A parallel-plate air capacitor has initial capacitance C. Its plate separation is slowly decreased from d₁ to d₂ while it remains connected to a battery. Select the correct statements.

Select all that apply

• Option A

  Work done by electric force = work done by external agent.

• Option B

  Work done by external force = -∫ F⃗·dx⃗, where F⃗ is the electric attraction at plate separation x.

• Option C

  Work done by electric force ≠ negative of the work done by the external agent.

• Option D

  Work done by the battery = 2 × change in electrostatic energy stored in the capacitor.