Open AccessThe path of an electron in combined radial magnetic and electric fields
Author(s) -
H. S. Allen
Publication year - 1911
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1911.0037
Subject(s) - electric field , physics , magnetic field , electron , focus (optics) , conic section , vertex (graph theory) , computational physics , atomic physics , optics , geometry , mathematics , quantum mechanics , graph , discrete mathematics
1. In the course of an investigation with a focus tube, in which the anti-cathode was a magnetic pole, some interesting observations were made with regard to the distribution of the fluorescence on the walls of the tube as the magnetic field varied. In order to explain the changes observed, the path of an electron in a radial field was investigated mathematically, and was found to lie on a right circular cone whose vertex coincides with the magnetic pole. If the surface of the cone is developed into a plane the trace of the path is a conic section, with the vertex as focus. This result continues to hold when an electric field, with its lines of force radiating from the same point, is superposed on the magnetic field. Although the actual distribution of electric intensity in a highly exhausted tube must differ widely from that here considered, the investigation sufficiently explains the facts observed.Theoretical . 2. The object is to find the path of a particle of massm carrying a chargee in combined magnetic and electric fields, when the lines of force are radial and are such as might be due to a single pole of strengthμ coincident with an electric chargek .