Name ______________________
Date _______________
Measurement of the charge to mass ratio, e/m, of the electron
PRE-LAB PREPARATION SHEET
Before coming to lab, answer the following questions.
1) Using the formulas for the force on a particle of charge, e, moving
perpendicular to a magnetic field, B, and the centripetal force on any
object moving in a circle, show that
|r| = mv/(eB).
2) Using conservation of energy, find the velocity of a particle with mass m
and charge e after it has been accelerated through a potential different of
V.
3) Using your answers from parts (1) and (2), show that the charge to mass
ratio (e/m) for moving particle described is:
e/m = 2V/(r2B2)
p
R
R
4) In this lab we will be using a
magnetic from a particular apparatus
referred to as a Helmhotz coil. This is a
set of two parallel sets of coils of wire of
radius R and N coils. The two coils are
placed a distance R apart. Using the
formula for the magnetic field at the
center of coil of wire, show that the
magnetic field at the a point, p, midway
between the center of the two coils is
equal to
B=(4/5)3/20NI/R
5) Using the formula above, what is the magnetic field/ampere for a set of
coils with 130 turns and a radius of 0.152m?
6) In this experiment, what will allow us to view the path of the electron
beam?
7) In our experiment, there will be three internal power supplies. What do
they control?
Measurement of the charge to mass ratio, e/m, of the electron
Equipment

EP-20 e/m Electron Apparatus (Helmholtz coils)

