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A parallel-plate air capacitor has capacitance C, plate separation d, and potential difference V is applied between the plates. The force of attraction between the plates is

  1. \(\frac{CV^2}{2d}\)
  2. \(\frac{CV}{2d}\)
  3. \(\frac{CV^2}{d}\)
  4. \(\frac{C^2V^2}{2d}\)

Correct answer: \(\frac{CV^2}{2d}\)

Solution

For a capacitor maintained at constant voltage, the attractive force can be obtained from the rate of change of energy with separation. Using \(C = \varepsilon_0 A/d\), the result is \(F = \frac{CV^2}{2d}\).

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