When an $EM$ wave propagates through a vacuum,then:

An electromagnetic wave travels along the $z$-axis. Which of the following pairs of space and time-varying fields would generate such a wave?

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec{E} = 30(2 \hat{x} + \hat{y}) \sin \left[2 \pi \left(5 \times 10^{14} t - \frac{10^7}{3} z\right)\right] \text{V m}^{-1}$. Which of the following option$(s)$ is(are) correct?
[Given: The speed of light in vacuum,$c = 3 \times 10^8 \text{ m s}^{-1}$]
$(A)$ $B_x = -2 \times 10^{-7} \sin \left[2 \pi \left(5 \times 10^{14} t - \frac{10^7}{3} z\right)\right] \text{Wb m}^{-2}$.
$(B)$ $B_y = 2 \times 10^{-7} \sin \left[2 \pi \left(5 \times 10^{14} t - \frac{10^7}{3} z\right)\right] \text{Wb m}^{-2}$.
$(C)$ The wave is polarized in the $xy$-plane with a polarization angle $\theta = \tan^{-1}(0.5)$ with respect to the $x$-axis.
$(D)$ The refractive index of the medium is $2$.

$A$ radio receiver antenna that is $2 \, m$ long is oriented along the direction of the electromagnetic wave and receives a signal of intensity $5 \times 10^{-16} \, W/m^2$. The maximum instantaneous potential difference across the two ends of the antenna is

About $5 \%$ of the power of a $100 \; W$ light bulb is converted to visible radiation. What is the average intensity of visible radiation
$(a)$ at a distance of $1 \; m$ from the bulb?
$(b)$ at a distance of $10 \; m$? Assume that the radiation is emitted isotropically and neglect reflection.

$A$ plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}},$ with its polarization along the direction $\hat{k}$. The correct form of the magnetic field of the wave would be (here $B_{0}$ is an appropriate constant)