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.

An infinitely long thin wire carrying a uniform linear static charge density $\lambda $ is placed along the $z-$ axis (figure). The wire is set into motion along its length with a uniform velocity $V = v{\hat k_z}$. Calculate the pointing vector $S = \frac{1}{{{\mu _0}}}(\vec E \times \vec B)$ .

A plane electromagnetic wave, has frequency of $2.0 \times 10^{10}\, Hz$ and its energy density is $1.02 \times 10^{-8}\, J / m ^{3}$ in vacuum. The amplitude of the magnetic field of the wave is close to$....nT$

$\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{\circ} \frac{ Nm ^{2}}{ C ^{2}}\right.$ and speed of $1 ight$ $\left.=3 \times 10^{8}\, ms ^{-1}\right)$

This question has Statement $-1$ and Statement $-2$ . Of the four choices given after the statements, choose the one that best describes the two statements

Statement $-1$ : Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals

Statement $-2$ : The state of ionosphere varies from hour to hour, day to day and season to season

Which of the following is not transported by electromagnetic waves?

The electric fields of two plane electromagnetic plane waves in vacuum are given by

$\overrightarrow{\mathrm{E}}_{1}=\mathrm{E}_{0} \hat{\mathrm{j}} \cos (\omega \mathrm{t}-\mathrm{kx})$ and

$\overrightarrow{\mathrm{E}}_{2}=\mathrm{E}_{0} \hat{\mathrm{k}} \cos (\omega \mathrm{t}-\mathrm{ky})$

At $t=0,$ a particle of charge $q$ is at origin with a velocity $\overrightarrow{\mathrm{v}}=0.8 \mathrm{c} \hat{\mathrm{j}}$ ($c$ is the speed of light in vacuum). The instantaneous force experienced by the particle is