In the figure two capacitors in series have been shown. The rigid centre section of length b is movable horizontally. We have to show that the equivalent capacitance of the series combination is independent of the position of the central section and is given by

.

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For the configuration of the capacitor plates let the separation between the plates be x and . Electric field between the plates is

Therefore, potential differences between the pairs of plates are

But as

we have

And

As