6. 1 Electric Polarization p The electric polarization P is the dipole moment per unit volume at a given point P= N1 where p- the average electric dipole moment per molecu N-the number of molecules per unit volume
6.2 The Bound Charge Densities Pb and ob The displacement of charges within the dielectric gives rise to net volume and surface charge densities V·P Pn where n is the normal to the surface pointing outward Figure 6-1 Under the action of an electric field E which is the resultant of an external field and of the field of the dipoles within the dielectric, positive and negative charges in the molecules are separated by an average distance s In the process a net charge dQ= NOs.da crosses the surface da, N being the number of molecules per unit volume and o the positive charge in a molecule. The vector da is perpendicular to the shaded surface. The circles indicate the centers of charge for the positive and for the negative charges in one molecule
The Surface Bound Charge Densities ob(see Fig 6-1) The positive charges move along E, and the negative charges move in opposite direction. The separation btwn them is s, forming a parallelepiped with cross section da The volume of this parallelepiped is dr=s·da the net charge accumulated on da is dQ= NQs da= Np da=P da where Q is the point charge of a molecule
Thus the bound surface charge density is Pn da where n is the unit vector normal to the surface C onclusion e bound surface charge densi ity is the normal component of the polarization P at the surface
The bound volume charge density pb As just shown, the net charge flowing out of a volume T across an element da is p. da Thus the total net charge flowing out of the surface s bounding t is a Thus the net charge that remains within T is-Q Pda By the divergence theorem IsP da=-(VP)d Thus pb=-VP