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# Measurement of Electron e/m Using a Modified Magnetron

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.
This Demonstration proposes a simplified version of a magnetron, which might be used in a student laboratory measurement of . A modified diode vacuum tube, filled with gas at low pressure (~ torr), generates electrons by thermionic emission from a rectangular tungsten cathode (at temperatures in the range of 800–1000 ºC). The anode or plate, with variable positive potential , collects the emitted electrons. The diode is placed in an air core solenoid, which produces a uniform magnetic field along its axis (, where is the number of coils per unit length and is the current through the solenoid). The plate current is measured as a function of voltage and magnetic field. For correct combinations of and , the curvature of the electron trajectories returns the electrons to the cathode and reduces the current to the anode to zero. A measurement of , to three significant figures, is given by choosing values of and that are just sufficient to give an ammeter reading of zero. A useful strategy is to fix the value of and then decrease until the reading jumps to zero.
In Details, the formula for the ratio is derived. The currently accepted value equals C/kg. Several sources mention a variant of this experiment carried out using a Ferranti GRD7 valve. We have not been able to track down the original reference.

### DETAILS

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%.

### PERMANENT CITATION

Contributed by: S. M. Blinder
After a suggestion by H. K. Nahan
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