Answer : Option A

Explanation :

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.