Download 10. Thomson method

Experiment No. - 10
SPECIFIC CHARGE e/m
OBJECTIVE: To determine the value of specific charge (e/m) of an electron by Thomson’s method.
APPARATUS USED: Cathode ray tube, high voltage power supply for cathode ray tube, d.c.
voltage for deflection of electron beam, magnetometer, a pair of bar magnets, centimeter scales.
FORMULA USED: The specific charge of an electron is given by
e
Vy

C / kg
m lLB 2 d
(1)
where,
V=Voltage applied across the horizontal deflecting plates
y =Total deflection of the green spot on the screen
l =Length of the deflecting plates
d=Separation between the deflecting plates
L=Distance of screen from the deflecting plates
B=Intensity of the applied magnetic field.
Constants used
B  BH Tan
BH  3.435  10 5 Tesla
l  0.045m
d  0.0245m
L  0.125m
THEORY: Electrons in a CRT are deflected in the vertical direction by applying a potential between
the vertical deflection plates of the CRT. A magnetic field perpendicular to the deflecting electric
field is produced using a pair of the bar magnets. The position of the magnets is adjusted so as to
cancel the deflection of the electrons. The knowledge of the deflecting potential and the magnetic
field of the bar magnets leads to a calculation of the specific charge.
As we know that the electron has a negative charge whose magnitude e equals 1.6x10-19
Coulomb and mass (m) equal to 9.1 x 10-31 Kg. Millikan's Oil Drop method enables us to measure the
electron charge but the mass of the electron cannot be measured directly. It is calculated by
measuring the value of e/m. The aim of this experiment is to determine value of e/m by Thomson's
method. This involves the motion of an electron in a cathode ray tube (CRT). A simplified form of a
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cathode ray tube. The electrons are emitted from the cathode and accelerated towards the anode by an
electric field. A hole in the accelerating anode allows the electrons to pass out of the electron gun and
between the two sets of deflection plates. The metallic coating inside the tube shields the right end
free of external electric fields and conducts away the electrons after they strike the fluorescent screen
where they form a luminous spot.
DESCRIPTION OF C. R. T.
Fig. 1 CRT
The assembled diagram of the principal components of a CRT. The assembly of cathode, control
grid, focusing anode and accelerating electrode is collectively called as ‘electron gun’. A good
vacuum, with a pressure of around 0.01 Pa (10-7 atm) or less is maintained in the interior of the tube.
At a higher pressure than the maintained vacuum, collisions of electrons with air molecules would
scatter the electron beam excessively. The cathode, at the left side in the figure, is raised to a high
temperature by the heater, so as to emit electrons from cathode.
The accelerating anode, with a small hole at its center, is maintained at a high positive
potential, of the order of 1 to 20 kV, relative to the cathode. This potential difference gives rise to an
electric field directed from right to left between anode and cathode. The electrons passing through the
hole in the anode form a narrow beam and travel with constant horizontal velocity from anode to
fluorescent screen.
The area, where electrons strike the screen, glows brightly. The control grid in CRT regulates the
number of electrons reaching to anode and hence the controls brightness of the spot on screen. The
focusing anode ensures that electrons leaving the cathode in slightly different directions are focused
down to form a narrow beam so that electrons are converged to a definite point on screen.
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The beam of electrons passes between two pairs of deflecting plates. An electric field between the
first pair of plates deflects the electrons horizontally, and an electric field between the second pair
deflects them vertically. If no deflecting fields are present, the electrons travel in a straight line from
the hole in the accelerating anode to the center of the screen, where they produce a bright spot.
If an electric field, E is applied between the two plates perpendicular to the direction of
electron beam passing through the space between the plates, the force acting on an electron in the
upward direction of motion is given by
F=eE
(2)
Where, F is the force acting on an electron, e is the electronic charge.
Under the action of magnetic field alone, the electrons are deflected downward. Initially only the
magnetic field B is turned on. R is the radius of the semicircular path traversed by an electron in the
magnetic field. The force acting on the electron is given by,
evB 
mv 2
R
e
v

m BR
(3)
Now the electric field E is switched on, Then
eE  evB ,
v
E
B
(4)
e
E
 2
m B R
(5)
In fig. 2 the path of electrons is shown as in the circular are EP, CE and CF are radii of the circular
arc.
Fig. 2 Geometry of the electron path
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From the fig. 2 it is clear that ∆CEG’ and OGP are similar
G E PO

