A parallel plate capacitor with air between the plates has capacitance and is charged to a potential difference by a battery. The battery is then disconnected, and a dielectric slab of dielectric constant is inserted to completely fill the space between the plates. What is the new potential difference across the capacitor and the new stored electrostatic energy ?

Answer and explanation

Correct answer: D.

  1. Step 1: With the battery disconnected, the charge on the plates remains strictly conserved: .
  2. Step 2: The new capacitance increases by factor : .
  3. Step 3: Compute new potential: . The new stored energy is .
Answer
.
Why not the others: incorrectly multiplies voltage by ; uses initial stored energy without dividing by ; assumes voltage remains constant (which occurs only if battery remains connected).

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