The Displacement field It is useful to separate the charge density into the bound charge rb and free charge rf: The displacement field: Note that that the electric field is irrotational, so E can be written as a gradient of a scalar. However, in general The vector D obeys different boundary conditions than E. field term matter term

polarization vector points in the same direction as E A common strategy: first find D for the specified free charge. Then determine P and E. Example: A long straight wire, carrying uniform line charge l, is surrounded by a rubber insulation out to a radius a. Find the electric displacement. We note that this expression holds everywhere: inside and outside the insulation. Outside, P=0; hence, What about electric field inside the insulation? How the dielectrics respond to an applied field? The answer to this question can be in principle obtained by quantum-mechanical calculations of electron-molecular structures. In most cases, however, this is not practical. Instead, we will introduce an empirical connection between P and E (or D and E), called the constitutive equation. polarization vector points in the same direction as E P

Isotropic Linear Dielectrics: Electric field proportional to polarization vector (dilute gasses, glass, plastics…). Remember: crystals are different! permittivity susceptibility dielectric constant Note that for dielectrics dielectric constant

Boundary conditions above below the normal component of the D-field is discontinuous across any interface: the tangential component of E is continuous across any interface

If both dielectrics are isotropic: 1 2