= Solution
Maxwell's <displacement current> is the electric-field contribution needed to make <Ampère's law> consistent with <charge conservation>. In macroscopic form,
$$
\boxed{\nabla\times\mathbf H=\mathbf J_f+\frac{\partial\mathbf D}{\partial t}.}
$$
The <displacement current> density $\mathbf J_d=\partial_t\mathbf D$ has units $\mathrm{A\,m^{-2}}$. Since $\mathbf D=\epsilon_0\mathbf E+\mathbf P$, it contains the <vacuum> field term and, in matter, the polarization-current contribution. It need not represent <free charge> moving through a material.
Taking the <divergence> gives $0=\nabla\cdot\mathbf J_f+\partial_t(\nabla\cdot\mathbf D)$. <Gauss's law>, $\nabla\cdot\mathbf D=\rho_f$, then yields the <continuity equation> $\partial_t\rho_f+\nabla\cdot\mathbf J_f=0$. Without the <displacement> term, Ampère's original law would incorrectly require every current distribution to be divergence-free even while charge accumulates.
A charging parallel-plate <capacitor> makes this concrete. Ignoring fringing, $D=Q/A$, so the <displacement current> across its <dielectric> gap is $I_d=A\partial_tD=dQ/dt$, equal to the conduction <electric current> in its wire. The <integral> law
$$
\oint\mathbf H\cdot d\boldsymbol\ell
=\int_S\mathbf J_f\cdot d\mathbf S+\frac{d}{dt}\int_S\mathbf D\cdot d\mathbf S
$$
therefore gives the same answer whether the spanning surface cuts the wire or passes through the gap. Together with <Faraday's law>, this field term also permits self-consistent <electromagnetic waves> in <vacuum>, with <speed> $c=1/\sqrt{\mu_0\epsilon_0}$.
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