. For this analysis set the y-intercept
to zero. Show the linear fit on the graph. The slope is the coefficient of r2, and is proportional
to e/m and inversely proportional to V. Solve for e/m. Repeat the analysis for the second
value of V. Discuss your results. Your report should include appropriate error analysis.
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