Displacement Current

While the capacitor charges, the electric field between the plates changes.
Maxwell showed this changing field acts like a current, the displacement current:
I_d = ε₀ dΦ_E/dt
It is always equal to the current in the wires, so current is continuous through the gap, and it also makes a magnetic field (the rings):
∮ B·dl = μ₀ (I + ε₀ dΦ_E/dt)
When the capacitor is full, both currents become zero.