Influence of an external electric field on an uncharged capacitor.
Fig A shows an uncharged capacitor with no external electrical field. There is no net charge on each of the plates. Since the net charge on each of the plates is zero, no electric field is produced outside the plates. The dielectric between the plates consists of polar molecules, randomly oriented since there is no electric field in the dielectric.
Fig B shows the same capacitor but now immersed in a uniform electric field. By convention, the direction of the field is the direction of the force that a positive charge would experience if placed in the field. Due to the influence of the field, I believe the charges on the capacitor plates will be redistributed, so that there is now a voltage between the outer surfaces of the plates (between points 1 and 2, separated by distance d) equal to the voltage drop of the field between the points. However, there is still no net charge on either plate. If I draw a closed Gaussian surface around each plate, there will be no field outside the plates due to the charge on the plates. Consequently, it appears that there is no field in the dielectric due to the charges on the plates.
In other words, is my depiction of the situation in Fig B correct with respect to the influence of the external electric field on the dielectric between the plates?
Thank you for your consideration.
ADDITIONAL INFORMATION
I have added Fig C, which shows the same capacitor as Fig A and B except that it has been charged by a battery and has voltage $V=Ed$.
Best Answer
There will be a field E inside the plates. Draw your Gaussian surface to surround only the right side of the left plate, not the whole plate. This gives E between the plates. If you draw it around the whole plate, the surface integral is zero because E enters at the left and leaves out the right side of the plate.