Previously in the thread titled Electrostatics - Coulomb's Law, Coulomb's Law was defined aswell as the Electric Field Strength.
If we take the Vector quantity E which is the electric field strength (a vector as it has both magnitude and direction) and multiply it by the permittivity ε, we get a new vector D.
So D = εE = ε * Q/4π ε r2 , the ε cancles out leaving us with D = Q/4π r2

Notice how the electric flux density is independant of the permittivity ε. What does this mean?
Well say we had an electric field acting on a type of material, then from the formula for the electric field strength we know that the value of E is dependant upon the material used by the value of the permittivity ε. But the electric flux density D will remain the same no matter what material you use.
Basically although changing the types of materials will effect the electric field strength E, it will not affect the electric flux density D.

 

what do you think about E on boundary?
The book said the tangential component of an E field is continuous across an interface even though the permittivities are in different to each medium.
E1(tan) = E2(tan)
I'm confused of it.

 

The flux density D tells you how many lines of force (field lines, if you think like that) pass through an area. Thus, whatever the material is, if the area is the same and flux is the same then D is the same for all these materials. However, E is different for each material because each material permits in a different degree (ε) the flux to pass through it.

 

Think about it like this.. If you have a strand of any dielectric 1m long, and you attach 0V to one end, and 50kV to the other, regardless of the permittivity there will be a voltage drop of 50kV/m..

 

Just a general note about what I have learned from studying electromagnetics. Electromagnetic laws are extremely simple to remember, but the mathematics behind their use is very intense. You must know your vector calculus very well to implement them!

Simplifications, such as when one does basic magnetic modeling, should not be confused with what was mentioned above. This can usually be done with ease.

Steve

 

looking for ssomething related to the derivation of the calculus of GAUSS's THEOREM

 

D = Q/4π r2

Notice how the electric flux density is independant of the permittivity ε. What does this mean?

It means you have stumbled across a law of nature.

This is a simplified form of one of Maxwell's equations; specifically Gauss' Law. The total charge enclosed in a volume equals D (normal to the surface of the volume) integrated over the surface.

 

I like mik3's answer I think in picatures.