Question

hi, can anyone explain the relationship between D, electric field displacement and phi, electric flux density to me?

Answer 1

D is the elctric field due to free charges only (\[\rho _{free}\]
When there is situation envolving dialectric metirials there are also bounded charges \[\rho _{bounded}\] = \[\rho _{b}\] the bounded charges cant move freely in the metrial but they are diapoles and they have an efect on the electric field.

So the flux density of D involves only free charges
Becuase of historicl an exprematel reasons the constant \[\epsilon _{0}\] is not a patr of this equation and we get
\[\int\limits_{}^{}D*da=Q _{free}\]

I will try to elaborate tomrrow if it will be needed.
Basicly you consider that the manitude of polirazation per unit volume (P) is linear to the external field, and from that u can get equations for the real field with the effect of the dialectric matter.

There is more info on wiki and in the feynman lectures on physics
Enjoy!

(this subject has a few more notation issues, mainly because of historical and other things - but the main thing the idea is the linear propotion between P and
\[E _{0}\ ] that is the field from free charges)
so \[\chi\] will represnt this linear proportion
and \[\kappa\] is \[(1+\chi\)] and so on...

Answer 2

in materials=displacement
in free space= electric flux

they are equivalent- equal (depending on the medium) free space or materials
Vector fields
If you want a scientific explanation the person above mine is cool...:)

Answer 3

Im a simple nerd...

Answer 4

with kids so i try to simplify it... bare with me.

Answer 5

Thanks a lot! Makes more sense now