Fine Beam Tube T
Electricity
Cathode ray tubes
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Fine beam tube
DETERMINE THE SPECIFIC CHARGE OF AN ELECTRON
• Demonstrate the deflection of electrons in a uniform magnetic field along a closed circular path
• Determine the Helmholtz coil current I
H
in relation to the accelerating voltage U of an electron gun where the electrons
are moving in a circular path of constant radius r
• Determine the specific charge of an electron e/m from the measurements
UE307070
08/06 UK
BASIC PRINCIPLES
In the fine beam tube, the electrons move along a circular
path in a uniform magnetic field. The tube contains neon
gas at a precisely set pressure. The gas atoms are ionised
along the length of the circular path due to collisions with
electrons. As a result, they are excited and emit light,
thereby indirectly making the circular path of the elec-
trons visible. The radius of the path can then be meas-
ured directly with a ruler. Since the accelerating voltage U
of the electron gun and the magnetic field B are known, it
is possible to calculate the specific charge of an electron
e/m from the radius of the circular path r.
An electron moving with velocity v in a direction perpendicu-
lar to a uniform magnetic field B experiences a Lorentz force
in a direction perpendicular to both the velocity and the
magnetic field.
BveF ⋅⋅= (1)
e: elementary charge
This gives rise to a centripetal force on the electron in a cir-
cular path with radius r, where
r
vm
F
2
⋅
=
and (2)
m is the mass of an electron.
Thus,
r
vm
Be
⋅
=⋅
(3)
The velocity
v depends on the accelerating voltage of the
electron gun:
U
m
e
v ⋅⋅= 2 (4)
Therefore, the specific charge of an electron is given by:
()
2
2
Br
U
m
e
⋅
⋅
= (5)
If we measure the radius of the circular orbit in each case for
different accelerating voltages
U and different magnetic
fields
B, then, according to equation 5, the measured values
can be plotted in a graph of
r
2
B
2
against 2U as a straight line
through the origin with slope
e/m.
B
F
v
r
Fig. 1: Deflection of electrons moving with velocity v in a magnetic
field B by a Lorentz force F along a closed circular path of
radius r
UE307070 3B SCIENTIFIC® PHYSICS EXPERIMENT
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LIST OF APPARATUS
1 Fine beam tube on a connector base U8481420
1 Pair of Helmholtz coils, d = 295 mm U8481500
1 Tube power supply unit 0-300 V, 0-50 V,
4-12 V U8521371
1 DC power supply unit, 12 V, 5 A, e.g. U8521149
1 DC voltmeter, 300 V, e.g. U17450
1 Set of 15 safety leads U13802
SAFETY INSTRUCTIONS
The fine beam tube is a thin-walled, evacuated glass bulb.
Handle with care: danger of implosion!
• Do not expose the fine beam tube to any mechanical
stress or strain.
• In order to avoid any mechanical stress or strain, con-
nect only one experiment lead to each contact pin.
Danger: high voltage is applied to the fine beam tube. Avoid
contact with any part of the body.
• Only use safety experiment leads for connections.
• Make the connections only when the power supply unit
is switched off.
• Set up or dismantle the tubes only when the power
supply unit is switched off.
SET-UP
Note:
To get a clearer view of the electron beam, conduct the ex-
periment in a darkened room.
While setting up the experiment, make sure that all power
supply units are switched off and all voltage controls are
turned fully to the left.
Connecting the fine beam tube to the tube power supply
unit:
• Connect the 50-V output and 12-V output ground sockets
(black) together.
• Connect the positive terminal of the 300-V output to the
anode (red sockets) and the negative terminal to the
cathode (black sockets).
• Connect the voltmeter in parallel to the 300-V output.
• Connect the negative terminal of the 50-V output to the
Wehnelt cylinder (blue sockets).
• Connect the positive terminal of the 12-V output to the
cathode heater (green sockets).
• Connect the PE socket of the tube power supply unit to
the PE socket of the fine beam tube.
Connecting the pair of Helmholtz coils:
• Connect the coils in series to the 12-V DC power supply
unit, as shown in Fig. 3, so that equal current passes
through both coils.
Fig. 2: Experiment set-up for determining the specific charge of an electron
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