Electrostatics in Materials Revisited: The Case of Free Charges Combined with Linear, Homogeneous, and Isotropic Dielectrics

Abstract

Here we revisit the electrostatics of material systems comprising of free charges and linear, homogeneous, and isotropic (LHI) dielectrics. We focus on D(r) suggesting that this is the primary vector field of electrostatics. We show that D(r) is sufficient to conceptually describe all underlying physics and to mathematically accomplish all necessary calculations, beforehand, independently of the secondary vector fields P(r) and E(r) that, if needed, can be easily calculated from D(r). To this effect, we introduce a P-D electric susceptibility, χε, with −1≤χε≤0, that couples linearly P(r) with D(r) (instead of the standard P-E electric susceptibility, χe, with 0≤χe∞, that couples linearly P(r) with E(r)). This concept restores the somehow misleading causality/feedback between P(r) and E(r) of the standard formulation, captures efficiently the underlying physics, enables electrostatics to obtain a form analogous to that of magnetostatics, and facilitates analytical/computational calculations in relevant systems. To document these claims, we provide technical means, among others, the free scalar potential, Ufr, and clarify the conditions that enable the calculation of D(r) on a standalone basis, directly from the free charge density, ρf, and the electric susceptibility, χε, of the LHI dielectrics. Our concept sets interesting perspectives for the treatment of all dielectrics.

Keywords

• electrostatics in materials
• dielectrics
• electric polarization
• electric susceptibility