The ampere's law is given as ∇.H = J Taking divergence on both sides ∇.(∇xH) = ∇.J i.e., ∇.(∇xH) = ∇.J = 0 ∴ divergence of curl is always zero But ∇.J = -r_v ... continuity equation. Hence the inconsistency. It can be removed as follows → Let ∇ x H = J + G where G is some unknown quality. Then ∇.(∇ x H) = ∇.(J x G) = 0 i.e. ∇.J + ∇.G = 0 i.e. ∇.J = -∇.G or ∇.G = (-r_v) i.e. ∇.G = r_v ...... Gauss's law in point form Differentiating on both sides. ∇.D = r_v Comparing (i) and (ii), G = D Thus ∇ x H = J + D Where J is conduction current density and D is displacement current density which is added to remove the inconsistency of Ampere's law.