Meter stick

Compass
Overview
You will be using a self-contained apparatus is designed for the
measurement of elm of the electron by observing the radius of their circular paths
under the influence of a uniform magnetic field. The magnetic field is provided by
a pair of Helmholtz coils surrounding the vacuum tube. The vacuum tube has a
downward pointing electron gun in an evacuated bulb that has a little helium
added so that the path of the electrons in the tube is visible. The overall
appearance of the apparatus is shown in figure 1 below.
Figure 1
Three internal power supplies provide the filament power, the coil current
and the accelerating potential for the electron beam. The filament supply is fixed,
while the accelerating voltage and the coil current are set by front panel controls.
The accelerating potential and the coil current can be measured by digital meters
on the front panel. The meters make it simple to accurately determine the forces
affecting the motion of the electrons within the tube. The diameter of the electron
path in the magnetic field can be measured using the etched glass internal scale
in the tube. The graduations and numerals of the scale are illuminated by the
collision of the electrons, making observation and reading even easier.
The helium gas added to the tube fluoresces when struck by the moving
electrons and produces a bright, clear view of the electron beam. An electrode is
provided for absorbing electrons after they have traced their circular path. Thus,
the circular tracing of the electron path is undisturbed by previously emitted
electrons, contributing to more accurate measurement.
Principle of Operation
The general configuration of the electron gun is shown in figure 2.
Electrons are emitted by an indirectly heated cathode at the top of the figure. The
cathode is connected to the negative of the high voltage supply. It is partially
shielded by a surrounding grid which has a small aperture to let some electrons
pass through. The anode is mounted below the grid and is connected to the high
voltage positive. Electrons escaping through the grid hole are rapidly accelerated
toward the anode by the potential between them. Most of the electrons hit the
anode, but some of them pass through the hole in the anode and form the
electron beam in the tube.
Figure 2
The energy given to the electron falling through the potential V is eV,
where V is the cathode anode potential (the “accelerating potential”) and e is the
charge on the electron. All of this energy is converted into kinetic energy of the
moving electron. The electron beam is traveling in the transverse magnetic field
of the Helmholtz coils, so it is deflected into a circular path by the Lorentz force,
evB where B is the magnetic field acting on the beam of electrons. This force
provides the centripetal force required to maintain the circular motion.
As you proved in the pre-lab portion of this procedure, the charge to mass
ratio of these moving electrons can be written as
e/m = 2V/(r2B2)
The magnetic field is provided by the Helmholtz coils surrounding the
vacuum tube. They are mounted so that their field is transverse to the tube axis
and the electron’s motion. These coils produce a uniform magnetic field
everywhere inside of the volume they enclose. This is a very useful property,
since it guarantees that there is a constant force on the moving electrons. In
addition to field uniformity, as you calculated in the pre-lab, the magnitude of the
magnetic field can be determined as:
B=(4/5)3/20NI/R
Here 0 is the permeability of empty space, N is the number of turns in
each of the pair of coils, I is the coil current and R is the coil radius.
Experimental Procedure
1. Measure the internal and external diameter of the Helmholtz coils on
several axes. They may not be quite round and the two coils may not be
quite the same. Average your measurements and determine the standard
error, so that you will be able to decide whether it has a significant effect
on the accuracy of your results.
Average radius of coil, R, _____________________
The number of turns in each coil is 130.
2. Set the apparatus on a level table. The room light should not be too bright,
because the electron beam will be hard to see.
3. In order to minimize the influence of geomagnetism, use a compass to
locate magnetic North and align the Helmholtz coils so they are parallel to
the needle. If this is not convenient, it can be disregarded with little effect
on the results.
This will have the effect of reducing the influence of geomagnetism on
the magnetic field parallel to the coil axis. The influence of geomagnetism
or other sources of magnetic fields can be observed by the deflection of
the circular motion of the electron beam while the apparatus is rotated.
The magnitude of this deflection is greater when a small current is flowing
through the coils.
4. With the power switch off, connect the line cord to the correct line voltage
power.
5. Turn on the power switch. The unit will perform a 30-second self-test,
indicated by the digital display changing values rapidly. During the self-
test, the controls are locked out, allowing the cathode to heat to the proper
operating temperature. when the self-test Is complete, the display will
stabilize and show “000”. Although the unit is now ready for operation, a 510 minute warm-up time is recommended before taking careful
measurements.
6. Turn the Voltage Adjust control up to 200V and observe the bottom of the
electron gun. The bluish beam will be traveling straight down to the
envelope of the tube.
Note: Both the Voltage and Current outputs are controlled by an onboard microprocessor. Because the microprocessor automatically locks
out the controls at both the minimum and maximum settings, there is no
need to provide a manual “stop” on the knobs. When the knob reaches the
maximum setting, it will still turn, although the value shown on the
appropriate display will not change. These features prevent excessive
voltage being applied to the tube.
7. By turning up the Current Adjust control up, you can increase the strength
of the magnetic field. Do this and observe the circular deflection of the
beam. When the current is high enough, the beam will form a complete
circle within the envelope. Adjust the current until the beam forms a circle
of between 9cm to 11cm and has an easily readable diameter using the
internal centimeter scale inside of the tube. The scale numbers fluoresce
when struck by the electron beam.
8. For an accelerating voltage of 200V, measure the beam diameter for coil
current settings.
Trial
Number
Accelerating
Voltage (V)
Coil Current
(I)
Beam
Radius, (r)
-
-
Average
1
2
3
4
5
-
e/m (C/kg)
9. Set the accelerating voltage to 300V, and repeat the measurements in
Steps 7 and 8.
10. Repeat Steps 7 and 8 for two additional accelerating voltages.
Questions
1. What is the direction of the beam of electrons before it is deflected by the
magnetic field?
2. If you are facing the front panel of the apparatus, which way is the current
flowing in the coils? (i.e. counter-clockwise or clockwise?)
3. Using small bar magnet, move it close to the tube and observe the
deflection of the beam. It is easy to see how properly designed magnets
can be used to focus and steer an electron beam. If you place the north
end of a bar magnet near the front of the tube, what geometric shape does
the electron beam form?
4. Turns the current off in your coils and gently place the compass you used
for alignment on the top of the tube. Slowly turn up the current in the coils.
How much current does it take to deflect the needle of the compass? That
is, how sensitive is the compass to changes in magnetic fields?
Measurement of the charge to mass ratio, e/m, of the electron
Homework
1) Two 300-turn coils of radius R are configured as Helmholtz coils. For R=
5.0cm. and I = 50 A. Plot the magnitude B of the net magnetic field as a
function of distance x along the common axis over the range x = -5 cm to x
= +5 cm, taking x = 0 at the midpoint P.
2) Return to your derivation of magnetic field at the mid-point between the two
Helmholtz coils. Let the separation of the coils be a variable s (not necessarily
equals to the coil radius R).
(a) Show that the first derivative of the magnitude of the net magnetic field
of the coils (dB/dx) vanishes at the midpoint P regardless of the value of s. You
would expect this to be true from symmetry.
(b) Show that the second derivative (d2B/dx2) also vanishes at P, provided
s = R. This accounts for the uniformity of B near P for this particular coil
separation.