Discussion
What is the amplitude of the displacement current density in \(A/m^{2}\) inside a capacitor where \(\overline{D} =\) \(3 \times 10^{-7} \sin(6 \times 10^{7} t - 0{\cdot}35x)\,\hat{a}_{z}\) \(C/m^{2}\) and \(\epsilon_{r} = 100\).
Answer: D
The amplitude is 18 A/m2.
The displacement current density is the time derivative of the electric flux density:
\[ \begin{aligned} J_{d} &= \frac{\partial D}{\partial t} \\ &= 3 \times 10^{-7} \times 6 \times 10^{7} \cos(\dots) \\ &= 18\cos(6 \times 10^{7}t - 0.35x)\ \text{A/m}^{2} \end{aligned} \]
The amplitude is 18 A/m2. The relative permittivity is not needed, because D is given directly; \(\epsilon_{r}\) would matter only if the field were given as E. The smaller options come from dropping or mis-multiplying the factors 3 and 6.
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