When a battery is attached to a capacitor, conduction current flow in wire outside capacitor. In the capacitor the Electric flux $\phi_E = EA$ Where, $\; E = \frac{Q}{\varepsilon_0 A}, \; Q = \varepsilon_0 EA$ ∴ $\; I = \frac{dQ}{dt} = \varepsilon_0 \; \frac{d\phi_E}{dt}$ 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 $I_d = \varepsilon_0 \; \frac{d\phi_E}{dt}$