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AP Physics C: E&M
10.3 Capacitors
AdvancedMCQMathematicalProportional Analysis23.6k
A parallel-plate capacitor with plate separation \(x_0\).
A parallel-plate capacitor with plate separation \(x_0\).
A parallel-plate capacitor with plate area \(A\) has its plates initially separated by a distance \(x_0\). The magnitude of the attractive force between the plates is measured in two independent experiments as the plate separation is increased from \(x_0\) to \(2x_0\):

Experiment 1: The capacitor is charged to a net charge magnitude \(Q_0\) and then disconnected from the power supply, keeping the charge constant.

Experiment 2: The capacitor remains connected to a battery supplying a constant potential difference \(V_0\).

By what factor does the attractive force between the plates change (ratio \(F_{\text{final}} / F_{\text{initial}}\)) in Experiment 1 and Experiment 2?

Experiment 1 (Constant Charge \(Q_0\))Experiment 2 (Constant Voltage \(V_0\))
(A)\(2\)\(\dfrac{1}{2}\)
(B)\(\dfrac{1}{2}\)\(\dfrac{1}{4}\)
(C)\(1\)\(\dfrac{1}{4}\)
(D)\(\dfrac{1}{4}\)\(\dfrac{1}{4}\)

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