I have an elementary doubt with the calculation of the capacitance of a capacitor of parallel plates that has a dielectric in the middle.
The Attempt at a Solution
Suppose the top plate has a positive charge and the bottom plate has a negative charge.
To calculate vector displacement in the upper plate, we occupy the gauss law, use a Gaussian box. On the outside of the top plate the polarization P is 0 and there is an electric field E. At the bottom of the plate there is an electric field E and a polarization P due to the dielectric.
If we consider only the top plate:
If we consider the complete system (both plates)
The field inside is 2 E.
What is the error, I do not understand. D is zero outside from capacitor?