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
The electric field in an electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=\hat{\mathrm{i}} 40 \cos \omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right) N \mathrm{NC}^{-1}$. The magnetic field induction of this wave is (in SI unit):
The electric field in an electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=\hat{\mathrm{i}} 40 \cos \omega\left(\mathrm{t}-\frac{\mathrm{z}}{\mathrm{c}}\right) N \mathrm{NC}^{-1}$. The magnetic field induction of this wave is (in SI unit):
- [JEE MAIN 2024]
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- [JEE MAIN 2022]
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- [JEE MAIN 2023]
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- [JEE MAIN 2022]
For plan electromagnetic waves propagating in the $z-$ direction, which one of the following combination gives the correct possible direction for $\vec E$ and $\vec B$ field respectively?
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- [JEE MAIN 2015]