GRE GR 1777, Problem 005 Solution

Physics GRE GR 1777
5. Electrodynamics (Maxwell’s Equations)
Solution) In Maxwell’s equations, Ampère’s law (with Maxwell’s correction) is
\nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}.
We can write this equation as
\nabla \times \vec{B} - \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t} = \mu_0 \vec{J},
where \vec{J} is the current (the electric displacement current). And \frac{\partial \vec{E}}{\partial t} is change of electric fields with respect to the time (rate of change of the electric flux).
If we assume that \nabla \times \vec{B} = 0, and the current flows through a surface S, then we can clearly see that the electric displacement current through S is proportional to the rate of change of the electric flux through S.
Therefore, the answer is (E).

Another (and better) solution)
The definition of electric displacement current is
\vec{J}_{D} = \epsilon_0 \frac{\partial \vec{E}}{\partial t} + \frac{\partial \vec{P}}{\partial t}.
If you know this definition, the problem would be solved more easily.

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