• summary_type: concept
• word_count: 170

Maxwell identified that Ampere's law fails for time-varying electric fields. A charging capacitor carries conduction current in the wires but none between the plates — yet the magnetic field is continuous. Maxwell introduced displacement current I_d = epsilon_0 * d(Phi_E)/dt to fix this. Between capacitor plates: E = Q/(epsilon_0A), so I_d = epsilon_0A*(dE/dt) = dQ/dt = I_c (equals the conduction current). The modified Ampere-Maxwell law: line integral of B.dl = mu_0*(I_c + I_d). Displacement current is not a real charge flow — it is the magnetic effect of a changing electric field. It exists wherever dE/dt is nonzero, even in vacuum. With this addition, Maxwell's four equations become fully symmetric: a changing B produces E (Faraday), and a changing E produces B (Ampere-Maxwell). This symmetry predicts self-sustaining oscillating fields that propagate through space — electromagnetic waves.