Discussion
The Maxwell's equation
\[ \begin{aligned} \nabla \times \bar{H} &= \Big(\bar{J}_{cond} \\ &\quad + \frac{\partial \bar{D}}{\partial t}\Big) \end{aligned} \]
for free space becomes :
Answer: C
In free space the equation becomes \(\nabla \times \bar{H} = \dfrac{\partial \bar{D}}{\partial t}\).
Free space has no conductors and no free charges, so the conduction current density \(\bar{J}_{cond} = \sigma\bar{E}\) is zero (\(\sigma = 0\)). Only the displacement current term remains.
Setting the whole right side to zero would also drop the displacement current, which is what lets electromagnetic waves propagate through free space. Keeping only \(\bar{J}_{cond}\) is the form for a good conductor at low frequency, the opposite case, and 'infinite' has no physical meaning here.
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