The oscillating electric and magnetic field vectors of an electromagnetic wave are along

The electric field for an electromagnetic wave in free space is $E = i 30 \cos (k z - 5 \times 10^8 t)$,where the magnitude of $E$ is in $V/m$. The magnitude of the wave vector $k$ is (velocity of electromagnetic wave in free space $= 3 \times 10^8 \ m/s$).

$A$ flood light is covered with a filter that transmits red light. The electric field of the emerging beam is represented by a sinusoidal plane wave
$E_x=36\,\sin\,(1.20 \times 10^7z -3.6 \times 10^{15}\,t)\,V/m$
The average intensity of the beam will be.....$W/m^2$

The magnetic field in a plane electromagnetic wave is given by
$B_y = (2 \times 10^{-7}) \sin (0.5 \times 10^3 x + 1.5 \times 10^{11} t) \, T$
$(a)$ What is the wavelength and frequency of the wave?
$(b)$ Write an expression for the electric field.

$A$ plane electromagnetic wave is travelling in the positive $X$-axis. At the instant shown,the electric field at the extremely narrow dashed rectangle is in the $-ve$ $Z$-direction and its magnitude is increasing. Which diagram correctly shows the direction and relative magnitudes of the magnetic field at the edges of the rectangle?

For a plane electromagnetic wave,the electric field is given by $\vec{E} = 10 \cos(10^7t + kx) \hat{j} \text{ V/m}$. Where $t$ is in seconds and $x$ is in meters,then: $(i)$ The wavelength of this wave is $188.4 \text{ m}$. $(ii)$ The wave vector of this wave is $0.33 \text{ rad/m}$. $(iii)$ The amplitude of the electric field of this wave is $10 \text{ V/m}$. $(iv)$ This wave is propagating in the positive $X$-direction.