The peak electric field produced by the radiation coming from the $8\, W$ bulb at a distance of $10\, m$ is $\frac{x}{10} \sqrt{\frac{\mu_{0} c }{\pi}} \,\frac{ V }{ m }$. The efficiency of the bulb is $10\, \%$ and it is a point source. The value of $x$ is ...... .

A carbon dioxide laser emits sinusoidal electro-magnetic wave that travels in vacuum in the negative $x-$ direction. The wavelength is $10.6\,\mu $ and $\vec E$ fields is parallel to $z-$ axis, with $E_{max} = 1.5 \times 10^6\, M\, v/m$. Then vector equations for $\vec E$  and $\vec B$ as a function of time and position are

A plane electromagnetic wave of frequency $50\, MHz$ travels in free space along the positive $x-$ direction. At a particular point in space and time, $\vec E = 6.3\,\hat j\,V/m$ . The corresponding magnetic field $\vec B$, at that point will be

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

Electromagnetic waves travel in a medium with speed of $1.5 \times 10^8 \mathrm{~ms}^{-1}$. The relative permeability of the medium is $2.0$ . The relative permittivity will be :

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.....$W/m^2$