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Let me give you an example of a reasoning I made in a simple case. Afterwards comes the question:
Start of reasoning.
Consider two standard ideal capacitor plates with a dielectric material in between them. Let's call the external field caused by the plates ##\vec{E_{ext}}## and the average macroscopic internal field caused by polarisation ##\vec{E_{int}}## The total field at any point is then on average ##\vec{E_{tot}}=\vec{E_{ext}}+\vec{E_{int}}##
One can prove that for homogenous polarisation ##\vec{E_{int}}=-\frac{\vec{P}}{\epsilon_{0}}## and thus ##\vec{E_{tot}}=\vec{E_{ext}}-\frac{\vec{P}}{\epsilon_{0}}##
Let's now look at the ##\vec{D}## field at any point in the material. The definition is ##\vec{D}=\epsilon_{0}\vec{E_{tot}}+\vec{P}##. Plugging the previous expression into D, results in:
##\vec{D}=\epsilon_{0} \vec{E_{ext}}##
End of reasoning.
QUESTION:
1) So in this case ##\vec{D}## seems to be not only independent of polarization but really equal to the external field up to a constant. Is this the correct way to interpret the ##\vec{D}##-field, as something that is equal to the E field that is caused by sources of free charges and neglect any E fields caused by polarization?
2) If I replace D with H and E with B , is the same interpretation correct?
Start of reasoning.
Consider two standard ideal capacitor plates with a dielectric material in between them. Let's call the external field caused by the plates ##\vec{E_{ext}}## and the average macroscopic internal field caused by polarisation ##\vec{E_{int}}## The total field at any point is then on average ##\vec{E_{tot}}=\vec{E_{ext}}+\vec{E_{int}}##
One can prove that for homogenous polarisation ##\vec{E_{int}}=-\frac{\vec{P}}{\epsilon_{0}}## and thus ##\vec{E_{tot}}=\vec{E_{ext}}-\frac{\vec{P}}{\epsilon_{0}}##
Let's now look at the ##\vec{D}## field at any point in the material. The definition is ##\vec{D}=\epsilon_{0}\vec{E_{tot}}+\vec{P}##. Plugging the previous expression into D, results in:
##\vec{D}=\epsilon_{0} \vec{E_{ext}}##
End of reasoning.
QUESTION:
1) So in this case ##\vec{D}## seems to be not only independent of polarization but really equal to the external field up to a constant. Is this the correct way to interpret the ##\vec{D}##-field, as something that is equal to the E field that is caused by sources of free charges and neglect any E fields caused by polarization?
2) If I replace D with H and E with B , is the same interpretation correct?