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)