SIZE DEPENDENCE OF FORCE BETWEEN PARALLEL PLANAR JELLIUM METAL-SURFACES AT SMALL SEPARATION

In earlier work, the jellium model has been employed, within the linea rized Thomas-Fermi (TF) approximation to calculate the force between t wo parallel planar conducting cylinders of infinite extension at small separation d. Such a theory has validity in the high density limit an d leads to the result F = Ad, where A is proportional to r(s)(-11/2), with r(s) the mean interelectronic spacing. Here the same model is emp loyed for two semi-finite conduction cylinders of equal radius R. A co mplete solution is presented for the electrostatic potential V, exact for all separations d within the TF model employed and numerical resul ts are presented for a range of values of d and R. Finally for finite d, the energy stored in the electrostatic field is studied. The consta nt A turns out to be size independent. Size effects enter the present model beyond the linear d regime of the force. It would be of interest if the size-dependence prediction thereby made could be rested using the atomic force microscope.