The separation between the plates of a parallel-plate

Question:

The separation between the plates of a parallel-plate capacitor is $0.500 \mathrm{~cm}$ and its plate area is $100 \mathrm{~cm}-\mathrm{square}$. A $0.400 \mathrm{~cm}$ thick metal plate is inserted into the gap with its faces parallel to the plates. Show that the capacitance of the assembly is independent of the position of the metal plate within the gap and find its value.

Solution:

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