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The approximate calculation of the electric field between a rod and a concentric ring by means of toroidal functions

The approximate calculation of the electric field between a rod and a concentric ring by means of toroidal functions

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The electric field set up when a live conductor in the form of a rod passes through the centre of an earthed ring of circular section is approximately calculated by replacing the rod by an hour-glass-shaped conductor of the same minimum radius. The resulting field is found terms of toroidal functions, numerical Tables of which are given. To find how closely the calculated results approach the true values for rod and ring, a systematic electrolytic-tank study is undertaken, and charts of the differences between theory and experiment are given. is found that the theoretical attack is successful in predicting the smallest figure to which the voltage gradient on the electrodes can be reduced, but that the conductor radii which will enable that figure to be realized are somewhat different in practice from those suggested by the theory.

References

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      • H. Frölich . (1958) , Theory of Dielectrics.
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      • A. Bolliger . Probleme der Potentialtheorie. Archiv für Elektrotechnik
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      • C. Neumann . (1864) , Allgemeine Lösung des Problems über den stationären Temperaturzustand eines homogenen Körpers welcher von irgend zwei nichtconzentrischen Kugelflächen begrenzt wird.
    4. 4)
      • W.M. Hicks . On Toroidal Functions. Philosophical Transactions of the Royal Society
    5. 5)
      • W.M. Hicks . On the Steady Motion of a Hollow Vortex. Philosophical Transactions of the Royal Society
    6. 6)
      • W. Fouquet . Dipolare Koordinaten und Kugelfunktionen. Zeitschrift für angewandte Mathematik und Mechanik
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