An EM wave from air enters a medium. The electric fields are $\overrightarrow {{E_1}} = {E_{01}}\hat x\;cos\left[ {2\pi v\left( {\frac{z}{c} - t} \right)} \right]$ in air and $\overrightarrow {{E_2}} = {E_{02}}\hat x\;cos\left[ {k\left( {2z - ct} \right)} \right]$ in medium, where the wave number $k$ and frequency $v$ refer to their values in air. The medium is nonmagnetic. If $\varepsilon {_{{r_1}}}$ and $\varepsilon {_{{r_2}}}$ refer to relative permittivities of air and medium respectively, which of the following options is correct?
An EM wave from air enters a medium. The electric fields are $\overrightarrow {{E_1}} = {E_{01}}\hat x\;cos\left[ {2\pi v\left( {\frac{z}{c} - t} \right)} \right]$ in air and $\overrightarrow {{E_2}} = {E_{02}}\hat x\;cos\left[ {k\left( {2z - ct} \right)} \right]$ in medium, where the wave number $k$ and frequency $v$ refer to their values in air. The medium is nonmagnetic. If $\varepsilon {_{{r_1}}}$ and $\varepsilon {_{{r_2}}}$ refer to relative permittivities of air and medium respectively, which of the following options is correct?
- [JEE MAIN 2018]
- A
$\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = 2$
- B
$\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = \frac{1}{4}$
- C
$\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = \frac{1}{2}$
- D
$\frac{{{_{{\epsilon r_1}}}}}{{{_{{\epsilon r_2}}}}} = 4$
Similar Questions
An electromagnetic wave, going through vacuum is described by $E = {E_0}\sin (kx - \omega \,t)$. Which of the following is independent of wavelength
An electromagnetic wave, going through vacuum is described by $E = {E_0}\sin (kx - \omega \,t)$. Which of the following is independent of wavelength
When light propagates through a material medium of relative permittivity $\varepsilon_{ r }$ and relative permeability $\mu_{r^{\prime}}$ the velocity of light, $v$ is given by: (c - velocity of light in vacuum)
- [NEET 2022]
In an electromagnetic wave, the amplitude of electric field is $1 V/m.$ the frequency of wave is $5 \times {10^{14}}\,Hz$. The wave is propagating along $z-$ axis. The average energy density of electric field, in $Joule/m^3$, will be
In an electromagnetic wave, the amplitude of electric field is $1 V/m.$ the frequency of wave is $5 \times {10^{14}}\,Hz$. The wave is propagating along $z-$ axis. The average energy density of electric field, in $Joule/m^3$, will be
An electromagnetic wave with frequency $\omega $ and wavelength $\lambda $ travels in the $+y$ direction. Its magnetic field is along $+x$ axis. The vector equation for the associated electric field (of amplitude $E_0$) is
An electromagnetic wave with frequency $\omega $ and wavelength $\lambda $ travels in the $+y$ direction. Its magnetic field is along $+x$ axis. The vector equation for the associated electric field (of amplitude $E_0$) is
Which scientist first time produced electromagnetic waves in laboratory?
Which scientist first time produced electromagnetic waves in laboratory?