Figure 5: e/m tube and Helmholtz coil electrical connections.
Measurement of the e/m ratio of an electron is a classic example of its particle behavior. An electron in a uniform magnetic field will orbit in a plane perpendicular to the field with a radius determined from Newton's Laws. In this lab a Helmholtz pair is used to produce a nearly uniform magnetic field. Electrons are produced from a hot cathode and focused into a narrow beam that is injected into the field with a non-zero angular momentum. The electron trajectory is visible because the tube is has a low partial pressure of argon. Some electrons colliding with the argon causing electronic excitations that decay via visible light production.
Equipment
Refer to Fig. 5 for the electrical connections to the e/m tube and the Helmholtz coils. Also note that the physical data for the Helmholtz coil construction are listed in Fig. 5.
Figure 5: e/m tube and Helmholtz coil electrical connections.
Apparatus
Before turning on any power supplies or plugging in any equipment, read all of the following instruction. Turn the 0-300V adjustment knob on the gun supply fully CCW before turning on power supply. Do not adjust the filament current knob for the 6.3VAC supply. Let the filament of the e/m tube warm up about a minute before applying the accelerating voltage. Reduce the accelerating voltage to zero before switching off the power supply.
Limit the accelerating voltage to 250 volts, although the supply will go higher.
Be very careful around the glass e/m tube. Hard knocks can cause the tube to implode, causing an expensive replacement as well as possible eye damage.
Part A: Operational Procedure
Plug in the stand with the HUD display and familiarize yourself with its use. The HUD display projects a scale that you can align in the plane of the electron orbit. Verify that the calibration of the projected scale is accurate. When the HUD scale is set correctly, there is no parallax between the projected scale and the object to be measured. Note that the projected scale may be rotated.
Turn on the Helmholtz supply and the gun supply. Turn up the gun energy to about 200 V. With the lights out slowly increase the Helmholtz coil current until the electron trajectory closes around on itself.
Part B: Experimental Procedures
Measure the diameter of the electron trajectory for several combinations of accelerating voltage and Helmholtz coil current (use at least 4 voltages and 4 currents). Include at least one accelerating voltage of 250 volts, the maximum that should be applied, and include at least one coil current that is the maximum the supply will furnish. When measuring the orbit radius, use different rotations of the projected scale for each current and voltage. This permits measurement of the diameter at different angular positions that can be averaged to reduce errors from non-uniform field effects.
Make a table with the following headings:
| Ve (V) | Im (amps) | R (m) | B (Tesla) | e/m (Coul/kg) | v (m/sec) |
Fill in the first three columns with your experimental data. The radii used in the table should be the averaged radii from the different orientations of the HUD display.
The remaining three columns are calculated from your experimental data. The magnetic field near the center of the tube due to the action of the Helmoltz coils can be calculated from:
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Eq. (7) |
The e/m values are computed by using Newton's second law for a circular orbit, the magnetic force on the electron, and the fact the kinetic energy of the electron is related to the electrostatic potential of the gun:
 |
Eq. (8a) | |
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Eq. (8b) | |
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Eq. (8c) |
Note that we are using non-relativistic equations. You should comment on their validity in your lab report. Your value of e/m should be independent of Ve or Im. Comment on the variations of your values in terms of experimental error. Compare your values of e/m with published the value.
 | School of Physics at Georgia Tech |