Simulation · Physics · Class 12
Charge sharing and the lost energy
From the lesson Energy stored in a capacitor in Electrostatic Potential and Capacitance. Change the values and watch what happens.
Charge sharing and the lost energyPhysics · Class 12
The idea behind it
NCERT §2.15
- Charging moves charge from the negative plate to the positive plate, which is at the higher potential, so external work is done at every step.
- When the charge is Q′ the voltage is Q′/C; moving a further δQ′ takes (Q′/C)δQ′. Adding these from 0 to Q gives W = Q²/(2C).
- Stored energy U = Q²/(2C) = ½CV² = ½QV. It is ½QV, not QV, because the voltage builds up from zero while the charge is moved.
- The energy can be pictured as stored in the field between the plates. For a parallel plate capacitor U = ½ε₀E² × Ad, where Ad is the volume of the gap.
- Energy density of an electric field u = ½ε₀E² (joules per cubic metre). This holds for any field, not only a capacitor's.
- Worked value: 900 pF charged to 100 V holds Q = 9 × 10⁻⁸ C and U = 4.5 × 10⁻⁶ J.
- Join that charged capacitor to an identical uncharged one: the charge shares equally, V halves to 50 V, and the total energy drops to 2.25 × 10⁻⁶ J. Charge is conserved; the missing half is lost as heat and electromagnetic radiation while charge flows.