Maxwell's equation in differential form from Ampere's law are obtained from ans.electric current areadielectric potential areammf areamagnetic flux volume

It seems like your question is a bit unclear. However, I'll try to explain how Maxwell's equations in differential form are obtained from Ampere's law.

1. Ampere's Law: This law states that the magnetic field in space is proportional to the electric current which is present in that space. In mathematical form, it is expressed as ∮ B . dl = μ0 I, where B is the magnetic field, dl is the infinitesimal length element, μ0 is the permeability of free space, and I is the current enclosed by the loop.

2. Maxwell's Addition: Maxwell added a term to Ampere's law to include the effect of changing electric fields. This term is known as the displacement current. The modified Ampere's law (Maxwell's version) is expressed as ∮ B . dl = μ0 (I + ε0 dΦE/dt), where ε0 is the permittivity of free space, and dΦE/dt is the rate of change of electric flux.

3. Differential Form: To convert this into differential form, we use the Stokes' theorem which states that the line integral of a vector field around a closed loop is equal to the surface integral of the curl of the field over the surface bounded by the loop. Applying this theorem, we get ∇ x B = μ0 (J + ε0 dE/dt), where J is the current density, and E is the electric field.

So, Maxwell's equation in differential form from Ampere's law is obtained by including the effect of changing electric fields (displacement current) and using the Stokes' theorem to convert the integral form into differential form.