A review of electric scalar charge and electric current line, surface and volume arrays and their densities

Abstract

Traditional formal definitions of electric current surface and volume densities differ from those of the electric scalar charge, and are inconsistent with the notions of their elemental surface and volume electric current distributions or arrays. While any (elemental) electric scalar charge may be represented by a single symbol or as a product of a density and an elemental space, the surface and volume electric current elements are always only represented in the latter format. Furthermore, the line elemental current is displayed even more differently from the others as its direction is embedded in the line’s elemental length. Here we show an analysis that eliminates all the above inconsistencies, and advances the notion of three different interpretations for the surface and volume densities of both scalar (electric scalar charge) and vector (electric current) quantities. The underlying feature is that while current is the flow or motion of electric scalar charges and is a vector, it cannot be represented only by the electric scalar charge’s time rate of change, which is still a scalar. Having identified a proper mathematical representation of current as vector quantity, we advocate that the basic concept of density of any physical quantity should remain the same at any level of study and application. Although the presentation is at an intermediate university/college level, its conception and application is universal.