A mechanical analogy and graphical method for explaining negative transconductance in crossed electrostatic and magnetic fields

The Numerous electronic devices utilize crossed electric and magnetic fields, but only the very simplest of cases may be analyzed by analytical methods. The purpose of this study is to demonstrate the use of a mechanical analogy and graphical methods in the solution of the more complex problems of this type. Specifically, these methods were employed to explain the phenomena of negative transconductance in crossed fields. To the best of the writer’s knowledge, the graphical method derived in this study is the first method, other than that of conformal mapping, which enables one to plot the path of electrons in crossed fields, and the first attempt to apply a mechanical analogy to such fields in vacuum tubes consisting of more than two elements.