word_count: 250

A charged capacitor stores energy in its electric field. Three equivalent formulas: U = (1/2)CV^2 = (1/2)QV = Q^2/(2C). The factor 1/2 arises because the average voltage during charging is V/2.

Energy density (per unit volume) in an electric field: u = (1/2)epsilon_0E^2 (vacuum) or u = (1/2)Kepsilon_0E^2 (dielectric). Total energy = integral of u over the volume. For parallel plates: U = u * (Ad) = (1/2)epsilon_0(V/d)^2*Ad = (1/2)CV^2.

When charging from a constant voltage source (battery), the battery delivers energy QV = CV^2, but only (1/2)CV^2 is stored. The other half is dissipated as heat in the circuit (regardless of resistance). This 50% charging efficiency is a fundamental result.

Force between plates: F = Q^2/(2epsilon_0A) = (1/2)epsilon_0E^2A (attractive). Electrostatic pressure: P = sigma^2/(2epsilon_0) = (1/2)epsilon_0E^2. Each plate is in the field of the other plate (E_other = sigma/2*epsilon_0), not the total field.

Self-energy of charge distributions: solid sphere U = 3kQ^2/(5R); shell U = kQ^2/(2R). These represent the energy needed to assemble the distribution from infinitesimal charge elements. As R -> 0, self-energy diverges — the classical self-energy problem.

JEE frequently combines energy concepts with dielectric insertion, plate separation changes, or charge redistribution between capacitors.