• $summary_{type}$: 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$\frac{Phi_E}{dt}$ to fix this. Between capacitor plates: E = $\frac{Q}{epsilon_0*A}$, so $I_d$ = $epsilon_0$A$\frac{dE}{dt}$ = $\frac{dQ}{dt}$ = $I_c$ (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.