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 :-
$E_y = 33\ cos\ \pi \times 10^{11} \left( {t - \frac{x}{c}} \right)$
$B_z = 1.1 \times 10^{-7}\ cos \pi \times 10^{11}\left( {t - \frac{x}{c}} \right)$
$E_y = 11\ cos\ 2\pi \times 10^{11} \left( {t - \frac{x}{c}} \right)$
$B_z = 11 \times 10^{-7}\ cos 2\pi \times 10^{11}\left( {t - \frac{x}{c}} \right)$
$E_y = 33\ cos\ \pi \times 10^{11} \left( {t - \frac{x}{c}} \right)$
$B_z = 11 \times 10^{-7}\ cos \pi \times 10^{11}\left( {t - \frac{x}{c}} \right)$
$E_y = 66\ cos\ 2\pi \times 10^{11} \left( {t - \frac{x}{c}} \right)$
$B_z = 2.2 \times 10^{-7}\ cos 2\pi \times 10^{11}\left( {t - \frac{x}{c}} \right)$
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 $\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ ]
Given below are two statements:
Statement $I$ : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates $EM$ waves.
Statement $II$ : In a material medium. The $EM$ wave travels with speed $v =\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$.
In the light of the above statements, choose the correct answer from the options given below
In the $EM$ wave the amplitude of magnetic field $H_0$ and the amplitude of electric field $E_o$ at any place are related as
A velocity selector consists of electric field $\overrightarrow{ E }= E \hat{ k }$ and magnetic field $\overrightarrow{ B }= B \hat{ j }$ with $B =12 mT$.
The value $E$ required for an electron of energy $728 eV$ moving along the positive $x$-axis to pass undeflected is:
(Given, , ass of electron $=9.1 \times 10^{-31} kg$ )
The speed of electromagnetic wave in vacuum depends upon the source of radiation