Lecture ( 10 ) Polarization in Dielectrics , Dielectric Constant and Strength , and Continuity Equation

Polarization in Dielectrics
A dipole results from the displacement of the charges and the dielectric is said to be polarized



Polarization of a nonpolar atom or molecule

The dipole moment is P = Q d , if there are N dipoles in a volume ?v of the dielectric , the total dipole moment due to electric field is

We define polarization P ( C / m2 ) as the dipole moment per unit volume of the dielectric

Conclude : the major effect of the electric field on the dielectric is the creation of dipole moments that align themselves in the direction of ( E ) [this type of dielectric is said to be nonpolar]
The potential ( dV ) at an exterior point ( O ) due to dipole moment ( P dV ) is



Where

Applying the vector identity



Substituting this into equation ( dV ) and integrating over the entire volume (v’) of the electric , we obtain


We refer to ?_ps and ?_pv as bound ( or polarization ) surface and volume charge densities

If ?_v is the free charge volume density, the total volume charge density ?_tis given by

Hence

Where

Conclusion :
The net effect of the dielectric on the electric field ( E ) is to increase ( D ) inside it by amount ( P ) , some case the polarization ( P ) vary directly as the applied field ( E )

Where ?_e known as the electric susceptibility of the material

3.5 Dielectric Constant and Strength
Dielectric Constant




Dielectric Strength



Dielectric breakdown is said to have occurred when a dielectric become conducting


















3.6 Continuity Equation and Relaxation Time
Continuity Equation




Invoking divergence theorem

But

Substituting eq. ( 1 ) and eqs. ( 3 ) into eq. ( 2 ) gives

Or

For steady currents , ( (??_v)/dt=0 ) and hence ( ? .J=O ) showing that the total charge leaving a volume is the same as the total charge entering it.
The Relaxation Time





Note :
Relaxation time is short for good conductors and long for good dielectrics