A monochromatic beam of light has a frequency $v = \frac{3}{{2\pi }} \times {10^{12}}\,Hz$ and is propagating along the direction $\frac{{\hat i + \hat j}}{{\sqrt 2 }}$. It is polarized along the $\hat k$ direction. The acceptable form for the magnetic field is
A monochromatic beam of light has a frequency $v = \frac{3}{{2\pi }} \times {10^{12}}\,Hz$ and is propagating along the direction $\frac{{\hat i + \hat j}}{{\sqrt 2 }}$. It is polarized along the $\hat k$ direction. The acceptable form for the magnetic field is
- [JEE MAIN 2018]
- A
$\frac{{{E_0}}}{C}\left( {\frac{{\hat i - \hat j}}{{\sqrt 2 }}} \right)\cos \left[ {{{10}^4}\left( {\frac{{\hat i - \hat j}}{{\sqrt 2 }}} \right)\cdot \vec r - \left( {3 \times {{10}^{12}}} \right)t} \right]$
- B
$\frac{{{E_0}}}{C}\left( {\frac{{\hat i - \hat j}}{{\sqrt 2 }}} \right)\cos \left[ {{{10}^4}\left( {\frac{{\hat i + \hat j}}{{\sqrt 2 }}} \right)\cdot \vec r - \left( {3 \times {{10}^{12}}} \right)t} \right]$
- C
$\frac{{{E_0}}}{C}\hat k\cos \left[ {{{10}^4}\left( {\frac{{\hat i + \hat j}}{{\sqrt 2 }}} \right)\cdot \vec r + \left( {3 \times {{10}^{12}}} \right)t} \right]$
- D
$\frac{{{E_0}}}{C}\frac{{\left( {\hat i + \hat j + \hat k} \right)}}{{\sqrt 3 }}\cos \left[ {{{10}^4}\left( {\frac{{\hat i + \hat j}}{{\sqrt 2 }}} \right)\cdot \vec r + \left( {3 \times {{10}^{12}}} \right)t} \right]$
Similar Questions
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 $EM$ 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.
The ratio of contributions made by the electric field and magnetic fleld components to the intensity of an electromagnetic wave is :
$(c=$ speed of electromagnetic waves)
The ratio of contributions made by the electric field and magnetic fleld components to the intensity of an electromagnetic wave is :
$(c=$ speed of electromagnetic waves)
- [NEET 2020]
Light wave is travelling along y-direction. If the corresponding $\vec E$ vector at any time is along the $x-$axis, the direction of $\vec B$ vector at that time is along
Light wave is travelling along y-direction. If the corresponding $\vec E$ vector at any time is along the $x-$axis, the direction of $\vec B$ vector at that time is along
Electromagnetic wave consists of periodically oscillating electric and magnetic vectors
Electromagnetic wave consists of periodically oscillating electric and magnetic vectors
The magnetic field of a beam emerging from a filter facing a floodlight is given by B${B_0} = 12 \times {10^{ - 8}}\,\sin \,(1.20 \times {10^7}\,z - 3.60 \times {10^{15}}t)T$. What is the average intensity of the beam ?
The magnetic field of a beam emerging from a filter facing a floodlight is given by B${B_0} = 12 \times {10^{ - 8}}\,\sin \,(1.20 \times {10^7}\,z - 3.60 \times {10^{15}}t)T$. What is the average intensity of the beam ?