Please consider the following arrangement of infinitely extended charged plates. In z-direction the system also extends to infinity. The charged plate in the middle of the figure is 2x negatively charged and is placed in a vacuum region. The positively (green) charged plates are to compensate the negative charge and are placed in a high dielectric medium (e.g. eps=80) which also extends to infinity. Is the field outside of this capacitor arrangement still zero? In my understanding it should be zero independent of the dielectric environments of the individual plates.
Is the field outside of this capacitor arrangement still zero?
Yes, it will be zero. There will be a field only between the red and green plates. The space outside the two green plates will not be affected. The dielectric medium will polarize, generating two charge distributions, one negative on the surface in contact with the green plates, and one positive on the free surface between the plates green and red plates. This will decrease the electric field in the region occupied by the medium. The medium outside the two plates will not be polarized.