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
A lamp emits monochromatic green light uniformly in all directions. The lamp is $3\%$ efficient in converting electrical power to electromagnetic waves and consumes $100\,W$ of power . The amplitude of the electric field associated with the electromagnetic radiation at a distance of $5\,m$ from the lamp will be nearly.......$V/m$
A lamp emits monochromatic green light uniformly in all directions. The lamp is $3\%$ efficient in converting electrical power to electromagnetic waves and consumes $100\,W$ of power . The amplitude of the electric field associated with the electromagnetic radiation at a distance of $5\,m$ from the lamp will be nearly.......$V/m$
- [JEE MAIN 2014]
The energy of an electromagnetic wave contained in a small volume oscillates with
The energy of an electromagnetic wave contained in a small volume oscillates with
- [JEE MAIN 2023]
If a source is transmitting electromagnetic wave of frequency $8.2 \times {10^6}Hz$, then wavelength of the electromagnetic waves transmitted from the source will be.....$m$
If a source is transmitting electromagnetic wave of frequency $8.2 \times {10^6}Hz$, then wavelength of the electromagnetic waves transmitted from the source will be.....$m$
Given below are two statements:
Statement $I$ : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates $EM$ waves.
Statement $II$ : In a material medium. The $EM$ wave travels with speed $v =\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$.
In the light of the above statements, choose the correct answer from the options given below
Given below are two statements:
Statement $I$ : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates $EM$ waves.
Statement $II$ : In a material medium. The $EM$ wave travels with speed $v =\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$.
In the light of the above statements, choose the correct answer from the options given below
- [JEE MAIN 2022]
Electromagnetic waves are transverse in nature is evident by
Electromagnetic waves are transverse in nature is evident by
- [AIEEE 2002]