= Solution
For a charging <parallel-plate capacitor> of area $A$, neglect fringing. The field in the gap is $E=Q/(\epsilon_0A)$, so the <displacement current> through the gap is
$$
\boxed{I_D=\epsilon_0\frac{d}{dt}\int\mathbf E\cdot d\mathbf S=\epsilon_0A\frac{dE}{dt}=\frac{dQ}{dt}=I.}
$$
An <Amperian loop> around the feed wire can bound a surface cutting the wire, which has conduction current $I$, or a bulging surface passing through the dielectric gap, which has no conduction current. Including displacement current makes both surfaces give the same magnetic circulation. It is also required by <charge conservation>: the divergence of the <Ampère-Maxwell equation> and <Gauss's law> yields $\nabla\cdot\mathbf J+\partial\rho/\partial t=0$, the <continuity equation>.
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