Abstract
IN his “Electric Waves” (see p. 361) Mr. Macdonald considers that electric waves may be propagated round a ring without being subject to any loss by radiation. The question whether this is possible is of great interest, as such waves might play an important part in atomic phenomena. It seems, however, that such waves cannot exist, except possibly in exceptional cases. For consider a spherical surface to be drawn enclosing the whole of the vibrating system. The electric force cannot vanish at all points of this surface, for the sphere may be as close to the conductors as we please. From the value of the force, and the condition that at infinity any motion that there may be must consist of outwardly progressing waves., we can find by spherical harmonic analysis the field at any point outside the sphere. The result is that in any case the field cannot at all distant points be of an order lower than that of I/r ; there must j be loss of energy by radiation. For a thin circular wire I a fundamental mode of vibration is determined, to a first approximation at least, in Proc. Camb. Phil. Soc., vol ix. p. 326; and the case of a wave progressing round the wire can be deduced by compounding two such vibrations differing in phase. The determination of the resultant disturbance at a great distance involves Bessel's functions in general, but it can be proved without difficulty that for points on or near to the axis of the ring it consists of divergent waves. The consequent rate of loss of energy is of the order of unity, while the energy held is of the order of log (α/…), where … is the radius of the wire and α that of the circle. The decrement is hence of the order of 1/log (α/…), as found in the paper referred to.
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POCKLINGTON, H. Permanent Electric Vibrations. Nature 67, 486 (1903). https://doi.org/10.1038/067486c0
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DOI: https://doi.org/10.1038/067486c0
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