Magnetic Deflection of Electrons Using Vacuum Tubes

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By Tim Raney ...bald engineer guy with glasses.

This paper summarizes experiments using a vacuum tube to determine the magnetic field necessary to prevent electrons from reaching the anode in a high vacuum diode. In addition to determining this “magnetic cut-off” for a given electron energy, the experiment includes determining the magnetic flux of an air-core solenoid and calculating the velocity for 10 volt electrons. This summary also lays the foundation for determining the electron charge to mass ratio (e/m) using data collected in this experiment. This experiment is based on the “Hull Method” devised by the inventor of the magnetron diode tube in 1921 (Hoag and Korff, 1948). This paper is limited in its treatment and does not include the many other interesting physics experiments an experimenter can do with vacuum tubes, i.e., ionization potentials and thresholds; research in elementary plasma physics, etc.

The equipment consisted of a conventional anode circuit for a 705A half-wave diode. The 705A tube is a high voltage diode with a peak inverse voltage (PIV) rating of 10KV. Of importance to this experiment is the diode anode and cathode geometry (not shown in schematic). The experimenter can use other diodes with similar electrode geometry; the 705A was selected based on its availability. The cathode is a tungsten filament coaxially mounted with respect to a cylindrical anode. Filament electron emission is perpendicular to the axis of the anode. Consequently, the magnetic field from a coaxial solenoid is at right angles to the electron flow. The filament supply consisted of a 5-volt transformer with bridge rectifier and a 5-ohm, 8-ampere, slide-wire rheostat. The anode supply was a variable DC power supply. A milliammeter was used in the anode circuit and all circuits were protected by the requisite switches and fuses. The equipment also included an air-core solenoid with 30 turns of #14 magnet wire. Its circuit consisted of a step-down transformer, bridge rectifier, filter capacitor and variable resistor. The solenoid was mounted coaxially with the tube envelope as shown.

Results and Data
The following data are based on observations and calculations resulting from the experiment. SI units are used unless otherwise noted.

Experimental Data:

Calculation of magnetic flux for the solenoid is derived from B = 2pKl (NI/r), where B is in Tesla, Kl is equal to 6.28X10-7, the magnetic permeability of free space; N = 30 [turns of wire]; I = current (in amperes); radius (r) = 0.0318 meters (Sears and Zemansky, 1965). Current ranged from 5 to 15 Amperes. The data resulting from this equation shows a linear relationship between current and flux in the solenoid. The anode current (Ip) to flux shows an inverse relationship, i.e., Ip decreases as magnetic flux increases, showing that fewer electrons reach the anode at higher flux values. The anode current continues to decrease to the magnetic cut-off point, where no electrons reach the anode. This cut-off point occurred when the magnetic flux was approximately 0.0520 Tesla (520 Gauss) and higher. If the electrons had a greater kinetic energy, i.e., a higher potential applied to the anode circuit, a greater magnetic flux would be required to deflect the electrons from the anode.

The velocity for the 10 volt (10 eV) electrons was calculated using:  Vl = 10 volts and charge (C) is 1.6 X 10-19 Coulombs the electron rest mass is 9.109 X 10-31 kg:

The experiment showed that above 0.0520 Tesla (520 Gauss), IP for the 705A diode was zero or very close. This result indicates this magnetic field is sufficient to deflect electrons completely with a kinetic energy of 10 eV. A linear inverse relationship exists between IP and magnetic flux and indicates that at higher energies, the electrons would require correspondingly greater magnetic fields for complete deflection to occur.  Since these relationships are linear, estimates of the magnetic cut-off can be made at higher electron energies.  Additionally, with the data from this experiment, it is also possible to determine the charge to mass ratio (e/m) for an electron, since all variables have either been calculated or determined through the experiment. However, unless the physical dimensions of the electrodes are accurately known, the results will be inaccurate by at least an order of magnitude. Ways to resolve this dilemma include using a “burned out” diode and carefully breaking it and accurately measuring the cathode, anode and the relative electrode spacing. Another option is to use an optical instrument known as the cathetometer to make accurate measurements. This device is a small telescope with scale that is designed to read thermometers (etc.) from a short distance, i.e. 30-cm.

The experimental results also indicate the electrons acquire a velocity of 1.87 X 106 meters per second as they travel from the cathode when a potential of 10 volts is applied. Under the influence of the magnetic field, the electrons describe a circular or cycloidal trajectory where they completely miss the anode if the magnetic field is strong enough.  If the electrons are deflected and do not reach the anode, electron flow in the anode circuit ceases.  This point depends on the particular tube, magnetic field and anode potential. The equipment and procedures used in this experiment are also applicable to other high vacuum diodes at different potentials. However, a possible limitation is the ability to produce stronger magnetic fields to deflect the higher kinetic energy electrons that result from using greater potentials.

As electron energy increases, i.e., when higher anode potentials are applied, velocity and the kinetic energy also increase significantly. This increase requires a correspondingly higher magnetic field in the solenoid as mentioned above. Additionally, as velocity increases rapidly with applied potential, the experimenter must account for the electrons’ change in mass as it approaches the velocity of light (c). To determine the velocity of these near-relativistic electrons, the experimenter must apply the principles of relativity. The classical equation (above) for determining electron velocity is not appropriate. An electron gains mass as its velocity increases (since mass and energy are equivalent, E = mc2; any increase in electron velocity requires energy).  As this electron goes faster, it possesses more kinetic energy than it did at rest. A high velocity electron is heavier because energy has been applied to it, verses when at rest.

An experimenter can use commercial vacuum tubes to study important areas of physics that include ionization, charged particle behavior and elementary plasma physics. This experiment was successful in determining the magnetic field required to deflect electrons of from the anode and is a starting point for many other experiments using commercial vacuum tubes.

The following references were used in the preparation of this paper. Where page numbers are not listed, these references were used in a general way.

Chabay, R.W. and Sherwood, B.A., Electric and Magnetic Interactions.  John Wiley and Sons, Inc., New York, 1995.

Hoag, J.B. and Korff, S.A., Electron and Nuclear Physics, (3rd Ed.). D. Van Nostrand Company, Inc. New York, 1948, pg. 37 and tables 9 and 10, pgs. 486-487.

Sears, F.W. and Zemansky, M.W., University Physics (3rd Ed., Part 2). Addison-Wesley Publishing Company, Inc., Reading, MA, 1965.

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