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AP Physics C: E&M
10.3 Capacitors
AdvancedMCQMathematical14.2k
Side view of a tilted-plate capacitor with non-parallel plates.
Side view of a tilted-plate capacitor with non-parallel plates.
A capacitor consists of two rectangular conducting plates of length \(L\) and width \(W\) tilted at a small angle \(\theta\) relative to one another, such that the plate separation increases linearly from \(d\) at \(x = 0\) to \(d + L\theta\) at \(x = L\), where \(L\theta \ll d\). Let \(C_0 = \dfrac{\varepsilon_0 W L}{d}\) be the capacitance of an ideal parallel-plate capacitor of identical dimensions with uniform separation \(d\). Which of the following expressions represents the best approximation for the total capacitance \(C\) of the tilted-plate capacitor?

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