  Two conducting nanostructures on a conducting base-plate, and with a common
applied electrostatic field, interact because their electrons are a common
electron-thermodynamic system. Except at small separations, the interaction
reduces the apex field enhancement factor (FEF) of each nanostructure, by means
of "charge blunting". A parameter of interest is the fractional reduction (-d)
of the apex FEF, as compared with the apex FEF for the same emitter when
standing alone on the base-plate. For systems of two or a few identical
post-like emitters, or regular arrays of such emitters, details have been
investigated by methods based on numerical solution of Laplace's equation, and
by using line-charge models. For post separations c comparable with post height
h, several authors have shown that the variation of (-d) with c is well
described by formulae having exponential or quasi-exponential form. By
contrast, explorations of the two-emitter situation using the
"floating-sphere-at-emitter-plane potential" (FSEPP) model have predicted that,
for large c-values, (-d) falls off as 1/c*c*c. Numerical Laplace-type
simulations carried out by de Assis and Dall'Agnol (arXiv:1711.00601v2) have
confirmed this limiting dependence for six different situations involving pairs
of protruding nanostructures; hence they suggest it as an universal law. By
using the FSEPP model for the central structure, and by adopting a "first
moments" representation for the distant structure, this letter shows that a
clear physical reason can be given for this numerically discovered general
limiting (1/c*c*c) dependence. An implication is that the quasi-exponential
formula found useful for c comparable with h is simply a good fitting formula.
A second implication is that the FSEPP model, which currently is used mainly in
nanoscience, may have much wider applicability to electrostatic phenomena.
