The magnetic field of a plane electromagnetic wave is given by

$\overrightarrow{ B }=2 \times 10^{-8} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ j } T$ The amplitude of the electric field would be.

If a source of electromagnetic radiation having power $15 kW$ produces $10^{16}$ photons per second, the radiation belongs to a part of spectrum is.(Take Planck constant $h =6 \times 10^{-34}\,Js$ )

Figure given shows the face of a cathode-ray oscilloscope tube, as viewed from in front. $i.e.$ the electron beam is coming out normally from the plane of the paper. The electron beam passes through a region where there are electric and magnetic fields directed as shown. The deflections of the spot from the center of the screen produced by the electric field $E$ and the magnetic field $B$ separately are equal in magnitude. Which one of the diagrams below shows a possible position of the spot on the screen when both fields are operating?

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 carbon dioxide laser emits sinusoidal electro-magnetic wave that travels in vacuum in the negative $x-$ direction. The wavelength is $10.6\,\mu $ and $\vec E$ fields is parallel to $z-$ axis, with $E_{max} = 1.5 \times 10^6\, M\, v/m$. Then vector equations for $\vec E$  and $\vec B$ as a function of time and position are