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1887

A new theorem in electrostatics with applications to calculable standards of capacitance

A new theorem in electrostatics with applications to calculable standards of capacitance

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© The Institution of Electrical Engineers
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The paper presents what is believed to be a new theorem in electrostatics, showing that the direct capacitance of a very general type of cylindrical 3-terminal capacitor is a constant, namely (logε 2)/4π2.The presentation and proof of this theorem is followed by a detailed analysis of a cylindrical 3-terminal capacitor of rectangular cross-section, in which the effects of various practical limitations are evaluated in quantitative terms. The results of similar analyses of cylindrical 3-terminal capacitors of other cross-sections are stated.As a consequence of this work, it appears that such cylindrical 3-terminal capacitors are extremely attractive as precise calculable standards of capacitance, only one precision length measurement being necessary to enable their capacitance to be computed to a high order of accuracy.

Inspec keywords: standards; capacitors; capacitance

Subjects: Capacitors

References

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      • A.M. Thompson , D.G. Lampard . A New Theorem in Electrostatics with Applications to Calculable Standards of Capacitance. Nature
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      • C. Snow . Formulas for computing Capacitance and Inductance. National Bureau of Standards Circular , 544
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      • L.C. Woods . Subsonic Plane Flow in an Annulus or a Channel with Spacewise Periodic Boundary Conditions. Proceedings of the Royal Society , 63 - 85
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