The electric field in an electromagnetic wave is given by $E =56.5 \sin \omega( t - x / c ) \;NC ^{-1}$. Find the intensity of the wave if it is propagating along $x-$axis in the free space. (Given $\left.\varepsilon_{0}=8.85 \times 10^{-12} \;C ^{2} N ^{-1} m ^{-2}\right)$

Calculate the electric and magnetic fields produced by the radiation coming from a $100\; W$ bulb at a distance of $3\; m$. Assume that the efficiency of the bulb is $2.5 \%$ and it is a point source.

A particle of charge $q$ and mass $m$ is moving along the $x-$ axis with a velocity $v,$ and enters a region of electric field $E$ and magnetic field $B$ as shown in figures below. For which figure the net force on the charge may be zero :-

Light with an average flux of $20\, W / cm ^{2}$ falls on a non-reflecting surface at normal incidence having surface area $20\, cm ^{2} .$ The energy recelved by the surface during time span of $1$ minute is $............J$

Electric field in a plane electromagnetic wave is given by ${E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}$ The velocity of electromagnetic wave in this medium is :

(Given ${C}=$ speed of light in vacuum)

Suppose that the electric field amplitude of an electromagnetic wave is $E_{0}=120\; N / C$ and that its frequency is $v=50.0\; MHz$.

$(a)$ Determine, $B_{0}, \omega, k,$ and $\lambda .$

$(b)$ Find expressions for $E$ and $B$