# Part A by UU38XsT

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```									                          SKH St. Mary’s Church Mok Hing Yiu College
Physics Experiment
Form 7S

Student Name : _________________ (            )                                Date : ____________
Group Number : _____
Marks : ___________
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E34 Measurement of the specific charge of electron
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Objective : To study the behavior of electrons in electromagnetic fields, and to determine the
ratio e/m (the "specific electronic charge").

Apparatus :    Deflection e/m Tube                                    1
Helmholtz Coils                                        1 pair
Universal Stand                                        1
EHT Power Supply                                       1
Decade Resistance Box                                  1
Digital Multimeter                                     1
Low voltage smoothed d.c. power supply                 1
Connecting wires                                       10

Theory : In this experiment we will use a cathode ray gun as a source of electrons. The electrons
are accelerated to a velocity, v, by the potential difference Va (anode voltage). The
speeding electrons then enter the bulb of the deflection tube where electric and magnetic
fields can be applied to the electron beam. If Va is fixed the electron velocity is also
fixed. When a current, I, passes through the Helmholtz coils, a fairly uniform magnetic
field is generated in the bulb:
8  o NI
B     3
 I
5       2
R
where N = the number of turns in each coil, I is the current through the coils, R is the
 N
coil radius, μ0 = 4π x 10-7 H m-1 and   8 o .     3
5     R       2

The coils are arranged so that B is perpendicular to v and so the path of the electrons is
circular, with radius of curvature r:
mv 2
FB  qv  B                                           (1)
r
e   v
and hence                                                                         (2)
m rB
Therefore, if we know I, v and r we could determine e/m.
If the electron beam passes two points (0,0) and (x, y) on the fluorescent screen in the
deflection tube, from geometry, the radius r of the circular path can be obtained by
x2  y2
r
2y
There are two methods to determine the velocity v. One method is to consider the
relationship between the accelerating voltage, Va, and the kinetic energy: K = ½ mv2.
qVa = ½ mv2                                          (3)
Setting q = e and substituting into Eq. (2), gives:
e      2V
 2 2a 2                                              (4)
m  I r

E34 Specific Charge of Electron - 1
To determine v in Eq. (2) another way, we will apply an electric field, E, and a magnetic
field B′ such that FE = - FB’. Thus, a = 0 and v = constant. Note that we want the same
Va as before in order to measure the same v. This method can be thought of as the
"crossed electric and magnetic fields method" or “null deflection method”.
To understand this method, consider the that the electrons will move in a straight line if
FE = FB’
eE = evB’
V
For parallel metal plates E  a where d is the separation of plates
d
Va
and hence                   v                                                 (5)
B' d
By combining Eqs. (2) and (5) and measuring r, B, E and B′, the ratio e/m can be
determined by
e        Va

m  2 I ' Ird

Procedure :

CAUTIONS & WARNINGS before you begin:
It is VERY IMPORTANT that you read the following:
The potential difference Va that accelerates the electrons is on the order of 3000 V.
This is dangerous and caution must be observed.
Therefore, in all procedures in this lab, YOU MUST:
A. Keep calm and think before you reach for something.
B. Always dial down the voltage using the lever and turn to OFF the switch on the
back of the kilovolt power supply while making any changes in the circuit or if
you are not at that moment making an observation!

Part A: Magnetic deflection method
In this section of the laboratory, you will accelerate the electrons using an AC source to “boil”
electrons off the deflection tube cathode. Then a high voltage power supply will be applied to
accelerate the electrons past a pair of horizontal deflecting plates. An electric field will be applied
across these plates (also controlled with the high voltage power supply). A magnetic field will be
established in the Helmholtz coils (using an entirely different circuit and low voltage power
supply). Finally, the electric and magnetic fields will be varied and measured, along with the
resulting deflection and radius of the electron beam.
1.   Assemble the deflection e/m tube, Helmholtz coils, universal stand, power supplies,
DMM, and decade box as shown in Figure 1 and Figure 2. It is important to line up the
Helmholtz magnetic coils perpendicular to the Earth’s magnetic field in order to reinforce
the magnetism’s effort to straighten out the electron beam.

Figure 1

E34 Specific Charge of Electron - 2
2.    Figure 2 is a schematic diagram of this set-up. Connect the low voltage smoothed d.c. power
supply, the decade resistance box and the DMM to the Helmholtz coils. This set up provides
d.c. current through the Helmholtz coils to establish the magnetic field.
Helmholtz
Figure 2                                                 coil
Z         A

Va                                                     IB DMM
EHT power                             6.3 V a.c.
supply                                      Vf
`                    ~ 3 kV d.c.

