A light beam is described by $E=800 \sin \omega\left(t-\frac{x}{c}\right)$

An electron is allowed to move normal to the propagation of light beam with a speed of $3 \times 10^{7}\;{ms}^{-1}$. What is the maximum magnetic force exerted on the electron ?

An antenna is placed in a dielectric medium of dielectric constant $6.25$. If the maximum size of that antenna is $5.0\, mm$. it can radiate a signal of minimum frequency of $GHz .$

(Given $\mu_{ r }=1$ for dielectric medium)

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

A plane electromagnetic wave propagating in $\mathrm{x}$-direction is described by

$\mathrm{E}_{\mathrm{y}}=\left(200\  \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 \mathrm{t}-0.05\  \mathrm{x}\right] \text {; }$

The intensity of the wave is :(Use $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

A plane $EM$ wave travelling along $z-$ direction is described$\vec E = {E_0}\,\sin \,(kz - \omega t)\hat i$ and $\vec B = {B_0}\,\sin \,(kz - \omega t)\hat j$. Show that

$(i)$ The average energy density of the wave is given by $U_{av} = \frac{1}{4}{ \in _0}E_0^2 + \frac{1}{4}.\frac{{B_0^2}}{{{\mu _0}}}$

$(ii)$ The time averaged intensity of the wave is given by  $ I_{av}= \frac{1}{2}c{ \in _0}E_0^2$ વડે આપવામાં આવે છે.

A plane electromagnetic wave with frequency of $30 {MHz}$ travels in free space. At particular point in space and time, electric field is $6 {V} / {m}$. The magnetic field at this point will be ${x} \times 10^{-8} {T}$. The value of ${x}$ is ..... .