$A$ plane electromagnetic wave propagating along the y-direction can have the following pair of electric field $(\vec{E})$ and magnetic field $(\vec{B})$ components.

An electron is constrained to move along the $y$-axis with a speed of $0.1 c$ ($c$ is the speed of light) in the presence of an electromagnetic wave,whose electric field is $\overrightarrow{E} = 30 \hat{j} \sin(1.5 \times 10^7 t - 5 \times 10^{-2} x) \, V/m$. The maximum magnetic force experienced by the electron will be: (given $c = 3 \times 10^8 \, m/s$ and electron charge $q = 1.6 \times 10^{-19} \, C$)

Find the direction of vibration of the electric field if the vibration of the magnetic field is in the positive $x-$ axis and the propagation of the electromagnetic wave is along the positive $y-$ axis.

The equation of a light wave,normally incident on a surface,is given by $B = (100 \text{ nT}) \sin(2\pi(10^{15}t - (3 \times 10^{-7})x) + \frac{\pi}{6})$. Find the intensity of light on that surface in $W/m^2$.

During the propagation of electromagnetic waves in a medium,

$A$ radio transmitter transmits at $830 \, kHz$. At a certain distance from the transmitter,the magnetic field has an amplitude of $4.82 \times 10^{-11} \, T$. The electric field and the wavelength are respectively: