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Two conducting nanostructures on a conducting base-plate, and with a commonapplied electrostatic field, interact because their electrons are a commonelectron-thermodynamic system. Except at small separations, the interactionreduces the apex field enhancement factor (FEF) of each nanostructure, by meansof "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 whenstanding alone on the base-plate. For systems of two or a few identicalpost-like emitters, or regular arrays of such emitters, details have beeninvestigated by methods based on numerical solution of Laplace's equation, andby using line-charge models. For post separations c comparable with post heighth, several authors have shown that the variation of (-d) with c is welldescribed by formulae having exponential or quasi-exponential form. Bycontrast, 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-typesimulations carried out by de Assis and Dall'Agnol (arXiv:1711.00601v2) haveconfirmed this limiting dependence for six different situations involving pairsof protruding nanostructures; hence they suggest it as an universal law. Byusing the FSEPP model for the central structure, and by adopting a "firstmoments" representation for the distant structure, this letter shows that aclear physical reason can be given for this numerically discovered generallimiting (1/c*c*c) dependence. An implication is that the quasi-exponentialformula 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 innanoscience, may have much wider applicability to electrostatic phenomena.

Physical explanation of the universal "inverse-3rd-power-of-separation"  law found numerically for the electrostatic interaction between two  protruding nanostructures