The electric field for a plane electromagnetic wave travelling in the $+y$ direction is  shown.  Consider a point where $\vec E$ is in $+z$ direction. The $\vec B$ field is

The electric field of an electromagnetic wave in free space is given by $\vec E$$=10 cos (10^7t+kx)$$\hat j$ $volt/m $ where $t$ and $x$ are in seconds and metres respectively. It can be inferred that

$(1)$ the wavelength $\lambda$ is $188.4\, m.$

$(2)$ the wave number $k$ is $0.33\,\,  rad/m.$ 

$(4)$ the wave is propagating along  $+x$ direction. 

Which one of the following pairs of statements is correct ?

The kinetic energy possessed by a body of mass $m$  moving with a velocity $ v$  is equal to $\frac{1}{2}m{v^2}$, provided

The electric field of a plane electromagnetic wave is given by

$\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \cos (\mathrm{kz}+\omega \mathrm{t})$ At $\mathrm{t}=0,$ a positively charged particle is at the point $(\mathrm{x}, \mathrm{y}, \mathrm{z})=\left(0,0, \frac{\pi}{\mathrm{k}}\right) .$ If its instantaneous velocity at $(t=0)$ is $v_{0} \hat{\mathrm{k}},$ the force acting on it due to the wave is

A plane electromagnetic wave travelling along the $X$-direction has a wavelength of $3\ mm$ . The variation in the electric field occurs in the $Y$-direction with an amplitude $66\  Vm^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively :-

A plane electromagnetic wave, has frequency of $2.0 \times 10^{10}\, Hz$ and its energy density is $1.02 \times 10^{-8}\, J / m ^{3}$ in vacuum. The amplitude of the magnetic field of the wave is close to$....nT$

$\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{\circ} \frac{ Nm ^{2}}{ C ^{2}}\right.$ and speed of $1 ight$ $\left.=3 \times 10^{8}\, ms ^{-1}\right)$