Basic Elements of Electrostatics

Classical electromagnetic phenomena can be understood completely in terms of Maxwell’s equations (a set of partial differential equations for electric and magnetic fields) and a set of supplementary equations, which address the response of different materials to these fields. For this reason one could begin with the specification of these equations and concentrate on the discussion of methods for their solution and on their interpretation in terms of physical concepts. It is, however, more useful to follow the historical development of the theory and assemble the relevant equations piece by piece. If one follows this path, the first topic one has to address, is electrostatics, which involves qualitative statements on electric charges and the structure of matter. The more quantitative aspects are concerned with the fundamental electric forces between stationary charged objects, as expressed in Coulomb’s law. The basic form of this law characterises the forces between pairs of ideal point charges. An extended charged body can be imagined to consist of a superposition of point charges. The superposition principle allows the consideration of arbitrary charge distributions and the characterisation of stationary electric fields in terms of the theorem of Gauss. This theorem can be used for the direct calculation of electric fields of simpler charge distributions and for establishing the basic differential equation of electrostatics, the Poisson equation. With the aid of these equations the treatment of more advanced aspects, as the response of materials to external stationary electric fields, is possible.