U = (1/2)CV^2 = (1/2)QV = Q^2/(2C). All three forms are equivalent (from C = Q/V). The factor 1/2 arises because the average voltage during charging is V/2. The energy is stored in the electric field between the plates, not on the plates themselves. Energy density (per unit volume): u = (1/2)epsilon_0E^2 (in vacuum) or u = (1/2)Kepsilon_0E^2 (in dielectric). Total energy = integral of udV over the volume where E exists. For parallel plates: U = (1/2)epsilon_0E^2*(Ad) = (1/2)(epsilon_0*A/d)*V^2 = (1/2)CV^2 (consistent). The concept of energy density is powerful for JEE — it shows energy is localized where the field exists.
Part of JES-02 — Electrostatic Potential, Capacitance & Energy
Energy Stored in a Capacitor
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