A capacitor has square plates, each of side a, making an angle with each other as shown in the figure. We have to show that for small the capacitance is given by

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A capacitor has square plates, each of side a, making an angle with each other as shown in the figure. For calculating the capacitance of this capacitor, we will assume that it is a parallel combination of strip-capacitances along the length a each of area

.

The separation of the strip-capacitance at length x from the end as shown in the figure will be

.

The capacitance of the strip-capacitor at length x will be

.

Therefore, the capacitance of the capacitor shown in the figure will be

In the approximation

integral reduces to