In a plane $EM$ wave, the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10} \mathrm{~Hz}$ and an amplitude of $50 \mathrm{Vm}^{-1}$. The total average energy density of the electromagnetic field of the wave is :

[Use $\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ ]

The electric field part of an electromagnetic wave in vacuum is

$E = 3.1\,NC^{-1}\,cos\,[\,(1.8\,rad\,m^{-1})\,y + (5.4\times 18^8\,rad\,s^{-1})\,t\,]\,\hat i$

The wavelength of this part of electromagnetic wave is......$m$

$TV$ waves have a wavelength range of $1-10 \,meter$. Their frequency range in $MHz$ is

A beam of light travelling along $X$-axis is described by the electric field $E _{ y }=900 \sin \omega( t - x / c )$. The ratio of electric force to magnetic force on a charge $q$ moving along $Y$-axis with a speed of $3 \times 10^{7}\,ms ^{-1}$ will be.

[Given speed of light $=3 \times 10^{8}\,ms ^{-1}$ ]

Nearly $10 \%$ of the power of a $110\,W$ light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of $1\, m$ from the bulb to a distance of $5\,m$ is $a \times 10^{-2}\,W / m ^{2}$. The value of ' $a$ ' will be.

The electric field of a plane electromagnetic wave is given by $\vec E = {E_0}\hat i\,\cos \,\left( {kz} \right)\,\cos \,\left( {\omega t} \right)$ The corresponding magnetic field $\vec B$ is then given by