In the figure line diagram has been drawn of a air capacitor. Alternate plates are connected together. We consider a pile of n plates of alternate polarity, each having an area A and separated from adjacent plates by a distance d. We have to show that this capacitor has a maximum capacitance of

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In the configuration shown in the figure if the left-hand outer plate has charge +q, the right-hand outer plate will have charge -q. Each of the inner plates will have charge -2q or +2q, alternately as shown. This is required for the field between the plates to be uniform and the alternate plates to have the same polarity. The total +ve charge on the plates of the condenser connected to the +ve terminal of the battery will be

.

And the total negative charge on the plates will be

.

Let V be the potential difference across the external source of EMF. The magnitude of the electric field between any pair of plates will be

.

By applying Gauss theorem across any plate as shown, we note that

,

or

And

The capacitance of the combination C will be determined by the requirement that effectively we have a parallel plate capacitor in which charges on the plates is and , and potential difference across them is V.

And