Energy of the electric field
Charging a body requires work against the repulsion of the charges; this work becomes the energy of the electric field. Since the potential rises linearly from zero to φ, the average potential is φ/2, so W = qφ/2. Electric capacitance is C = q/φ (unit 1 F = 1 C/V; in practice mF, μF, nF, pF), giving W = Cφ²/2 = q²/(2C). A capacitor is two conductors (plates) separated by a dielectric; its capacitance is C = q/U, and for a parallel-plate capacitor C = εε₀S/d, where ε₀ = 8.85·10⁻¹² F/m. The capacitor’s energy is W = qU/2 = CU²/2 = q²/(2C). This energy is concentrated in the field between the plates; for a parallel-plate capacitor of volume V = Sd, W = εε₀E²V/2. The volume density of field energy is w = W/V = εε₀E²/2 (unit J/m³). A charged capacitor slowly loses its energy and discharges almost instantly through a low-resistance circuit; so never touch a charged capacitor.
Only by calculation and with the teacher: fill a table of the energy at 10 V for capacitors of 1 μF, 10 μF and 100 μF. Do not charge a real capacitor, connect it to the mains or touch it.