An electromagnetic wave with frequency $\omega $ and wavelength $\lambda $ travels in the $+y$ direction. Its magnetic field is along $+x$ axis. The vector equation for the associated electric field (of amplitude $E_0$) is
$\vec E = {E_{0\,}}\,\cos \left( {\omega t - \frac{{2\pi }}{\lambda }y} \right)\hat x$
$\vec E = -{E_{0\,}}\,\cos \left( {\omega t + \frac{{2\pi }}{\lambda }y} \right)\hat x$
$\vec E = -{E_{0\,}}\,\cos \left( {\omega t + \frac{{2\pi }}{\lambda }y} \right)\hat z$
$\vec E = {E_{0\,}}\,\cos \left( {\omega t - \frac{{2\pi }}{\lambda }y} \right)\hat z$
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 :
Which scientist first time produced electromagnetic waves in laboratory?
A monochromatic beam of light has a frequency $v = \frac{3}{{2\pi }} \times {10^{12}}\,Hz$ and is propagating along the direction $\frac{{\hat i + \hat j}}{{\sqrt 2 }}$. It is polarized along the $\hat k$ direction. The acceptable form for the magnetic field is
For a transparent medium relative permeablity and permittlivity, $\mu_{\mathrm{r}}$ and $\epsilon_{\mathrm{r}}$ are $1.0$ and $1.44$ respectively. The velocity of light in this medium would be,
The monoenergetic beam of electrons moving along $+ y$ direction enters a region of uniform electric and magnetic fields. If the beam goes straight undeflected, then fields $B$ and $E$ are directed respectively along