1. 4. Electric Fields in Matter
4.1 Polarization
Insulators: All charge is attached to the atoms or molecules.

3. Point charge in a homogenously charged sphere
(v - Volume)

4. Molecules

5. Polar molecules have a permanent dipole.

7. 4.2 The Field of a Polarized Object
Polarization P (dipole moment per unit volume)
tells how strongly the atoms/molecules
are polarized and/or aligned with the electric field.
Take a small volume v that contains, say,
N=1000 atoms.
Potential generated by the
microscopic dipoles:

8. Bound charges
volume charge density
surface charge density

10. Example 4.2
Electric field of a uniformly polarized sphere.

11. constant field
dipole at the center of the
sphere

12. The field inside a dielectric
Deriving the expressions for the bound charges we considered
pure dipoles.
The real dielectric contains physical dipoles. The electric
field is much more complicated near the molecular dipoles.
The macroscopic field is the average over a small volume
that contains many molecules.
The average field of the pure and molecular dipoles is the same.

13. 4.3 The Electric Displacement
Total charge
Free charge (at our disposal)
Bound charge (induced, comes along)
Electric displacement (auxiliary field)
But
in general
Boundary
conditions

14. Example 4.4 Long straight wire with uniform line charge is surrounded
by a rubber insulation. Find the electric displacement.

15. 4.4 Linear Dielectrics
Most macroscopic fields are weak as compared to the atomic
and molecular fields. The polarization is weak.
linear dielectric
electric susceptibility
permittivity
permittivity of free space
relative permittivity,
dielectric constant

16. Dielectric constants
Table

17. a) When the space is filled with a homogenous dielectric.
On may calculate D in the same way as E in the vacuum if
the different boundary conditions for E and D do not play
role. In this case, one simply replaces
This is the case if:
a) When the space is filled with a homogenous dielectric.
b) When the symmetry of the problem makes

18. Charge embedded in a homogenous dielectric material.
Bound charges partially screen q.

19. Parallel plate capacitor filled with a dielectric.
Dielectrics are used to:
Increase the capacity
Keep the plates apart
Increase the dielectric strength (field strength without a spark)
Air: dielectric constant
dielectric strength

20. Ceramic capacitors
A cut section of a
multiplayer capacitor
with a ceramic dielectric.

21. Foil wound capacitor.
Frequently used dielectrics:
Paper
Mica
Polysterene

22. Example 4.5
Metal sphere of radius a carries a charge Q. It is surrounded
by a linear dielectric material. Find the potential at the center.

23. Displacement at a boundary without free charge.

24. 4.4 Boundary Problems with Linear Dielectrics
Within a homogenous linear dielectric,
Laplace’s equation holds.
Boundary conditions on the surface between two
dielectrics:

25. Example 4.7 A sphere of homogeneous dielectric material is placed
into an otherwise uniform
electric field. Find the field
inside the sphere.

26. Example 4.8 Find the electrical field inside and outside the
dielectric and the force
on the charge.

27. 4.5 Energy in a dielectric system
Capacitor
For linear dielectrics

29. Force on a dielectric