Download Electron Charge-to-Mass Ratio

Determination of the Electron Charge-to-Mass Ratio, "e/m"
Figure 1. the Thomson Tube used in the e/m experiment
Purpose:
To study the behavior of electrons in electromagnetic fields, and to determine the ratio e/m (the
"specific electronic charge").
Equipment:
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Teltron 525 Deflection e/m Tube
Teltron 502 Helmholtz Coils
Teltron 501 Universal Stand
Pasco 8000 Low Voltage DC Power Source ( 12.0 VDC )
Teltron 813 High Voltage Power Source (0 - 5000 Vdc & 6.3 Vac)
Digital Multimeter (DMM)
Decade Resistance Box
Electrical Patch Cords (w/ Banana Plugs)
Insulating Corks
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 (anode voltage), Va. The speeding
electrons then enter the bulb of the Teltron 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:
B = αI
(I in amperes, B in Tesla)
where
α = 4.23 × 10 −3
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:
FB = qv × B = ma =
mv 2
r
Eq. 1
and hence
e
v
=
m rB
Eq. 2
Therefore, if we know I and r we can determine e/m if we know the velocity v.
There are two methods to determine the velocity. One method is to consider the relationship
between the accelerating voltage, V, and the kinetic energy: K = 12 mv 2
qV = 12 mv 2
Eq. 3
Setting q = e and substituting into Eq. 2, gives:
e
2V
= 2 2 2
m Rα I
Eq. 4
Thus by experimental measurement of V, R, and I the charge to mass ratio can be determined.
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 velocity, v. This method can be thought of as the "crossed electric
and magnetic fields method."
To understand this method, consider the that the electrons will move in a straight line if
FE = FB '
eE = evB ′
and hence
v=
E
B′
Eq. 5
By combining Equations 2 and 5, and measuring r, B, E and B' , the ratio e/m can be determined.
E
V
'
E
d
B
=
='
RB RBB R (α I )(α I ' )
e
V
eq 6.
=
m R (α 2 II ' )d
Where d is the distance between the two plates inside the Teltron tube.
e
v
= =
m rB
Experiment:
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 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: Measuring the Electron Beam Radius and Determining e/m
In this section of the laboratory, you will accelerate the electrons using an AC source to “boil”
electrons off the Teltron tube filament. Then a high voltage power supply will be applied to
accelerate the electrons. A magnetic field will be established in the Helmoltz coils (using an
entirely different circuit and low voltage power supply). The magnetic field will deflect the
electrons. From this deflection, one may determine the charge to mass ratio of the electron.
1. Attach two Helmholtz coils to the stand such that the plugs face away from the center.
Carefully place the Thompson tube into the stand between the coils. Note that the plastic
blue stem at the end goes into the larger opening.
2. Build the circuit to the Helmholtz coils using the low voltage power source and a DMM
as an ammeter. Use figure 2 as a guide. The DIGI 35A power supply should replace the
U33000 power source in the figure. Be sure the magnetic fields of the Helmholtz coils
work together rather than canceling each other out.
3. Be sure to use the 10A setting on the DMM.
Figure 2: Circuit diagram to measure the electron beam radius.
4. Connect the 6.3VAC power supply (located on the high voltage power supply) to the
filament labeled as F3 and F4. This is the filament voltage, UF, providing electrons.
5. Connect the positive high voltage to ground and also to the electric field plates labeled
G7 and A1. This is also connected to the anode which will be your accelerating voltage,
UA.
6. Connect the negative high voltage to the cathode labeled C5.
7. Insulating corks may be placed on any exposed banana plugs.
8. Have the professor or lab tech check your circuit before continuing.
9. Turn on the low voltage power supply and increase the voltage until you have a current
around 300 mA. Never exceed 2A. Record the coil current.
10. Turn on the high voltage power supply and increase the voltage to 2500 V. Record this
voltage.
11. Note the deflection of the electrons on the luminescent screen. Record the distance along
the scale from the corner of the screen that the electrons exit the screen. Each major tick
mark is one centimeter.
12. Decrease the high voltage power supply to 0 V. Then turn off all power supplies.
Part B: Measuring e/m by Means of Field Compensation
An electric field will now be applied across the past a pair of horizontal deflecting plates
(controlled by another high voltage power supply). By balancing the two forces due to the
electric and magnetic fields, one may determine the charge to mass ratio of the electron.
1. A schematic for this setup is shown in figure 3. Note the additional high voltage (500V)
power supply. The power supply may be higher but will be referred to as the 500V power
supply. This will be added to control an electric field on the horizontal deflecting plates.
Figure 3: Schematic for measuring the electron charge-to-mass ratio using field
compensation.
2. The circuit for the Helmholtz coils will remain unchanged.
3. Remove the connection of G7 from ground. Connect G7 to the positive terminal of the
500V power supply.
4. Connect the negative terminal of the 500V power supply to the same ground as the high
voltage power supply.
5. Have the professor or lab tech check your circuit before continuing.
6. Turn on the high energy power supply. Slowly increase the voltage to 2500V.
7. Turn on the 500V power supply and slowly increase the voltage to 500V. This will
deflect the beam in the opposite direction of the magnetic field.
8. Turn on the voltage supply to the Helmholtz coils. Adjust this voltage (and coil current)
until the magnetic field of the coils balances the electric field of the deflection plates.
Hence, the path of the electrons should be “straight”. Record this current.
9. Decrease the high voltage and 500V power supplies to 0 V. Turn off all power supplies.