Surface charges from a sensing pixel perspective
Maurice M. Klee · American Journal of Physics · 2020
A new technique is presented for understanding how charges distribute themselves on the surface of a conductor during current flow. The technique uses a set of three-dimensional calculation cells (“pixels”) that cover the conductor's surface and contain internal charge. The pixels have two faces separated by an infinitesimal, but finite, distance, with one face being conductive and the other non-conductive. Each pixel acts as a sensor by responding to (“sensing”) the net Coulomb electric field at its conductive face due to charges in other pixels and charges at the current source and sink (collectively, the external charges). Through a feedback process implemented as a series of time steps, the pixels' internal charges adjust themselves until, at each pixel, a balance is achieved between the electric flux at the conductive face due to the external charges and that due to the pixel's internal charge. Specifically, at each time step, for each pixel at which there is flux imbalance, charge will move into or out of the pixel's conductive face in the direction that reduces the imbalance. The charge distribution for the set of pixels that gives balanced flux for each of the pixels is the system's steady state and for systems where retardation effects are not significant, e.g., biological systems, the time series is the path by which the system reaches that state. Fluxes are calculated using solid angles and because solid angles do not vary with a change in scale, the charge distribution, when expressed in terms of charges/pixel, as opposed to charges/area, depends only on the system shape.