1. §9-3 Dielectrics Dielectrics：isolator Almost no free charge inside
The charges within it are bound in the range of
a molecule.
CH4
1. classify
Non-polar molecules dielectrics
The centers of positive and negative charge coincide in the absence of external E-field.

2. Polar molecules dielectrics
The centers of positive and negative charge do not coincide in the absence of external E-field.
H2O

3. 束缚电荷 2. The polarization of dielectrics bound charges
The polarization charges appear in dielectrics when an external E-field is supplied.
The polarization of the non-polar molecules
束缚电荷
Displacement polarization

4. 束缚电荷  The polarization of the polar molecules
Orientation polarization
束缚电荷

5. The difference between free charge and bound charge
Can move in the conductors freely and can leave the conductors.
Can not move in the dielectrics freely and can not leave the dielectrics.

6. 3. The electrostatic field in dielectrics
=external field + polar field
Special example：
Two metal plates + uniform dielectrics block
--relative permitivity

7. The relation of area charge densities between bound charge and free charge:

8. §9-4 Gauss’ law in dielectrics
Gauss’ Law in vacuum: =?
Special example：
Two metal plates + uniform dielectrics block S
From above:

9. S
permittivity
Gauss’ law of E-field in dielectrics
Free charge

10. Definition:
-- electric displacement vector
E-displacement flux ( D flux)
-- Gauss’ Law of
Free charge
Notes
 flux depends on the free charges in the Gaussian surface. But the itself depends on free charges and bound charges inside and outside Gaussian surface.

11.  -lines can describe the distribution of vividly.
The difference between -line and -line.
-line:originate on entire positive charges and terminate on entire negative charges.
Free and bound
-line:originate on positive free charges and terminate on negative free charges.
line

12. [Example 1]A metal sphere with radius R charges positive q0
[Example 1]A metal sphere with radius R charges positive q0. Put the sphere in the infinity uniform dielectrics(relative permittivity is r). Calculate: E- field outside the sphere. The area density of bound charge close to the metal spherical surface and the amount of bound charge on this thin surface.
Solution:The distribution of charges and E-field : spherical symmetry.
Choose Gaussian surface S : spherical surface with radius r

13. Direction:
 On the metal spherical surface, the area density of free charges:
the area density of bound charges in dielectrics close to sphere:

14. The amount of bound charges
----q has opposite sign with q0 ，and q < q0

15. [Example 2]Two parallel conductor plates have charge area density +、- respectively. Their potential difference is V0=300V as the space between them is vacuum. Keep the charges of the plates are constant and fill dielectrics (r=4)in half of their space. See in figure. Find：the potential difference between two plates=？the area density of bound charge on the top and bottom surface of the dielectrics=？

16. Solution ： Assume the area of plate is S，their distance is d
In vacuum:
After fill dielectrics in half space:
Assume at the area possessing dielectrics:
at the vacuum area :
then 

17. and 
Uniting  and 

18. The E-field between two plates:
The potential difference between two plates:

19.  the area density of bound charge
Bottom surface
Top surface

20. §9-2 Capacitors and their Capacitance
Capacitance—the ability (capacity) of holding charges.
1. The capacitance of an isolated conductor
--concern with the shape and size of the conductor.
Special example：
Charged spherical conductor:
has nothing to do with q、 U.

21. Two plates carry equal but opposite charges.
Definition
The capacitance of an isolated conductor:
C has nothing to do with Q、 U.
C depends on the shape , size of the conductor and the dielectrics surrounding it.
2. The capacitance of capacitor
Capacitor ：consist of two isolated conductors that they are closed to each other.
Conductor plates
Two plates carry equal but opposite charges.

22. Definition
The capacitance of a capacitor:
C has nothing to do with q、 V.
C depends on the shape , size, distance of the conductors and the dielectrics surrounding it.
3. Calculation of the capacitance

23. (1) A parallel plate capacitor
Assume charges q on conductor plates
Neglect fringing effect, we have
then

24. (2) A cylindrical capacitor
Two coaxial cylinders
Assume A charges +q, B charges -q
a<r<b:

25. (3) A spherical capacitor
Consist of a concentric spherical shell and a sphere.
Assume A charges +q, B charges -q

26. The common steps to calculate capacitance C :
 Assume conductors charge q .
 Find the E-field distribution between two plates.
 Calculate the potential difference between two plates.
 Calculate C by using the definition of C .

27. [Example] Two plates separation d are filled in air between them to consisting of a capacitor with capacitance of C.If a sheet of paper with thickness d1 and relative permittivity  r is inserted between the two plates, calculate to capacitance C.

28. , Solution: Assume a charge q on plate， then E-field distribution:
The potential difference:

29. 4.Capacitors in series and in parallel

30. (2) In series

31. §9-5 the energy in an E-field
1. Energy of a charged capacitor
A parallel plate capacitor has no charge initially.
Electrification for it,
as the capacitor has 、 ,
the work done by external force to move dq from B to A，
Work changes into potential energy

32. So the capacitor stores potential energy when it is charged Q：
can be used for any shape of capacitor.
This potential energy can be regarded as the energy
of the E-field which is set up by Q

33. 2. Electric field energy
A parallel plate capacitor: S,d ,and be filled with  dielectrics,
volume
Definite electric energy density in dielectrics：
The space filled with E-field

34. [Example] A parallel plate capacitor filled with air has S，d
[Example] A parallel plate capacitor filled with air has S，d. A copper plate with thickness d’is inserted capacitor parallel. The capacitor is charged till potential difference U. Then cut off the battery and remove the copper plate away. Find：How much work must we do for the copper plate removed away?
The work for removing copper plate away
=The increment of E- field energy of capacitor

35. Solution: Two methods
use
Before and after the copper plate is removed away, Q does not change.
Beforeis removed away,
Afteris removed away,

36. As Q does not change, 

37. use
Before and after the copper plate is removed away, Q does not change. The E in air does not change.But the space filled with E becomes larger.

38. E-field distribution in space,
[Example] A spherical shell with radius R and uniform charge Q is placed in vacuum. Calculate the E-field energy of the system.
Solution
E-field distribution in space,