displacement current
A changing electric field acts like a current, even where no charges flow. Maxwell realised that the gap between a capacitor's plates, with no wire crossing it, still behaves as though a current passes through — a current made not of moving charge but of changing electric field. It answers a puzzle: how can a magnetic field appear where no real current flows?
Precisely, Maxwell added a term to Ampere's law so that a changing electric flux produces a magnetic field just as a real current does. This displacement current is I_d = epsilon_0 dPhi_E/dt, where Phi_E is the electric flux. In a charging capacitor the conduction current in the wire stops dead at the plates, but the growing electric field between them supplies an equal displacement current, so the magnetic field all around remains continuous with no break.
This was the missing piece that made the equations consistent and, astonishingly, predicted electromagnetic waves: a changing electric field makes a magnetic field, which by Faraday's law makes an electric field, and the self-sustaining pair travels as light. The honest clarification is that despite the name, no charge crosses the gap — a displacement current is a genuine changing electric field, and it exists even in empty vacuum.
While a capacitor charges, no charge crosses the gap, yet a compass held near the gap deflects exactly as if the wire's current had continued straight through — the displacement current supplies the missing magnetic field.
The changing field between charging plates acts as a current that keeps the magnetic field continuous.
Despite the name, no charge flows across the gap. It is a changing electric field, not moving charge, that produces the magnetic field, and it exists even in empty vacuum.