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

Abstract

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 (log_ε 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.