Module 2 : Electrostatics
Lecture 11 : Conductors and Dielectric
  Gauss's Law in a Dielectric :
We have seen that the effect of polarization of a dielectric is to produce bound charges of volume density and surface density , given by
 
  The total electric field of a system which includes dielectrics is due to these polarization charge densities and other charges which may be present in the system. The latter are denoted as free charges to distinguish them from charges attributable to polarization effect. For instance, the valence charges in a metal or charges of ions embedded in a dielectric are considered as free charges.
  The total charge density of a medium is a sum of free and bound charges
 
  We can now formulate Gauss's law in the presence of a dielectric. Gauss's Law takes the form
 
  Substituting , we get
 
  The electri displacement vector is defined by
 
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