What is meant by displacement current ? A capacitor is being charged by a battery. Show that Ampere-Maxwell law justifies continuity and constancy of the current flowing in the circuit.

Displacement current: the current due to a varying electric field between the plates of a capacitor. Ampere–Maxwell law: ∮ B⃗·dl⃗ = μ₀ (I_c + I_d). Outside the capacitor, I_d = $\displaystyle 0$, so I = I_c. Inside the capacitor, I_c = $\displaystyle 0$, so I = I_d = ε₀ dΦ_E/dt = ε₀ (d/dt)(Q/ε₀) = dQ/dt = I_c. Hence I_c + I_d has the same value at all points, i.e. the current is continuous and constant through the circuit.