The electric field associated with an electromagnetic $(EM)$ wave in vacuum is given by $\vec{E} = \hat{i} 40 \cos (kz - 6 \times 10^{8} t)$,where $E$,$z$,and $t$ are in $V/m$,$m$,and $s$ respectively. The value of the wave vector $k$ is .... $m^{-1}$.

Energy stored in electromagnetic oscillations is in the form of

The vectors $\vec{E}$ and $\vec{B}$ of an electromagnetic wave in vacuum are

About $20 \%$ of the power of a $100 \ W$ bulb is converted to visible radiation. Assuming that the radiation is emitted isotropically and neglecting reflection,the average intensity of visible radiation at a distance of $5 \ m$ is $\frac{\alpha}{25 \pi} \ W/m^2$. The value of $\alpha$ is

In a plane electromagnetic wave,$U_E$ and $U_B$ are the average energy densities of the electric field and magnetic field,respectively. Then,which of the following is the correct option?

$A$ 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 of $66\, Vm^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively: