Image forces on a collection of charged particles near conducting surfaces

In a recent study, Vauge (2002) showed that particles in a charged aerosol system confined to a conducting cavity do not experience image forces provided the aerosol is treated as a continuous distribution in space. However, in reality, since an aerosol is a collection of discrete charges and not a continuum, we propose that the collective image–particle interactions have to be analysed using statistical techniques based on configuration averaging. Two cases are considered: (i) charged particles confined to a conducting spherical cavity and (ii) those distributed outside a conducting sphere which is insulated from the ground. It is shown that in both the cases, a given charged particle experiences an average attractive electric field due to its image charge and the average field due to the images of other charged particles present in the aerosol vanishes. This arises because the position of the particle is delta correlated with the position of its image charge, whereas it is non-correlated with the positions of the image charges of other particles. The proposition of Vauge conforms to the case of an image field at an arbitrary point and not to that on a charged particle. The study also investigates, for the first time, the root mean square fluctuations in the electric fields arising due to particle–particle and image–particle interactions. However, for the charge densities normally encountered in aerosol systems, these contributions are found to be quite small.