Laboratory Manual
Physics 2DL
Modern Physics
Department of Physics
University of California, San Diego
Professor Brian Keating
Spring 2010
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EXPERIMENT #4
Charge to Mass ratio of the Electron
GOALS
Physics
• Measure the charge-to-mass ratio e/m for electrons.
Technique
• A low pressure He-gas-filled tube allows the electron trajectories to be seen by eye.
• Helmholtz coils produce a uniform magnetic field.
Errors
• You should calculate your best estimate for e/m = and your “standard error”
as
from your N measurements xi of e/m.
Question: Which causes a larger systematic error in your e/m measurement:
(a) a 5% error in V, the acceleration voltage; or
(b) a 2% error in z0, the separation between the coils of the Helmholtz magnet?
References
• Serway, Moses, Moyer §3.2
• Tipler & Llewellyn §3-1
THE EXPERIMENT
The e/m tube to be used in the lab contains an electron gun to produce a beam of electrons, a very low
pressure helium vapor atmosphere to render the beam visible, and a glass scale to permit measurements of
the trajectory of the electrons. The simple electron gun is pictured schematically in Fig. 1. The gun has a
hot filament, which serves as the emitting cathode, along the axis of the cylindrical anode can.
4-1
Figure 0.
Figure 1
The filament is heated white hot (~2000 Kelvin, giving kBT ~ 0.2 eV) by the current flowing through it
from the filament supply. The filament is a tungsten wire with a low “work function” energy: W ~ 2.6 eV.
A small fraction
of the “surface” electrons escape the metal; this is called
“thermionic emission.” These electrons are accelerated toward the cylindrical anode can by the voltage Va
applied between the filament and the anode. Most of these electrons strike the inner surface of the anode
with a kinetic energy eVa, and are absorbed. Some electrons, however, pass out through a narrow slot in
the anode (also with kinetic energy eVa), forming a flat ribbon beam of electrons which we use for the
experiment.
The tube itself has a small amount of helium vapor added to its otherwise good vacuum. A few of the
beam electrons strike helium atoms and excite them (Expt. 5); then the excited helium atoms emit visible
radiation and we can thus, "see" where the electron beam is.
4-2
Figure 2
Another feature of this special e/m tube is that it contains a glass scale to permit measurements of the
trajectory of the electrons.
When a uniform magnetic field is established throughout the tube, the electron beam will be bent into a
circle, as shown by the dotted line in Fig. 2. The radius of the circular electron path is related to the
magnetic field and the electron energy in the following simple way. An electron moving in magnetic field
experiences a force perpendicular to its velocity – the Lorentz force. It results to centripetal acceleration
and curved motion,
,
or
.
(1)
The electron velocity is determined by the cathode-anode voltage Va applied to the gun, as
.
(2)
Thus we obtain
,
and finally,
.
(3)
4-3
In order to perform this experiment we must know r, Va, and B. r is measured using a glass scale and Va is
simply an applied and measured potential from a variable power supply. How do we obtain and measure
B?
We employ a uniquely useful arrangement of conductors called Helmholz coils. They are simple, hooplike coils which are positioned on a common axis and separated by a distance z0 equal to their radius a.
Connected in series with the same polarity, they each have the same current I. In this arrangement, they
give a magnetic field which is homogeneous over a fairly large volume near the center. The field is
,
(4)
where the second form presumes z0 = a.
Here, N=130 is the number of turns per coil, I is the current, a =0.15 m is the coil radius, and = 4! " 10-7
Weber/Ampere-meter. B is in Webers/m2, called Tesla; 1 Tesla = 104 Gauss.
The complete apparatus for this experiment, in addition to the vacuum tube and Helmholtz coils, consists
of a power supply which controls accelerating potential and the coil current.
Basic lab measurements
Set the gun anode power supply to Va = 200 Volts and measure the beam diameter for 8 coil current
settings (a 5-10 minutes warm-up time is recommended before taking careful measurements). The
electron beam has a finite width. There are various energy losses from the beam electrons, including
scattering from helium atoms, and those electrons which have suffered least loss or no loss have the
largest radii of curvature. Therefore, you should measure the outside radius of the electron beam.
Repeat the measurements at Va = 300 Volts and Va = 400 Volts.
Make a separate computation of e/m for each combination of Va and B. Compute the average, and
estimate the statistical error. Estimate your systematic errors from a, Va and any other effects you can
think of.
The accepted value of e/m is 1.76 x 1011 Coulomb/kg.
Optional: Verify if the Earth's magnetic field of 6 x 10-5 T (0.6 Gauss) is negligible in this experiment by
rotating the apparatus.
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