# Consider the following statements regarding Maxwell’s equation in differential form: a) For free space: ∇ × H = (σ + jωε) E b) For free space: ∇ ⋅ D ≃

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Consider the following statements regarding Maxwell’s equation in differential form:

a) For free space: ∇ × H = (σ + jωε) E

c) For steady current: ∇ × H = J

d) For static electric field: ∇ ⋅ D = ρ

What of the above statements are correct?

1. a and b
2. b and c
3. c and d
4. d and a

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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

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

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