Displacement Current

Maxwell noticed that Ampere's original law failed in the gap of a charging capacitor, where no conduction current flows yet a magnetic field is still observed around the region. To restore consistency he proposed that a time-varying electric field, and hence a changing electric flux, behaves like a current called the displacement current, given by i_d = \varepsilon_0 \frac{d\Phi_E}{dt}. Between the plates the surface charge grows, the electric field rises, and this increasing electric flux supplies exactly the current needed to keep Ampere's law continuous across the gap. A steady conduction current is wrong because the gap is an insulator carrying no real charge flow. A constant magnetic flux is irrelevant since it is the electric, not magnetic, flux that matters here. A stationary point charge produces no time variation and therefore no displacement current at all. This idea, central to the NCERT chapter on Electromagnetic Waves, unified electricity and magnetism and predicted electromagnetic radiation. It is worth stressing that the displacement current is not a flow of charge at all but a consequence of the field changing in time, yet it produces a magnetic field indistinguishable from that of a real current. Dimensionally \varepsilon_0,(d\Phi_E/dt) reduces to amperes, confirming it is a genuine current term that closes the gap in Ampere's law.