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8
3B SCIENTIFIC
Dual Beam Tube D 1000654
Instruction sheet
12/12 ALF
®
PHYSICS
1,2 4-mm sockets for filament
and cathode
3 4-mm plug for connecting
anode
4 4-mm plug for connecting
plate
5 Axial electron gun
6 Perpendicular electron gun
7 Deflector plate
8 Boss
9 Fluorescent screen
12
1. Safety instructions
Hot cathode tubes are thin-walled, highly
evacuated glass tubes. Treat them carefully as
there is a risk of implosion.
• Do not subject the tube to mechanical
stresses.
• Do not subject the connection leads to any
tension.
• The tube may only be used with tube holder
D (1008507).
If voltage or current is too high or the cathode is
at the wrong temperature, it can lead to the tube
becoming destroyed.
• Do not exceed the stated operating parameters.
When the tube is in operation, the terminals of
the tube may be at high voltages with which it is
dangerous to come into contact.
• Only change circuits with power supply
switched off.
• Only exchange tubes with power supply
switched off.
When the tube is in operation, the stock of the
tube may get hot.
56
973 4 8
• Allow the tube to cool before dismantling.
The compliance with the EC directive on electromagnetic compatibility is only guaranteed
when using the recommended power supplies.
2. Description
The dual beam tube can be used to determine
the specific charge e/m from the diameter of the
path followed by electrons fired into the tube
from a perpendicularly mounted gun with a vertically aligned magnetic field and observation of
the spiral path followed by electrons fired axially
into a co-axial magnetic field.
The dual beam tube is a partly evacuated electron tube, filled with helium at low pressure and
equipped with both axial and perpendicular electron guns. The electron beams are perpendicular to one another and a common deflector plate
is provided for both guns. The electron beam
source is an oxide cathode heated indirectly via
a heating coil. The electron paths show up as a
fine, slightly greenish beam due to impact excitation of the helium atoms.
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3. Technical data
R
μ
=
Filament voltage: max. 7.5 V AC/DC
Anode voltage: max. 100 V DC
Anode current: max. 30 mA
Deflector voltage: max. 50 V DC
Glass bulb: 130 mm dia. approx.
Total length: 260 mm approx.
Gas filling: Helium at 0.1 torr pressure
4. Operation
To perform experiments using the dual beam
tube, the following equipment is also required:
1 Tube holder D 1008507
1 DC power supply 500 V (@230 V) 1003308
or
1 DC power supply 500 V (@115 V) 1003307
1 Helmholtz pair of coils D 1000644
1 Analogue multimeter AM50 1003073
4.1 Setting up the tube in the tube holder
The tube should not be mounted or removed
unless all power supplies are disconnected.
• Push the jaw clamp sliders on the stanchion
of the tube holder right back so that the jaws
open.
• Push the bosses of the tube into the jaws.
• Push the jaw clamps forward on the stan-
chions to secure the tube within the jaws.
4.2 Removing the tube from the tube holder
• To remove the tube, push the jaw clamps
right back again and take the tube out of the
jaws.
5. Example experiments
5.1 Determination of e/m
An electron of charge e moving at velocity v perpendicularly through a magnetic field B experiences a force F that is perpendicular to both B
and v and the magnitude of which is given by:
evBF =
This causes the electron to follow a circular
electron path in a plane perpendicular to B. The
centripetal force for an electron of mass m is
2
F ==
mv
evB
which implies
v
B = tesla
e
R
m
Rearranging the equation gives
v
e
m
=
BR
If the beam is subjected to a known magnetic
field of magnitude B, and v and R are both calculated then the ratio e/m can be determined.
The law of conservation of energy means that
the change in kinetic energy plus the change in
potential energy of a charge moving from point 1
to point 2 is equal to zero since no work is performed by external forces.
1
⎛
⎜
2
⎝
1
⎞
2
− eUeUmvmv
2
2
()
⎟
1
2
⎠
12
0
=−+
The energy of an electron in the dual beam tube
is given by:
1
=
A
2
mveU
2
By solving for v and replacing it in the equation
v
e
m
=
BR
the following emerges
2
U
e
m
A
=
22
RB
The term e/m is the specific charge of an elec-
tron and has the constant value (1.75888 ±
0.0004) x 10
11
C/kg.
