Download Unit 7 Charge-to-mass ratio of the electron

Unit 7 Charge-to-mass ratio of the electron
Keywords：
J. J. Thomson, Lorentz Force, Magnetic Fields
Objective：
Observe the results of electron beam influenced by the magnetic field and
calculate the charge-to-mass ratio of the electron.
Apparatus：
e
apparatus (the external form of the Model J2433-2 Lorentz Force
m
Demonstrator), power supply（0~300V；0~20V；6V), connector.
Principle：
When the cathode is heated, it shoots rays at the screen in the back of anode. If a
U-shaped magnet moves across the tube, the light-spot will deflect up and down.
J.J. Thomson had done the experiment in 1897. His most famous achievement
was the discovery of the 'electron' at that time. He not only did the research about
the characters of rays from the cathode but also discussed its quantity. At the
same time, J.J. Thomson also obtained the charge-to-mass ratio of the electron.
J.J. Thomson's experiment and subsequent theories won him the Nobel Prize in
physics in 1906. Besides, Millikan measured the elementary charge in 1909.
Because of their distributions, the mass of electron is easily calculated and the
characters of electron are much more obvious.
As we known, when a charge "q" moves with a velocity "v" vertically to the
magnetic
it is influenced by a force "F", which is
v field,
v v
F = qv × B
（1）
According to the "right-hand rule", the centripetal force "F" is
perpendicular to "v" as a constant. The charge is moving in the way of uniform
motion. As shown in figure 1, the direction of magnetic field is out
perpendicular to the paper.
7-1
Fig. 1
Suppose that the mass of electron is "m", and by uniform motion we can get:
（2）
Where "a" is acceleration
"r" is the radius of circle
Combine (1) and (2), we can get the equation:
v2
m
= Bev
（3）
r
(Consider scalar only, not vector)
The energy of electron from an electronic gun is:
1
eV = mv 2
（4）
2
Where "V" is the potential from end to end of the electronic gun
Substitute (4) into (3), we can get the charge-to-mass ratio of the electron:
2V
e
（5）
= 2 2
m B r
The coil of magnetic field we use in this experiment is Helmhotzs Coil.
When these two coils are set side by side and the distance between them is "R"
(As shown in figure 2), they generate a nearly uniform magnetic field to the
center point C. The magnetic field parallels the axis of two circular centers.
According to the following equation, the magnitude of magnetic field is:
8µ 0 Ni
B=
（6）
125R
µ 0 = 4π × 10 −7 Weber/amp.m
N: the numbers of coils are 145 (one side)
i: current
R: the radius of magnetizing coil is 14 cm
From （5）、（6）:
125R 2V
e
=
m 32 µ 0 2 N 2 i 2 r 2
7-2
（7）
e
ratio by substituting the numbers of
m
Helmhotzs Coils, radius of coil, the radius of charge in uniform motion, the
potential from end to end of the electronic gun, and the current of coils into
equation (7).
Therefore, we can obtain the
Instructions：
( I ) Observe the electron beam incident vertically to the magnetic field
1. The connection is shown in figure 4.
2. Turn the power on. Before operation, be sure that each switch is adjusted
to minimum. Set the deflector voltage adjust to OFF. Set the current
direction in the magnetizing coil to CLOCKWISE. Turn the accelerator
voltage adjust knob clockwise to increase the voltage and you may see a
rectilinear orbit of the moving electrons.
3. Keep the accelerator electrode voltage at 150V. Vary the amount of
current for totally 10 times and repeat the procedure to find each radius of
circular trace. (The range is from 0.9A to 1.4A) Measure each radius of
circle and do the plot versus current.
4. Keep the magnetizing current as constant. Vary the amount of the
accelerator electrode voltage for totally 10 times and repeat the procedure
to find each radius of circular trace. (The range of the accelerator
electrode voltage is from 150V to 300V) Measure each radius of circle
and do the plot versus voltage.
e
5. Calculate the charge-to-mass ratio of the electron ( ) and the average of
m
them.
( II ) Observe the electron beam incident vertically to the magnetic field
1. Discuss the relation between the pointer point out with an angle and the
radius of the trace: Vary the amount of pointer point out angle for totally
7 times and measure each radius of circle.
2. Do the plot of radius to the pointer point out angle θ and the plot versus
sinθ.
Questions:
Q1: What is the theory amount of the ratio
e
?
m
Q2: How will the electron beam be when you adjust the accelerator
electrode voltage?
Q3：How will the electron beam be when you adjust the magnitude and the
7-3
direction of the magnetizing current?
Q4: Why can you see the electron beam? Is the glass container vacuous?
Q5: Is the trace of moving electrons influenced by terrestrial magnetism?
Remark：
1.
2.
3.
4.
When you plug in the connector, be careful of the pole.
The tube of Lorentz Force is a short lifetime electron device. In order to
extend the lifetime, be sure to set the acceleration voltage adjust to
minimum before operation. After pre-warming for 5 minutes, turning
the accelerator voltage to 100V~200V and the orbit of the moving
electrons can be seen.
When experiment is finished, turn the accelerator voltage to zero, then
turn the power switch to "OFF".
Time of the experiment may not exceed one hour in order to extend the
lifetime.
Fig. 2 the connection of
S1：5 V
S2：0~300 V
S3：0~20 V
e
apparatus
m
the power switch of lamp (in order to heat the filament）
the power switch of accelerator voltage (in order to accelerate the electrons）
the power switch of magnetic fields
7-4
Fig. 3 apparatus of
Current of the magnetic coil
e
m
Accelerator voltage
Fig 4. The connection of
7-5
e
apparatus
m