Basic Equations of Electrostatics

Besides the Gauss’ law, through which the sources and sinks of the stationary electric fields of electrostatics are introduced, a second set of equations characterises the absence of vortex structures for such fields. Both sets of equations can be written in integral or in differential form. The integral form allows a general discussion of the behaviour of fields passing through layers of charge and the distribution of charges in conducting materials. The differential form leads, after the introduction of the concept of the electric potential and the proper representation of charge densities with the aid of distributions (especially the \(\delta \) -function), to a compact version of electrostatics in terms of the Poisson/Laplace equations. The introduction of the electric potential will be investigated in detail for simple charge arrangements. The final part of the second chapter addresses the ability of the electric field to store energy using the practical concept of the energy density.