Boundary conditions for Electrostatic fields

In our discussions so far we have considered the existence of electric field in the homogeneous medium. Practical electromagnetic problems often involve media with different physical properties. Determination of electric field for such problems requires the knowledge of the relations of field quantities at an interface between two media. The conditions that the fields must satisfy at the interface of two different media are referred to as boundary conditions .

In order to discuss the boundary conditions, we first consider the field behavior in some common material media.

In general, based on the electric properties, materials can be classified into three categories: conductors, semiconductors and insulators (dielectrics). In conductor , electrons in the outermost shells of the atoms are very loosely held and they migrate easily from one atom to the other. Most metals belong to this group. The electrons in the atoms of insulators or dielectrics remain confined to their orbits and under normal circumstances they are not liberated under the influence of an externally applied field. The electrical properties of semiconductors fall between those of conductors and insulators since semiconductors have very few numbers of free charges.

The parameter conductivity is used characterizes the macroscopic electrical property of a material medium. The notion of conductivity is more important in dealing with the current flow and hence the same will be considered in detail later on.

If some free charge is introduced inside a conductor, the charges will experience a force due to mutual repulsion and owing to the fact that they are free to move, the charges will appear on the surface. The charges will redistribute themselves in such a manner that the field within the conductor is zero. Therefore, under steady condition, inside a conductor .