Parallel Plate Capacitor Dilemma

📌 CONCEPT: The electrostatic potential energy stored in a capacitor is directly proportional to the square of the potential difference and inversely proportional to the distance between the plates.

📐 RULE / FORMULA: The formula for electrostatic potential energy stored in a capacitor is U = (1/2)CV^2, where C is the capacitance and V is the potential difference.

💡 WORKED EXAMPLE: Given a 2 μF capacitor charged to 300 V, the initial electrostatic potential energy is U1 = (1/2) * 2 * 10^-6 * (300)^2 J. If the distance between the plates is doubled, the capacitance decreases by half, and the new electrostatic potential energy is U2 = (1/2) * (1/2) * 2 * 10^-6 * (300)^2 J. Comparing U1 and U2, we see that U2 is one-fourth of U1, so the electrostatic potential energy decreases by a factor of 4.

⚠️ COMMON MISTAKE: Students often forget that capacitance is inversely proportional to distance, leading to incorrect calculations when the distance between the plates changes.