Question #80605

An electromagnetic wave propagating in a medium has an electric field given by $E(x,t) = E_0 \cos(kx + \omega t)$, where $E_0$ is the amplitude in $\text{V/m}$, $k$ is the wave number in $\text{m}^{-1}$, and $\omega$ is the angular frequency in $\text{rad/s}$. A stationary receiving antenna of effective length $d$ (in $\text{m}$) is located at $x = -\frac{\pi}{3k}$. The antenna outputs an electromotive force $\varepsilon(t) = d \cdot E\left(-\frac{\pi}{3k}, t\right)$. This emf is applied across a series circuit consisting of a resistor $R$ (in $\Omega$) and a capacitor $C$ (in $\text{F}$). If the capacitive reactance is $X_C = \sqrt{3}R$, which of the following expressions represents the steady-state instantaneous current $I(t)$ in the circuit?