12 V d.c.     Low voltage
power supply

Z        A

3.    The electrical lead from the decade box should connect to the DMM’s “Amps” jack, and the
DMM’s “Common/Ground” jack should connect to the “A” terminal of the first coil. Set the
DMM function to Amps on the 1 A range.
4.    Connect the 6.3 V a.c. terminals on the EHT power supply to the 4 mm sockets in the
plastics cap at the end of the tube. This connection provides power to the anode filament.
The filament current “boils” off electrons providing a source of electrons for the gun.
5.    Connect the positive “+” terminal of the EHT power supply to the 4 mm plugs mounted on
the side of the neck of the tube. This connection to the anode of the gun provides the
accelerating potential Va.
6.    Also connect the positive “+” terminal of the EHT power supply to the 4 mm plugs
connected to the deflection plates. Note that the plates are at the same potential and hence
there is no E field.
7.    Connect the negative “-” terminal of the EHT power supply to the gun socket marked “ -” to
provide a common return path.
8.    Place insulating corks on all exposed plugs and check the circuit.
9.    Turn on the EHT power supply and slowly increase Va to 3000 V by reading the top scale of
the meter on the power supply.
10.   Turn on the low voltage power supply and note the deflection of the electron on the
luminescent screen.
11.   In order to determine r, the radius of curvature of the electron path, adjust the decade
resistance box such that the electron beam passes through the point (9, 2) on the luminescent
screen and record the coil current I+.
12.   Reverse the connections to the Helmholtz coils and adjust the beam to pass through the point
(9, -2). Record the current I-. Then find the mean current I.
13.   Decrease the voltage Va to zero and turn off the EHT power supply and the low voltage
supply.
14.    Repeat the experiment by setting the EHT power supply to different voltages but adjusting
the beam to pass through the same point (9, ±2) each time. Tabulate your results. Hence find
the mean value of e/m.

Results :
Number of turns in each Helmholtz coil     N = ________
Coil radius      R = __________ m
8  o N = ____________ T A-1
     3
52 R
x2  y2
Radius of curvature of electron beam      r            __________ m
2y

E34 Specific Charge of Electron - 3
e   2V          -1
Va /V                I+ /A        I- /A        Mean I /A                2 2a 2 /C kg
m  I r

Mean value

The accepted value for the specific charge of electron is 1.76  1011 C kg-1. Calculate the
percentage error from the accepted value.
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Part B: Crossed Electric and Magnetic Fields Method
In this section of the lab you will first determine the electron velocity by providing “crossed”
electric and magnetic fields of the proper magnitude to allow the electron to move through
without deflection. In this case, the electric field is provided across the horizontal deflection plates
within the deflection tube. The magnetic field is produced by the Helmholtz coils. Finally, the
high voltage power supply applies the accelerating voltage, which in turn determines the electron
velocity. A schematic diagram of the connections for both the Helmholtz coils and the
deflection tube is shown in figure 3 below.
1.   To measure the velocity, v, of the electron, set up the circuit as shown in Figure 3. This
circuit differs from the previous set up in that the bottom deflection plate in connected to the
positive “+” terminal of the EHT power supply and the top deflection plate is connected to
the negative “-” terminal of the EHT power supply. Note that an electrostatic field is set up
across the deflection plates.
Helmholtz
Z
coil
A

Figure 3                  Va                                                      IB DMM
6.3 V a.c.
Vf
~ 3 kV d.c.
EHT power
12 V d.c.
Low voltage
supply                                                                  power supply

Z        A

2.   Measure the separation of the two metal plates inside the deflection tube.
3.   Turn on the EHT power supply and gradually increase Va to 3000 V. (Hence, the velocity, v,
is the same as before.) A curved beam is obtained on the luminescent screen, deflected
downwards.

4.   Switch on the low voltage power supply and adjust the coil current, I’, (and hence B’) by
changing the decade resistance until the path of the electrons is as straight as possible.
Record the new current, I’.
CAUTION!: Never let the total resistance of the box fall below 50Ω!
5.   Connect both metal plates to the + terminal of the EHT power supply as shown in Figure 2
so that there is no electric field between them. The beam, acted on only by the magnetic field
B, traces an arc of a circle.

E34 Specific Charge of Electron - 4
6.   Adjust the coil current such that the beam passes through the point (9, 2) on the grid of the
screen. Record the current reading I.
7.   Decrease Va to zero and turn off the EHT power supply and the low voltage power supply.
8.   Calculate e/m using the observed values I, I′, Va, d, and r, and compare to the accepted value.

Results :
Accelerating voltage      Va = ___________ V
Separation of metal plates      d = __________ m
Initial coil current    I’ = __________ A
Final coil current     I = __________ A
Number of turns in each Helmholtz coil      N = ________
Coil radius     R = __________ m
8  o N = ____________ T A-1
    3
52 R
x2  y2
Radius of curvature of electron beam      r            __________ m
2y
e
Specific charge of electron         _____________________________________________
m
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Calculate the percentage error from the accepted value of e/m.
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Discussion :
1.   How did your results compare to the accepted value?
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2.   What errors and problems, both systematic and random prevented a better value?
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3.   If you could improve the design and equipment to improve the accuracy and precision for
this measurement, how would you do so?
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E34 Specific Charge of Electron - 5

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