Correct Answer  Option 3 : ∇ × H = J
Maxwell Equations:
1) Modified Kirchhoff’s Current Law:
\(\nabla .\vec J + \frac{{\partial \rho }}{{\partial t}} = 0\)
J = Conduction Current density
2) Modified Ampere’s Law:
\(\nabla \times \vec H = \vec J + \frac{{\partial \vec D}}{{\partial t}}\)
Where \(\frac{{\partial \vec D}}{{\partial t}}\) = Displacement current density
3) Faraday’s Law:
\(\nabla .\vec E =  \frac{{\partial \vec B}}{{\partial t}}\)
4) Gauss Law:
\(\nabla .\vec D = \rho \)
Maxwell's Equations for timevarying fields is as shown:
Differential form

Integral form

Name

\(\nabla \times E =  \frac{{\partial B}}{{\partial t}}\)

\(\mathop \oint \nolimits_L^{} E.dl =  \frac{\partial }{{\partial t}}\mathop \smallint \nolimits_S^{} B.d S\)

Faraday’s law of electromagnetic induction

\(\nabla \times H =J+ \frac{{\partial D}}{{\partial t}}\)

\(\mathop \oint \nolimits_L^{} H.dl = \mathop \smallint \nolimits_S^{} (J+\frac{{\partial D}}{{\partial t}}).dS\)

Ampere’s circuital law

∇ . D = ρv

\(\mathop \oint \nolimits_S^{} D.dS = \mathop \smallint \nolimits_v^{} \rho_v.dV\)

Gauss’ law

∇ . B = 0

\(\mathop \oint \nolimits_S^{} B.dS = 0\)

Gauss’ law of Magnetostatics (nonexistence of magnetic monopole)
