When a battery is attached to a capacitor, conduction current flow in wire outside capacitor. In the capacitor the Electric flux ${\mathit{\varphi }}_{\mathit{E}}=\mathit{E}\mathit{A}$
Where, $\mathit{E}=\frac{\mathit{Q}}{{\mathit{\epsilon }}_0\mathit{A}},\mathit{Q}={\mathit{\epsilon }}_0\mathit{E}\mathit{A}$
∴ $\mathit{I}=\frac{\mathit{d}\mathit{Q}}{\mathit{d}\mathit{t}}={\mathit{\epsilon }}_0\frac{\mathit{d}{\mathit{\varphi }}_{\mathit{E}}}{\mathit{d}\mathit{t}}$
This maintains the current in the capacitor.

Amperes-Maxwell law states that displacement current comes into existence due to rate of change of electric flux w.r.t. time.

$\therefore$ Displacement current ${\mathit{I}}_{\mathit{d}}={\mathit{\epsilon }}_0\frac{\mathit{d}{\mathit{\varphi }}_{\mathit{E}}}{\mathit{d}\mathit{t}}$