A large copper sheet of thickness l is inserted between the plates of a parallel

Question

A large copper sheet of thickness l is inserted between the plates of a parallel-plate capacitor. (The distance between each plate and the sheet is (d' - l)/2, where d' is the distance between the plates.) Is the capacitance affected by the copper sheet (a conductor, not a dielectric)? If so, what is the new capacitance? If not, why not? (Recall that the capacitance of a parallel- plate capacitor is given by eDA=d, where eD is the permittivity of free space, A is the area of each plate, and d is the separation between the plates.)

Explanation / Answer

By the introduction of the conductor between the plates of the capacitor, the capacitance of the capacitor is increased. This is not surprising because, the charge on the capacitor is the same , but p.d across the plates is reduced. Hence the capacitance of the capacitor increases. From the relation Q = CV , we have C = Q/V , Now as the induced charges on the conductor are equal and opposite , no extra induced charges. But the potential differrence decreases,as the distance between the plates is reduced due to the introduction of the conducting slab. Hence capacitance C increases.

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