Displacement Current

Maxwell noticed Ampère's law (∮B·dl = μ₀I_c) breaks down when applied to a charging capacitor — no real current crosses the gap, yet B clearly exists around it.

He postulated a NEW current, the displacement current I_d = ε₀(dΦ_E/dt), produced by a changing electric flux — not by moving charges.

The complete Ampère–Maxwell law: ∮B·dl = μ₀(I_c + I_d). With this, the magnetic field is continuous everywhere — inside the wire AND inside the capacitor gap.

I_d has the SAME units (ampere) and produces the SAME magnetic field as a real conduction current of equal magnitude.

Inside a charging parallel-plate capacitor, dE/dt is uniform between the plates, so I_d = ε₀·A·(dE/dt) = C·(dV/dt) = I_c. The two currents are exactly equal.

The conception of displacement current closed Maxwell's equations and predicted that ANY changing E creates B and vice-versa — the seed of electromagnetic waves.

In a conductor, I_c dominates; in vacuum or a perfect dielectric, only I_d exists.