Figure1 Typical Set up
Introduction
In this activity we will measure the charge to mass ratio, e/m, of the electron. Our apparatus will be the PASCO Model SE-9638 e/m Apparatus as shown in figure 1. The method is similar to that used by J. J. Thompson in 1897. A beam of electrons is accelerated across a known potential difference, so the velocity of the electrons is known, into a region of uniform magnetic field. The magnetic field is perpendicular to the electron beam and produced by a pair of Helmholtz coils. Helmholtz coils produce a uniform magnetic field near the center of the cylinder defined by the coils, the magnitude of which can be calculated quite accurately.
Q1) If a beam of electrons is sent into a uniform magnetic field that is perpendicular to the beam, describe the resulting motion.
Description of the Apparatus
The
e/m Tube—The e/m tube (see Figure 2) is filled with helium at a pressure of
10-2mm
Hg, and contains an electron gun and deflection plates. The electron beam leaves a visible trail in
the tube, because some of the electrons collide with helium atoms, which are
excited and then radiate visible light. The
electron gun is shown in Figure 3. The
heater heats the cathode, which emits electrons. The electrons are accelerated by a potential
applied between the cathode and the anode.
The grid is held positive with respect to the cathode and negative with
respect to the anode. This helps focus
the electron beam.
The Helmholtz Coils—The geometry of Helmholtz coils—the radius of the coils is equal to their separation—provides a highly uniform magnetic field. The Helmholtz coils of the e/m apparatus have a radius and separation of 15 cm. Each coil has 130 turns. The magnetic field (B) produced by the coils is proportional to the current through the coils.
Mirrored Scale—A mirrored scale is attached to the back of the rear Helmholtz coil. It is illuminated by lights that light automatically when the heater of the electron gun is powered. By lining the electron beam up with its image in the mirrored scale, you can measure the radius of the beam path without parallax error.
Procedure
1. Set up
If you will be working in a lighted room, place the hood over the e/m apparatus. Flip the toggle switch on the e/m apparatus to the e/m MEASURE position. Turn the current adjust knob for the Helmholtz coils to the OFF position. Connect the power supplies and meters to the front panel of the e/m apparatus, as shown in Figures 4 and 5. On the DMM to be used as the ammeter, place the banana cable in the 10 A socket.
Figure 4 Schematic of Apparatus set up
Adjust the power supplies to the potentials shown in the table
below. The voltmeter in Figure 4 is not
necessary Use the reading from the
|
Electron
Gun |
|
|
Heater: |
6.3 VAC or VDC |
|
Electrodes: |
150 VDC |
|
HelmHoltz Coils: |
6 VDC |
2. Data Acquisition
Wait several minutes for the cathode to heat up. When it does, you will see the electron beam emerge from the electron gun. Check that the electron beam is parallel to the Helmholtz coils. If it is not allow your instructor or lab tech to adjust it. Adjust the focus knob to obtain as tight a beam as possible.
Slowly turn the current adjust knob for the Helmholtz coils clockwise. Watch the ammeter and take care that the current does not exceed 2 A.
Q2) As you increase the current to the Helmholtz coils, what effect is there on the beam? Why?
Adjust the current to the Helmholtz coils so that the beam
curves over the scale at a right angle. Carefully
read the current to the Helmholtz coils from your ammeter and the accelerating
voltage from the voltmeter on the
a.
Current to Helmholtz coils = I =
_________________________
b. Accelerating voltage = V = _____________________________
Carefully measure the radius of the electron beam. Look through the tube at the electron
beam. To avoid parallax errors, move
your head (up-down and side-side) to align the electron beam with the
reflection of the beam that you observe on the mirrored scale. Measure the radius of the beam as you see it
on both sides of the scale, and then average the results. Record your result below.
Electron beam radius = r = _____________________________
Increase the accelerating potential to 200 V.
Q3) What effect is there on the radius of the electron beam.
Q4) Explain why this is the case.
Adjust the current on the Helmholtz coils to return the beam to the previous position. However, don’t exceed 2 A.
Q5) Did you increase or decrease the current?
Q6) What effect did this have on the magnetic field strength?
Data Analysis
Q7) What force provides the centripetal force to curve the electron beam? Write the expression for this force. Use e to denote the charge of the electron.
Q8) Set the force you answered in Q7 equal to mv2/r and solve for the radius of the beam.
Q9) The electrons start essentially at rest at the cathode and are accelerated by a potential difference V between the cathode and anode. Find an expression for the speed of the electrons as they reach the anode.
Q10) Place this expression that you obtained for the speed in Q9) into the expression you obtained in Q8). solve this expression for the charge to mass ratio of the electron, i.e. e/m.
The magnetic field produced near the axis of a pair of
Helmholtz coils is given by the equation:
where a is the radius
of the Helmholtz coils, N = 130 is the number of turns on each Helmholtz coil, 
the permeability constant 
Tm/A and I is the current through the Helmholtz coils.
Q11) Determine the magnetic field strength for the case where you measured the radius of the beam.
Q12) Substitute your values for the magnetic field strength. accelerating potential and beam radius into the expression you obtained in Q10) to determine the e/m for the electron.
Q13) Look up the values of e and m for the electron in the text and determine the value of e/m .
Q14) Compare your value to the measured value by determining the percent difference between your measured value and the value you determined in Q13.
Figure 5
Note: The
digital ammeter is not shown is this diagram.
It is shown, however, in Figure 4.
The digital voltmeter shown in Figure 4 is not necessary. Use the reading on the