Question 20 - 2020 (06 Sep 2020 Shift 2)

For a plane electromagnetic wave, the magnetic field at a point $x$ and time $t$ is $\vec{B}(x, t) = [1.2 \times 10^{-7} \sin(0.5 \times 10^{3} x + 1.5 \times 10^{11} t)\hat{k}]$ T. The instantaneous electric field $\vec{E}$ corresponding to $\vec{B}$ is (speed of light $c = 3 \times 10^{8}$ ms$^{-1}$):

(1) $\vec{E}(x, t) = [-36 \sin(0.5 \times 10^{3} x + 1.5 \times 10^{11} t)\hat{j}]$ V/m

(2) $\vec{E}(x, t) = [36 \sin(1 \times 10^{3} x + 0.5 \times 10^{11} t)\hat{j}]$ V/m

(3) $\vec{E}(x, t) = [36 \sin(0.5 \times 10^{3} x + 1.5 \times 10^{11} t)\hat{k}]$ V/m

(4) $\vec{E}(x, t) = [36 \sin(1 \times 10^{3} x + 1.5 \times 10^{11} t)\hat{j}]$ V/m