A capacitor is made of two square plates each of side a making a very small angle α between them: the lower plate is horizontal and the upper plate is tilted upward through α, so that the gap is d at the left edge and d+α a at the right edge. The capacitance will be close to

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(3) (ε₀a²)/d(1-(α a)/(2d)). Take a strip of width dx at a distance x from the narrow edge; its gap is d+α x and its area is a dx. Strips side by side are in parallel, so their capacitances add. C=∫₀^a(ε₀a dx)/(d+α x)=(ε₀a)/α ln (1+(α a)/d). For α a d, ln(1+u)≈ u-(u²)/2 with u=(α a)/d. C≈(ε₀a)/α((α a)/d-(α²a²)/(2d²))=(ε₀a²)/d(1-(α a)/(2d)).

A capacitor is made of two square plates each of side a making a very small angle α between them: the lower plate is horizontal and the upper plate is tilted upward through α, so that the gap is d at the left edge and d+α a at the right edge. The capacitance will be close to

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