1. Chapter 4 Electrostatic Fields in Matter
4.1 Polarization
4.2 The Field of a Polarized Object
4.3 The Electric Displacement
4.4 Self-Consistance of Electric Field
and Polarization; Linear Dielectrics

2. 4.1 Polarization 4.1.1 Dielectrics
4.1.2 Induced Dipoles and Polarizability
4.1.3 Alignment of polar molecules
4.1.4 Polarization and Susceptubility

3. 4.1.1 Dielectrics According to their response to electrostatic field,
most everyday objects belong to one of two large classes:
conductors and
insulators (or dielectrics): all charges are attached to specific atoms or molecules.
Stretching and rotating are the two principle mechanisms
by which electric fields can distort
the charge distribution of a dielectric atom or molecule.

4. 4.1.2 Induced Dipoles and Polarizability
applied
A neutral atom
Polarized atom
Atomic polarizability
A simple estimate:
The field at a distance d from the center of a uniform charge sphere
At equilibrium,
(v is the volume of the atom)

5. 4.1.2 Usually the most general linear relation
( is polarizability tensor)
or in (x,y,z)
aij depend on the orientation of the axis you chose.
It’s possible to select axes such that aij = 0 for

6. 4.1.3 Alignment of Polar Molecules
Polar molecules have built-in, permanent dipole moments s
applied electric field
(uniform)
Torque

7. 4.1.3 If the applied electric field is nonuniform,
the total force is not zero.
for short dipole,

8. 4.1.4 Polarization and Susceptibility
The polarization of a polarized dielectric
dipole moment per unit volume
is electric susceptibility tensor
for linear dielectric
is electric susceptibility

9. 4.2 The Field of a Polarized Object
4.2.1 Bound charges
4.2.2 Physical Interpretation of Bound Charge
4.2.3 The Field Inside a Dielectric

10. 4.2.1 Bound charges
bound charges:
surface charge
volume charge

11. 4.2.2 Physical Interpretation of Bound Charge
and
represent perfectly genuine accumulations of charge.
for uniformly distributed dipoles
for a uniform polarization and perpendicular cut s

12. 4.2.2 (2) for a uniform polarization and oblique cut
for the polarization is nonuniform ,

13. 4.2.2 (3)
Ex.2
Ex.9 of chapter 3
potential of a dipole moment

14. 4.2.3 The Field Inside a DielectricV
averaged
microscopic
microscopic field is defined as the averaged field over region
large enough.
dielectric
microscopic field at P or
out

15. 4.2.2 (4)
Ex.3 as Ex.2 s
for points outside,

16. 4.2.3
Ex.3
(averaged field)
uniform or

17. 4.3 The Electric Displacement
4.3.1 Gauss’s Law in The Presence of Dielectrics
4.3.2 A Deceptive Parallel

18. 4.3.1 Gauss’s Law in The Presence of Dielectrics
bound
free
Gauss’s Law
Gauss’s Law
electric displacement

19. 4.3.1
Ex.4 R r
inside
need to know
outside
>

20. 4.3.2 A Deceptive Parallel or one equation
need 2 more equations [ i.e., ]
to get unique solution
one unknown V, one equation. ?
One equation: ?

21. Polarization; Linear Dielectrics
4.4 Self-Consistence of Electric Field and
Polarization; Linear Dielectrics
4.4.1 Permittivity, Dielectric Constant
4.4.2 Special Problems Involving Linear Dielectrics
4.4.3 Energy in Dielectric System
4.4.4 Forces on Dielectrics
4.4.5 Polarizability and Susceptibility

22. 4.4.1 Permittivity, Dielectric Constant
self- consistence
for linear dielectrics
permittivity
permittivity of free space
dielectric constant

23. 4.4.1 (2) Ex.5 ? for r < a for r > a for b > r > a
dielectric ?
for r < a
for r > a
for b > r > a
for r > b

24. 4.4.1 (3)
for b > r > a
at r = b
at r = a

25. 4.4.1 (4) ? even in linear dielectric may or may not ?
If the surface or the loop is entirely in a uniform linear dielectric,
But for
vacuum
Dielectric

26. 4.4.1 (5) Q

27. 4.4.2 Special problems Involving Linear Dielectrics
Ex.7 ?
Method 1.

28. 4.4.2 (2)
dielectric constant
Method 2.

29. 4.4.2 (3)
Ex.8

30. 4.4.2 (4)
Total bound charge
Method 1.

31. 4.4.2 (5)
Method 2. method of image

32. 4.4.2 (6) Satisfy Poission’s eq
The potential shown at above is the correct solution.

33. 4.4.3 Energy in Dielectric System
Suggestion:
to charge a capacitor up
with linear dielectric (constant K)
energy stored in any electrostatic system (vacuum)
with linear dielectric

34. 4.4.3 (2)
derivation:
, for linear dielectric,

35. 4.4.4 Forces on dielectrics
with Q constant

36. 4.4.4 (2)
with V constant, such as with a battery that does work,

37. 4.4.5 Polarizability and Susceptibility1.
polarization for linear dielectric
susceptibility
induced dipole moment of each atom or molecular
atom polarizability
What is the constant between α and Xe ?
non-self-consistent field 2. 3. 4. 5.
5 equations, 5 variables

38. 4.4.5 (2)

39. 4.4.5 (3) Clausius-Mossott formula
Lorentz-Lorenz equation in its application to optics