The electric field in a plane electromagnetic wave is given by

$\overrightarrow{{E}}=200 \cos \left[\left(\frac{0.5 \times 10^{3}}{{m}}\right) {x}-\left(1.5 \times 10^{11} \frac{{rad}}{{s}} \times {t}\right)\right] \frac{{V}}{{m}} \hat{{j}}$

If this wave falls normally on a perfectly reflecting surface having an area of $100 \;{cm}^{2}$. If the radiation pressure exerted by the $E.M.$ wave on the surface during a $10\, minute$ exposure is $\frac{{x}}{10^{9}} \frac{{N}}{{m}^{2}}$. Find the value of ${x}$.

An infinitely long thin wire carrying a uniform linear static charge density $\lambda $ is placed along the $z-$ axis (figure). The wire is set into motion along its length with a uniform velocity $V = v{\hat k_z}$. Calculate the pointing vector $S = \frac{1}{{{\mu _0}}}(\vec E \times \vec B)$ .

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

The ratio of amplitude of magnetic field to the amplitude of electric field for an electromagnetic wave propagating in vacuum is equal to 

The electromagnetic waves do not transport

A radio transmitter transmits at $830\, kHz$. At a certain distance from the transmitter magnetic field has amplitude $4.82\times10^{-11}\,T$. The electric field and the wavelength are respectively