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Illinois State University
Department of Physics
Physics 112
Physics for Scientists and Engineers III
Experimental Physics Laboratory 3
The charge to mass ratio of the electron
Introduction
At the end of the 19th century, a number of observations, including the ultra-violet
catastrophe, photoelectric effect, and existence of atomic spectra, suggested that the
classical theories of the day were incomplete or deficient. In 1897 J. J. Thompson showed
that the charge to mass ratio of an electron was a constant, establishing the electron as a
fundamental particle. More details can be found in Chapter 29 of Serway and Jewitt (6 th ed.)
[1] or almost any modern physics textbook. Schuster's method is used in this experiment
and more information can be found in the Taylor manual [2]. The basic idea is to take
electrons of known kinetic energy and determine the required B field to force them into a
circular trajectory of a specified radius. The charge to mass ratio can be calculated from the
results.
Helmholtz coil looking down
the axis
5 pins
Filament
accelerating grid
Electron tube
Figure 1.
A schematic of the set-up is shown in Fig. 1. It consists of an electron tube containing
a filament to emit electrons, an accelerating grid used to control the kinetic energy of the
electron beam, and a set of 5 pins used to determine the radius of the electron beam
trajectory. The outer circle represents the Helmholtz coil that is used to generate a
magnetic field pointing out of the page in the diagram.
Electrons with mass m emitted by the filament are accelerated through a potential
difference V maintained between the filament and accelerating grid, yielding a kinetic
energy,
1
2
KE=eV = m v ,
2
(1)
where v is the velocity of the electron. The electrons are then acted upon by a magnetic
field produced by a Helmholtz coil, which is actually two coils. The magnetic field B exerts a
force of magnitude
F B =−e v B ,
where the velocity and B field vectors are perpendicular to each other. This force causes the
electrons to travel in a circular trajectory of radius r, so the force is centripetal,
evB=
mv 2
.
r
Combining these results, the charge to mass ratio is
e 2V
=
.
m r 2 B2
Of course this requires calculating the value of the B field component directed along the axis
of the Helmholtz coil. We can consider the Helmholtz coil to consist of two rings of current
with radius R =147.5 mm and separated by a distance R, each with a current that is N =124
times the current in the wire since there are 124 loops in each half of the coil.
Consequently, the electrons are R/2 from each loop of the Helmholtz coil. The resulting B
field along the axis is
3
4 ( 2 ) μ0 N I .
B=( ) (
)
5
R
Adjustment of the accelerating voltage and coil current allows the trajectory of the
electron beam to be varied. The radii of the trajectories are 10, 20, 30, 40, and 50 mm when
the electron beam intersects the planes of the pins.
A wiring diagram of the experimental set-up is shown in Fig. 2. Be careful if you have
to wire up your own circuit and ask the instructor to check your wiring before plugging in
the power supply. Also confirm that all knobs on the power supply are turned all of the way
in the counter-clockwise direction. The filament voltage should be set to 9 V. The coil
voltage will be adjusted throughout the experiment as needed to make the electron beam
follow a circular path. The kinetic energy of the electrons is determined by the KE voltage
and should be set to 100 volts at the beginning of the experiment. Finally, the focus voltage
is adjusted as needed to create the best defined electron beam. The electron beam appears
orange because electrons transfer energy to neon gas in the electron tube and the excited
neon atoms emit the orange light.
ammeter
Electron
Tube
Base
Power Supply
A
KE
Focus
Coil
Filament
Figure 2.
Objective
In this exercise, you will determine the charge to mass ratio of the electron and
analyse the various contributions to the uncertainty in your measurements and results.
Procedure
Begin by connecting the circuit as shown in Fig. 2. After your instructor has approved
your circuit wiring, you may begin the experiment. For accelerating voltages of 100 V, 150
V, 200 V, 250 V, and 300 V, determine the coil voltage and current required to make the
electron beam intersect the plane of each set of pins in the electron tube. The coil current
cannot be raised to the level required to force the electrons to reach some of the pins.
Derive an equation that allows you to do a linear fit of accelerating voltage as a function of
the product of pin position and coil current. Fit your data with this equation and determine
the charge to mass ratio. Do not calculate the charge to mass ratio for each individual
measurement. Generally, it is a good idea to record every measurable quantity for each set
of parameters.
There are several ideas that you might want to explore when writing your lab report.
For example, what is the effect of the earth's magnetic field? How does the force that it
exerts on the electron beam compare to the coil generated field? What sort of error is
present when determining the uncertainty of the beam position? Is the error caused by the
resolution of a meter display or by the sighting mechanism in the electron tube? Perhaps it
is caused by some other factor. Is there a systematic error? Remember, just stating a cause
of uncertainty is of little value. You must show my numerical analysis its magnitude and
what it means for your data and results.
References
[1] Serway, R. A., and Jewett, J. A. Jr. Physics for Scientists and Engineers with Modern
Physics, Thomson, 6th ed. (2004).
[2] Brown, T. B. ed. The Lloyd William Taylor Manual, Addison-Wesley, 1959.