5.1.1 Determination of B
The Helmholtz coils have a diameter of 138 mm
and give rise to a magnetic flux in Helmholtz
configuration as given by
HB
= (4.17 x 10
0
-3
) I
tesla
H
and
262
−
1039.17
IB
⋅=
H
where
I
is the current in the Helmholtz coils.
H
The following are also true
U
m
e
2
H
A
22
RI
H
U
A
=
kI
2
R
5
1015.1 ⋅⋅=
and
5.1.2 Determination of R
Referring to the diagram Fig. 1, the beam
emerges from the electron gun at C travelling
along the axis of the tube. The electron is then
deflected in a circular path with the tube axis
forming a tangent. The centre of this circle is at
2
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B and it lies in the plane of DCD’ about 2 mm
behind the plane of EE’.
222
AC
ABBCR
2
R
DC
⎡
yx
+
=
⎢
y
2
⎢
⎣
DCBCACBCAB ⋅−+= 2
222
yx
+
====
2
22
⎤
⎥
⎥
⎦
y
22
B
EA
D
2 mm
C
D’
E’ A’
Fig. 1 Derivation of R
R
x
y
2y
• Connect up the tube as in Fig. 4.
• Dim the room lighting.
• Set the heater voltage U
to 7 V and wait
F
about 1 minute for the heater temperature to
achieve thermal stability (see remarks in
section 7).
• Set the anode voltage U
age U
• Set the current in the coils I
= 0 V).
P
to 90 V (plate volt-
A
so that the
H
deviated beam passes through point A on
the edge of the fluorescent screen of the
tube. Simultaneously focus the beam using
a plate voltage U
• Mark point A on the tube using a felt-tip pen.
• Increase U
A
of no more than 6 V.
P
and set I
so that the deflected
H
beam always passes through A. Enter all the
values into a table.
in volts IH in amps I
U
A
2
H
90
100
110
120
• Increase I
so that the deflected beam al-
H
ways passes through point E and enter the
values in a corresponding table.
• Mark point E on the tube using a felt-tip pen.
• Plot the graphs of the values from both tables.
• Use a vernier calliper to measure the diame-
ters AA’, EE’ and distance AE.
• Complete the table and calculate R².
AE
mm
x =
AE+2
mm
2
x
mm
2
2y =
EE’
mm
y =
EE’/2
mm
• Replace the values in the equation
U
m
e
A
22
RI
H
5
1015.1 ⋅⋅=
and calculate a mean value for e/m.
5.2 Deflection in a circular path and the determination of e/m
• Connect up the tube as in Fig. 5.
• Set the anode voltage U
voltage U
• Set the current in the coils I
= 0 V).
P
to 100 V (plate
A
so that the
H
deflected beam moves in a circular path with
the plane AA’ tangential to it.
It is practical in this instance to observe the beam
from above, from where it appears as a straight line
and can be focused using U
to a mximum of 6 V.
P
Note: the axial non-linearity of the beam has the
effect of pushing the beam out of the plane of
the electron gun. In order to obtain more accurate results, the tube should be turned within the
brace that holds it so that the circular path is in
the plane of the gun. I
should also be modified
H
so that plane AA’ makes a good tangent with the
path. A slight angle to the axis of the tube is
tolerable. The beam travels in a slightly spiralling path instead of an accurate circle.
• Increase U
and set I
A
so that the plane AA’
H
always forms a tangent to the deflected
beam. Tabulate I
against U
H
and plot the
A
graph.
• Evaluate R = AE/2 from experiment 5.1,
R² = AE²/4.
• Replace the values in the equation
U
m
e
A
22
RI
H
5
1015.1 ⋅⋅=
and calculate a mean value for e/m.
y2
mm
2
R
2
mm
2
3
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5.3 The effect of an axial magnetic field
• Place the tube in the stand at 90° to its nor-
mal alignment.
• Insert the coil in the slot of the tube holder so
that the fluorescent screen is enclosed by a
single Helmholtz coil. Alternatively it can be
mounted on stand equipment (refer to Fig. 2).
• Connect up the tube as in Fig. 6.
