Electron Charge to Mass Ratio
Introduction
J. J. Thomson, in 1897, was the first person to
measure the charge to mass ratio of the electron.
This was the first direct evidence that electrons
existed and had particle-like properties. Thomson’s
experiment involved the effect of a magnetic field
on moving electric charges. This experiment is a
variation from Thomson’s experiment but is also
based on the interaction of a magnetic field with a
moving electric charge.
The apparatus to be used in this experiment is
shown in Figure 1. A beam of electrons is
accelerated through a known electric potential, V, so
that the velocity of the electrons can be determined.
A pair of Helmholtz coils produces a uniform and
measurable magnetic field, B, at right angles to the
electron beam. The magnetic field deflects the
electron beam into a circular path.
field B is Fm = qvB. Since in this setup v  B, the
magnitude of Fm is given by
Fm  evB, where q  e  electron charge  (1)
Since the electrons are moving in a circle, they are
accelerating, with the magnetic force causing the
acceleration
Fm=ma
(2)
Using the centripetal acceleration in equation 2,
show that
e
v

m Br
(3)
It is now necessary to find v and B in terms of
directly measurable quantities.
To determine v, start with the fact that the electrons
are accelerated through potential V. So the kinetic
energy of each electron is eV = 1/2mv2. Combine
this fact with equation 3 to show that
(e/m) B2r2 = 2V
(4)
The magnetic field near the axis of a pair of
Helmholtz coils is given by the equation
B
N 0 I
4 / 53 / 2
a
(5)
Here N is the number of turns in each Helmholtz
coil, I is the current through the coils, a is the radius
of the coils, and o is the magnetic permittivity of
free space (1.26106 Tm/A).
Figure 1
Theory
The magnetic force, Fm, acting on a charged particle
of charge q moving with velocity v in a magnetic
Electron Charge to Mass Ratio
1
Procedure
The connections to the e/m apparatus are shown in
Figure 2. It is not necessary to use the DC ammeter
to measure the current in the coils because the
device providing the current has a meter that
measures the current as accurately as an ammeter.
While doing the experiment, keep within the
following ranges of values.
Heater
Electrode Voltage (V)
Helmholtz Coil Voltage
Helmholtz Coil Current (I)
6.3 V
150-300 VDC
6-9 VDC
0 - 2A
The Helmholtz coils are designed so that the
distance between the coils is equal to the radius of
the coils. So in order to obtain a value for a,
measure the horizontal distance between the centers
of the coils. Record this value which is the radius
of the coils used in Equation 6. The coils in this
apparatus have N = 130 turns.
The procedure for making measurements of e/m is
as follows:
Take several pictures if necessary.
Note: the most accurate value for r is
obtained by measuring between the
outside edges of the beam. This is
because many of the electrons strike
helium atoms which slows their speed
below the value used in the derivation of
Equation 3. These slowed electrons are
the source of the width of the beam.
Repeat for three values of voltage, V, within the
range 175- 300 V, and for three values of radius, r,
between 4.5 and 5.5 cm.
Determine the value of e/m from the slope of an
appropriate graph. Recall from equation 4, that the
voltage, V, is proportional to r2. Since Origin only
takes into account y-error-bars, you should put the
quantity with the larger fractional error on the yaxis. Which has the larger fractional error V or r2?
Determine whether your results are within your
experimental error of the accepted value e/m =
1.761011 C/kg.
1. Flip the toggle switch up to the e/m
MEASURE position.
2. Turn the current adjust knob for the
Helmholtz coils to the OFF position.
3. Set V (electrode voltage) to 300 V and
the Helmholtz coil voltage to 8.0 V.
Slowly turn the current adjust knob for
the Helmholtz coils clockwise until the
electron path is a complete circle with an
approximate radius of 5.0 cm. Be sure
that I never exceeds 2.0 A.
4. The radius of the beam circle will be
measured using a digital camera
mounted on a tripod. Turn off the flash
and set the exposure time of the camera
to 3.5s. Focus on the scale behind the
beam.
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Electron Charge to Mass Ratio