Surface independence of Ampère circulation during capacitor charging
= Surface independence of Ampère circulation during capacitor charging
A spanning surface that cuts a charging wire carries free current $I$. A surface passing through the <capacitor> gap instead carries displacement flux $\int\partial_t\mathbf D\cdot d\mathbf A=\dot Q=I$. Their common boundary has the same magnetic circulation only when both terms are included in <Ampère's law>.