A new theorem in electrostatics and its application to calculable standards of capacitance [5]

Abstract

Although capacitance has the dimensions of length only, usually two or more separate lengths are needed to compute the capacitance of the various forms that have been used as standards. In seeking aform of calculable capacitor involving a minimum number of determinations of length, we have investigated cylindrical systems and have discovered a particular class of capacitor in which the capacitance depends on one length only to the first order. For example, if a square cylinder is constructed from four conducting planes which are insulated from each other at the corners, then the direct capacitances per unit length of cylinder, between each pair of opposing inside faces, are equal and independent of the size of the square. This direct capacitance was calculated as cm./cm., and it was also calculated that if the cross-section was rectangular with a ratio of sides of 1 + δ, δ ≪ 1, then the mean of the two cross-capacitances was cm./cm. These calculations confirmed that, providing the asymmetry was not too great, a standard capacitor could be constructed which required only one length measurement for the computation of its capacitance. The length of the capacitor may be defined by insulating a length of one face from the remainder of that face, which remainder functions as a guard. © 1956 Nature Publishing Group.