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Electrons
Thermionic Emission
Deflection of Electrons in Electric Field
Deflection of Electrons in Magnetic Field
Determination of e/m
Cathode Ray Oscilloscope
Thermionic Emission (1)
 When a metal is
heated sufficiently,
its free electrons
gain enough kinetic
energy to leave the
metal. This process
is called thermionic
emission.
Thermionic Emission (2)
 In practice, thermionic
emission is caused by
heating a filament of
metal wire with an
electric current.
Thermionic Emission (3)
 The work done on each electron from the filament
is
W = eV
where V is the p.d. across the filament and the
anode.
 Electron-volt
The electron-volt is an amount of energy equal to
the work done on an electron moved through a p.d.
of 1V.
1 electron-volt = 1.6  10 19 J
Properties of Electron Beams
(Cathode rays)
 Cathode rays travel in straight lines.
 Cathode rays can cause fluorescence.
 Cathode rays can be deflected by electric
field and magnetic field.
 Cathode rays may produce heat and X-rays.
 Cathode rays can affect photographic plates.
Deflection of Electrons in a
Uniform Electric Field (1)
 Consider an electron beam directed between two
oppositely charged parallel plates as shown below.
 With a constant potential difference between the two
deflecting plates, the trace is curved towards the
positive plate.
+
d
-
Deflection of Electrons in a
Uniform Electric Field (2)
 The force acting on each electron in the field
is given by
eVP
F  eE 
d
where E = electric field strength,
Vp = p.d. between plates,
d = plate spacing.
Deflection of Electrons in a
Uniform Electric Field (3)
 The vertical displacement y is given by
1 2 1 eV p 2
y  at  (
)t
2
2 md
1 eV p x 2
 (
) 2
2 md v
This is the equation for a parabola.
Deflection of Electrons in a
Uniform Magnetic Field (1)
 The force F acting on an electron in a
uniform magnetic field is given by
F  Bev
Since the magnetic force F is at right angles to
the velocity direction, the electron moves round
a circular path.
Deflection of Electrons in a
Uniform Magnetic Field (2)
 The centripetal acceleration of the electrons
is
Bev
a
m
v 2 Bev
Hence a 

r
m
mv
r
eB
which gives
Determination of Specific
Charge - e/m
J. J. Thomson
Determination of Specific Charge
Using a Fine Beam Tube (1)
 The principle of the experiment is illustrated
by the diagram below.
××××××××
Electron gun
××××××××
F=Bev
×
×
×
×××××
v
× × × × × ×r × ×
××××××××
Determination of Specific Charge
Using a Fine Beam Tube (2)
Ber
Since v 
m
(For an electron moving in a
uniform magnetic field)
and the kinetic energy of the electron provided
by the electron gun is
1 2
mv  eV
2
Where V is the anode voltage.
Determination of Specific Charge
Using a Fine Beam Tube (3)
1 Ber 2
m(
)  eV
So
2
m
Rearrange the equation gives
e
2V
 2 2
m B r
The value of the specific charge of an electron
is now known accurately to be
(1.758803  0.000003)  1011 C/kg
Thomson’s e/m Experiment (1)
Thomson’s apparatus for measuring the ratio e/m
×
v×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
+
×
×
×
×
-
×
×
×
×
×
×
×
×
×
×
×
×
Thomson’s e/m Experiment (2)
 A beam of electron is produced by an
electron gun with an accelerating voltage V.
 The electron beam is arranged to travel
through an electric field and a magnetic field
which are perpendicular to each other.
 The apparatus is set-up so that an electron
from the gun is undeflected.
Thomson’s e/m experiment (3)
 As the electron from the gun is undeflected, this
gives
FE  FB
i.e.
eE  Bev
On the other hand,
eE
E
v
B
1 2
mv  eV
2
v
Bev
2
e
E
Combining the equations, we get

m 2VB 2
Cathode Ray Oscilloscope
(CRO)
 The structure of the cathode ray tube
Uses of CRO
 An oscilloscope can be used as
1. an a.c. and d.c. voltmeter,
2. for time and frequency measurement,
3. as a display device.
Lissajous’ Figures (1)
 Lissajous’ figure can be displayed by
applying two a.c. signals simultaneously to
the X-plates and Y-plates of an oscilloscope.
 As the frequency, amplitude and phase
difference are altered, different patterns are
seen on the screen of the CRO.
Lissajous’ Figures (2)
Same amplitude but different frequencies
Lissajous’ Figures (3)
Same frequency but different phase
In phase
π /4
π/2
π
3π/4
3π/2
5π/4
In phase
7π/2
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