-
-
AZ
Fig. 2 Setting up the coil (left: in the tube holder, right:
on stand equipment)
• Set the anode voltage U
V (plate voltage U
• Gradually increase the coil current I
P
With only one axial velocity vector v
to no more than 60
A
= 0 V).
H
the axial
a
.
non-linearity of the beam is corrected and coincides with the true axis of the field.
• Mark the position of the beam with a felt-tip
pen.
• Set I
• View the beam end-on through the coil.
to 1.5 A and increase U
H
a second velocity vector v
gradually so that
P
affects the beam.
p
The beam path turns into a helix. The beam no
longer goes around the axis of the field but returns to a different position along the axis after
every loop.
• Reverse the polarity of the magnetic field B
by reversing that of the Helmholtz coils and
observe what happens to the beam.
• Change the anode voltage and observe its
effect on the helical path of the beam. Then
restore the voltage to 60 V.
Fig. 3 Helical path of the deflected beam
6. Errors in the results
1. The circular beam path in experiment 5.2 is
visible because of photo-emission. The energy
involved in this process is lost and never replaced. This means that the beam actually tends
to follow a spiral path instead of a circle. For a
fixed radius R and a real circle U
A/IH
larger than the values that we measure. For this
reason the error in the value of e/m is always on
the negative side. Nevertheless results can be
achieved that are accurate to within 20%.
2. In experiments where the beams are de-
flected into semi-circular paths as in experiment
5.1 results are larger then the published value.
Points A and E, through which the beam is deflected, lie outside the homogeneous region of
the Helmholtz coils so that the magnetic flux is
reduced at these points. For a fixed radius R
and a truly homogeneous field U
A/IH
smaller than the values we measure. For this
reason the error in the value of e/m is always on
the positive side. Nevertheless results can be
achieved that are accurate to within 20%.
7. Remarks
1. Limiting of anode current: to avoid an exces-
sive degree of emission of positive ions towards
the electron emitting chemicals of the cathode,
the anode current should be limited to below 20
mA wherever possible. Higher current may be
tolerated for a short time but over long periods it
reduces the lifespan of the tube.
2. Thermal stability of the cathode: for the same
reason, you should avoid starting the electron
gun when the cathode is cold and only just heating up.
3. Focussing the beam: Small voltages U
plied to the deflector plates enable the beam to
be focussed. Voltages greater than 6 V cause
results to deteriorate.
² would be
² would be
ap-
P
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DC POWER SUPPLY 0 ... 500 V
3
0
0
0
0
2
4
0
0
0
0
1
5
0
0
0
3
0
0
2
4
0
0
1
5
0
0
4
6
2
0
VV VV
6
9
3
8
1
0
2
A
Z
A
Z
Fig. 4 Determining e/m using the axial electron gun
0 ... 500 V 0 ... 50 V
U
U
A
P
U
F
0 ... 12 V0 ... 8 V
U
H
I
A
DC POWER SUPPLY 0 ... 500 V
3
0
0
0
0
2
4
0
0
0
0
1
5
0
0
0
3
0
0
2
4
0
0
1
5
0
0
4
6
2
0
6
9
3
8
0
1
2
VV VV
0 ... 500 V 0 ... 50 V
0 ... 12 V0 ... 8 V
A
Z
U
U
A
P
U
U
F
H
I
A
A
Z
Fig. 5 Determining e/m using the perpendicular electron gun
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DC POWER SUPPLY 0 ... 500 V
3
0
0
0
0
2
4
0
0
0
1
0
0
5
0
0
3
0
0
2
4
0
1
0
0
5
0
4
6
2
0
8
6
9
3
0
VV VV
1
2
0 ... 500 V 0 ... 50 V
U
A
U
0 ... 12 V0 ... 8 V
P
U
F
U
H
ZA
I
A
Fig. 6 The effect of an axial magnetic field
A TELTRON Product from UK3B Scientific Ltd. ▪ Suite 1 Formal House, Oldmixon Crescent ▪ Weston-super-Mare
Somerset BS24 9AY ▪ Tel 0044 (0)1934 425333 ▪ Fax 0044 (0)1934 425334 ▪ e-mail uk3bs@3bscientific.com
Technical amendments are possible
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