CE GO
l
y

R L
R
lL
, putting the value in equation (4)
y
e

m
V
E
, using E 
lL
d
B2
y
e
Vy

m LlB 2 d
PROCEDURE:
1. A magnetometer is kept on the wooden bench such that the 90 0  90 0 diameter of its circular
scale is parallel to the length of the bench.
2. Adjust the set up such that aluminum pointer of the magnetometer coincides with the
0 0  0 0 markings.
3. Now place the cathode ray tube replacing the wooden bench. It will face towards north and
south, while the arms of the wooden stand towards east and west. This setting ensures that the
electron beam will travel along the magnetic meridian. As a result the horizontal component
of the earth’s magnetic field will be ineffective to influence the electron beam.
4. The set up is left undisturbed till the experiment is completed.
5. Connect the cathode ray tube the power supply and switch it on. Adjust the intensity and
focusing knobs to obtain a bright small sharp greenish spot at the center of the screen.
6. Adjust the potential at zero and note the initial reading of the spot on the vertical scale on the
screen.
7. Apply a steady potential difference across the deflecting plates of cathode ray tube and note
its reading.
8. The spot on the screen is found to be displaced vertically upwards and now note the final
position.
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9. Take the difference between the initial and final reading of the spot and find total upward
vertical displacement y1 .
10. Now place two bar magnets symmetrically one on each arm of the wooden stand such that
their opposite poles face each other and their common axis is perpendicular to the axis of the
cathode ray tube.
11. Adjust the distances of the magnets such that the spot traces back to its initial position
(Deflection produced by the electric field is annulled by the magnetic field)
12. Note the distances of the poles of the magnet from the wooden scale as r1 and r2 .
13. Remove the magnets from the arms of wooden stand and adjust the potential to zero and this
will bring the spot back to initial position.
14. Now reverse the polarity of the voltage and apply the same potential to the deflecting plates.
15. The spot on the screen is deflected vertiacally downwards. Note the final position of the spot.
16. Take the difference between the initial and final reading of the spot and find total downward
vertical displacement y 2 .
17. Place the magnets as in step 7 and adjust the distances of the magnets such that the spot traces
back to its initial position
18. Note the distances of the poles of the magnet from the wooden scale as r1 and r2 .
19. Calculate the mean value of
y1 and y 2
which gives the mean displacement y for the
applied potential.
20. Repeat the above procedure for a few readings.
21. Switch off the power supply and remove the cathode ray tube and the magnets from the
wooden stand.
22. Place the magnetometer in the middle of the gap with its center on the common axis of the
magnets.
23. Place the bar magnets on the wooden arms at the same distances as r1 and r2 and take the
readings of the ends of the pointer 1 and  2 .
24. Place the bar magnets on the wooden arms at the same distances as r1 and r2 , now take the
readings of the ends of the pointer  3 and  4 .
25. Find the mean value of  
1   2   3   4
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26. Find the intensity of the magnetic field B  BH tan  , where BH is the horizontal component
of the earth’s magnetic field.
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OBSERVATION: TABLE 1
S.
Voltage
Polarity
Position
Displacement
When spot comes
No.
applied
of the
of spot (mm)
of the spot(mm)
back to its initial
across
potential
position after
the
difference
applying magnetic
deflecting
field(cm)
plates
Initial
Final
V (volts)
Position
Position
(a)
1
2
3
V1 = 2
V2 = 4
V3 = 6
(b ~ a)
Position
Position
Y=
of East
of West
( y1 + y2 )/2
arm of
arm of
magnet
magnet
(b)
Direct
y1
Reverse
y2
Direct
y1
Reverse
y2
Direct
y1
Reverse
y2
TABLE 2
S.
When spot comes back to its
No.
initial position (cm)
1
2
3
Deflection of the compass needle (o)
Position of
Position of
Reading of Reading of other
East arm of
West arm of
one end of
end of pointer
magnet
magnet
pointer (o)
(o)
r1 =
r2 =
1 
2 
r1 =
r2 =
3 
4 
r1 =
r2 =
1 
2 
r1 =
r2 =
3 
4 
r1 =
r2 =
1 
2 
r1 =
r2 =
3 
4 
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Mean deflection (o)
θ=
θ1 +θ2 +θ3 +θ4
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PERCENTAGE ERROR:
Percentage error = (Calculated value ~ Standard value ) x 100
Standard value
(Standard value of e/m = 1.758 x 1011 C / Kg)
MAXIMUM PROBABLE ERROR:
Take logarithm of eq. (1), differentiate and then calculate by putting appropriate values.
 e / m
(e / m)

V y
B

2
V
y
B
As B  BH tan
B (BH tan )

 BH sec2 


B BH sec2  



B
BH tan 
sin  cos 
Hence maximum log error can be written as:
 e / m
(e / m)

V y


2
V
y
sin  cos 
RESULT: The value of e/m obtained by using Thomson’s method is = ..........................C/Kg.
PRECAUTIONS:
1. The Cathode ray tube should be accurately placed with its longitudinal axis in the magnetic
meridian.
2. The spot on the screen should not be allowed to remain in the screen for a long time.
3. The wooden stand should point in the east west direction.
4. Axis of magnets and axis of the tube must lie perpendicular to each other but in the same
horizontal plane.
5. The breaking of cathode ray tube might cause explosion and result in personal injury and thus
utmost care must be taken in handling the cathode ray tube might.
6. High potentials are employed in the power supply unit which should be treated with care.
7. Care is taken such that no magnetic meridian is in the immediate vicinity of the set up.
8. Oscillations of magnetometer needle should be of small amplitude.
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SOURCES OF ERROR:
1. The wooden stand should point might not be in the east west direction.
2. Axis of magnets and axis of the tube might not lie perpendicular to each other.
3. The spot might not be properly focused.
4. There can be error due to parallax.
REFERENCES:
1. K. K. Dubey and B. N. Dutta, Practical physics, Kalyani publishers, New Delhi.
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