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Motion of Charged Particles in Electric and Magnetic Fields

Problem 3.394

Magnetron is a device consisting of a filament of radius \(a\) and a coaxial cylindrical anode of radius \(b\) which are located in a uniform magnetic field parallel to the filament. An accelerating potential difference \(V\) is applied between the filament and the anode. Find the value of magnetic induction at which the electrons leaving the filament with zero velocity reach the anode.

Reveal Answer
B⩽2bb2−a22meVB \leqslant \frac{2 b}{b^{2}-a^{2}} \sqrt{\frac{2 m}{e} V}
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