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Local Electromagnetic Fields

Published online by Cambridge University Press:  20 January 2009

H. Bateman
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§ 1. The radiation of electromagnetic charges from a moving point.

Let the electric charge associated with a moving point Q at time s be f(s). This charge is supposed to vary on account of the radiation of electric charges from Q in a variable direction, which, at time s, has direction cosines l (s), m (s), n (s) Using ξ(s), η(s), ζ(s) to denote the coordinates of Q at time s, and defining the effective time τ by means of the equation

the electromagnetic field may be specified by means of the potentials

where

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , February 1925 , pp. 85 - 89
Copyright
Copyright © Edinburgh Mathematical Society 1925

References

page 85 note * This field was obtained by the author when attempting to solve another problem proposed to him by Professor P. Ebrenfest when the latter was in Pasadena in 1924.

page 86 note * This is a simple generalisation of the field discussed in Physical Review, Vol. 17 (1921), p. 64.CrossRefGoogle Scholar

page 88 note * A simple example of a local field is mentioned in Physical Review, Vol. 23 (1924), p. 782Google Scholar.

page 88 note † Proc. Roy. Soc. Edinburgh. Vol. 46 (1926), p. 116.Google Scholar

page 89 note * Whittaker, E. T., Proc. London Math. Soc. (2), Vol. 1 (1903)Google Scholar. Bateman, H. Electrical and Optical Wave Motion, p. 7Google Scholar.