An improved proximity force approximation for electrostatics

C. FOSCO; F. LOMBARDO; F.D. MAZZITELLI

ANNALS OF PHYSICS (NEW YORK)

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2012 vol. 327 p. 2050 - 2059

0003-4916

A quite straightforward approximation for the electrostatic inter- action between two perfectly conducting surfaces suggests itself when the distance between them is much smaller than the charac- teristic lengths associated with their shapes. Indeed, in the so called ‘‘proximity force approximation’’ the electrostatic force is evalu- ated by first dividing each surface into a set of small flat patches, and then adding up the forces due two opposite pairs, the contribu- tions of which are approximated as due to pairs of parallel planes. This approximation has been widely and successfully applied in dif- ferent contexts, ranging from nuclear physics to Casimir effect cal- culations. We present here an improvement on this approximation, based on a derivative expansion for the electrostatic energy con- tained between the surfaces. The results obtained could be useful for discussing the geometric dependence of the electrostatic force, and also as a convenient benchmark for numerical analyses of the tip–sample electrostatic interaction in atomic force microscopes.