Chapter 6 Dielectrics: I Electric Polarization p Bound Charges a Gauss Law Electric Displacemant D
Chapter 6 Dielectrics: I ◼ Electric Polarization P ◼ Bound Charges ◼ Gauss’ Law, ◼ Electric Displacemant D
In contrst to conductors dielectrics have no free charges that can move through the material under the influence of an electric field All electrons are bounded Positive and negative charges can move in opposite direction with a small displacement of atomic dimensions
In contrst to conductors, dielectrics have no free charges that can move through the material under the influence of an electric field. All electrons are bounded. Positive and negative charges can move in opposite direction with a small displacement of atomic dimensions
a dielectric in which this charge displacement has taken place is said to be polarized, and its molecules are said to possess induced dipole moments. See Fig6-1) These dipoles produce their own field Which adds to that of the external charge The dipole field and the external applied field can be comparable in magnitude
A dielectric in which this charge displacement has taken place is said to be polarized, and its molecules are said to possess induced dipole moments.(See Fig6-1) These dipoles produce their own field, which adds to that of the external charge. The dipole field and the external applied field can be comparable in magnitude
+ 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 Q 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 applied electric field also tends to orient molecular dipole moments so that the dipoles are aligned with the external field However, thermal motions of molecules tend to destroy this alignmant An equilibrium polarization is thus established in which there is a net alignment, on the average
The applied electric field also tends to orient molecular dipole moments, so that the dipoles are aligned with the external field. However, thermal motions of molecules tend to destroy this alignmant. An equilibrium polarization is thus established, in which there is a net alignment, on the average
6.1 Electric Polarization p The electric polarization P is the dipole moment per unit volume at a given point where p- the average electric dipole moment per molecule 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 Pb=-V. P, 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 d T=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 do d where n is the unit vector normal to the surface Conclusion: the bound surface charge density 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 P. da Thus the net charge that remains within T isQ Q=-/s P da By the divergence theorem -/ P da=-(v p)dr Th Us pb V·P