The key observation to solve the above problem is that the charge Q can be dragged out into a flat capacitor plate parallel to the 2 existing plates. Apparently, while the charge distribution on the 2 existing plates changes, the total charge induced on each plate remains the same, due to the principle of superposition.
How and why does the principle of superposition work here??
If I had 2 concentric spherical shells instead of 2 parallel plates, and I placed a charge in the region between the concentric shells, can I likewise drag the charge out into a shell and claim that the total induced charges on each of the 2 existing shells remains the same due to the principle of superposition?
If the answer to the above question is yes, when does the principle of superposition fail? Please do give some examples, that are ideally somewhat similar to the above questions, so as to elucidate the exact criterions that cause the principle of superposition to be inapplicable.