PNNL

Abstract

The solution of Poisson's equation for a point charge inside a closed conducting surface is a classical problem in electrostatics. The force on the charge due to the induced surface charge distribution, though more difficult to obtain, is of direct relevance to many precise physical instruments. We present a general treatment of this subject, employing a variety of analytical techniques for common conductor geometries-parallel plates, spheres, rectangular boxes and cylinders. A generic form is presented in which the "image charge" forces are expressed in terms of Taylor series about the center of symmetrical systems, with unitless coefficients varying with the geometry. Taken together the treatment here reveals an essential simplicity, namely, the unitless coefficients tend either toward unity or zero in physically sensible ways. This allows their estimation for more complex geometries not amenable to analytic treatment. Applications to ion cyclotron resonance mass spectrometry, including some results for extended charge distributions, are described.