Correct Answer - Option 3 : c and d

Maxwell’s equation for time-varying electromagnetic fields are:

1) In Differential or point form:

\(\vec \nabla \cdot \vec D = {ρ _v}\) ---(1)

**This is valid for both static and time-varying fields.**

**(Statement (d) is correct)**

In Integral form:

\(\mathop \oint \nolimits_s \vec D \cdot d\vec s = \mathop \smallint \nolimits_v {ρ _v}dV\)

2) \(\vec \nabla \times \vec H = \vec J + \frac{{\partial \vec D}}{{\partial t}}\) ---(2)

**For steady current, the change of field with time is zero**, i.e.

\( \frac{{\partial \vec D}}{{\partial t}}=0\)

∴ \(\vec \nabla \times \vec H = \vec J \)

(Statement (c) is correct)

With J = σ E and D = ϵ E, Equation (2) becomes:

\(\vec \nabla \times \vec H = σ \vec E + \frac{{ \epsilon\partial \vec E}}{{\partial t}}\)

In time-harmonic form, this can be written as:

∇ × H = (σ + jωε) E

**For free space, σ = 0, and ρ = 0:**

**∇ × H = jωε E (Statement (a) is incorrect)**

Similarly, for free space, Equation (1) becomes:

∇ ⋅ D ≃ 0 **(Statement (b) is incorrect)**