# Illustration Current Depends on the Choice of the Enclosing Loop in the Plate Capacitor

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An AC voltage $$U(t)$$ is applied to a plate capacitor. This causes a time-dependent current $$I(t)$$ to flow through the wire, charging and discharging the capacitor. This charging and discharging process causes the charge $$Q$$ on the electrodes to change with time and thus also the electric field $$E$$ between the electrodes.

By choosing a closed loop $$S$$ enclosing the current, Ampere's law gives either the current $$I$$ (in the case of $$A_1$$) or zero (in the case of $$A_2$$). Here $$A_1$$ and $$A_2$$ are possible surfaces with the edge $$S$$.

To resolve this contradiction, Ampere's law (fourth Maxwell equation of electrostatics) is extended with the so-called displacement current$$I_{\text e}$$ , which represents the temporal change of the E-field.