# Measurement of Electron *e*/*m* Using a Modified Magnetron

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The magnetron is an electronic tube (valve in British) used to produce microwave radiation. It was essential for the Allies' development of radar in World War II and is also the power source for microwave ovens. A functioning magnetron usually operates at voltages too high to be safe for student experiments. Moreover, the sought-after electron ratio is deeply embedded in the voltage, magnetic-field, and resonant radiation-frequency characteristics.

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Contributed by: S. M. Blinder (March 2011)

After a suggestion by H. K. Nahan

Open content licensed under CC BY-NC-SA

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An electron of mass and charge moving in an electric field and a magnetic field is given by the Lorentz force equation . For crossed electric and magnetic fields with constant magnitudes, the problem can be simplified. The speed of the electron in an accelerating voltage is given by . The perpendicular magnetic field will then deflect the electron into a circular orbit such that . Eliminating between the last two equations gives . When , where is the distance between the anode and cathode (assumed equal to 1 cm), the plate current drops to zero. The charge to mass ratio is then given by . The experimental error is in the range of 1%.

For more information on the magnetron, see http://www.radartutorial.eu/08.transmitters/tx08.en.html.

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