A radiation is emitted by $1000\, W$ bulb and it generates an electric field and magnetic field at $P$, placed at a distance of $2\, m$. The efficiency of the bulb is $1.25 \%$. The value of peak electric field at $P$ is $x \times 10^{-1} \,V / m$. Value of $x$ is. (Rounded-off to the nearest integer)

[Take $\varepsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1} m ^{-2}, c =3 \times 10^{8}$ $ms ^{-1}$ ]

An electric charge $+ q$ moves with velocity $\overrightarrow V  = 3\hat i + 4\hat j + \hat k$ in an electromagnetic field given by :  $\overrightarrow E  = 3\hat i + \hat j + 2\hat k$ and $\overrightarrow B  = \hat i + \hat j - 3\hat k$. The $y-$ component of the force experienced by $+ q$ is :-

The peak electric field produced by the radiation coming from the $8\, W$ bulb at a distance of $10\, m$ is $\frac{x}{10} \sqrt{\frac{\mu_{0} c }{\pi}} \,\frac{ V }{ m }$. The efficiency of the bulb is $10\, \%$ and it is a point source. The value of $x$ is ...... .

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by ${E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .$ The dielectric constant of the medium is equal to :

(Take $\mu_{{r}}=1$ )

A metal sample carrying a current along $X-$ axis with density $J_x$ is subjected to a magnetic field $B_z$ ( along $z-$ axis ). The electric field $E_y$ developed along $Y-$ axis is directly proportional io $J_x$ as well as $B_z$ . The constant of proportionality has $SI\, unit$.

Light is an electromagnetic wave. Its speed in vacuum is given by the expression