# Solved papers for JEE Main & Advanced Physics EM Waves JEE PYQ-Electro Magnetic Waves

### done JEE PYQ-Electro Magnetic Waves Total Questions - 55

• question_answer1) Which of the following are not electromagnetic waves?             [AIEEE 2002]

A)
Cosmic-rays

B)
y-rays

C)
$\beta$-rays

D)
X-rays

A)
spectrometer

B)
pyrometer

C)
nanometer

D)
photometer

• question_answer3) Which of the following radiations has the least wavelength?                 [AIEEE 2003]

A)
$\gamma$-rays

B)
$\beta$-rays

C)
$\alpha$-rays

D)
$X$-rays

• question_answer4) An electromagnetic wave of frequency $v=3.0MHz$passes from vacuum into a dielectric medium with permittivity$\varepsilon =4.0.$ Then,                                       [AIEEE 2004]

A)
wavelength is doubled and the frequency remains unchanged

B)
wavelength is' doubled and frequency becomes half

C)
wavelength is halved and frequency remains unchanged

D)
wavelength and frequency  both remain unchanged

• question_answer5) The rms value of the electric field of the light coming from the sun is 720 N/C. The average total energy density of the electromagnetic wave is                                           [AIEEE 2006]

A)
$4.58\times {{10}^{-6}}J/{{m}^{3}}$

B)
$6.37\times {{10}^{-9}}J/{{m}^{3}}$

C)
$81.35\times {{10}^{-12}}J/{{m}^{3}}$

D)
$3.3\times {{10}^{-3}}J/{{m}^{3}}$

• question_answer6) A fully charged capacitor C with initial charge ${{q}_{0}}$ is connected to a coil of self-inductance L at $t=0$. The time at which the energy is stored equally between the electric and the magnetic fields is [AIEEE 2011]

A)
$\sqrt{LC}$

B)
$\pi \sqrt{LC}$

C)
$\frac{\pi }{4}\sqrt{LC}$

D)
$2\pi \sqrt{LC}$

• question_answer7) An electromagnetic wave in vacuum has the electric and magnetic field $\vec{E}$ and $\vec{B}$, which are always perpendicular to each other. The direction of polarization is given by $\vec{X}$ and that of wave propagation by $\vec{k}$. Then                                                           [AIEEE 2012]

A)
$\vec{X}||\vec{B}$ and $\vec{k}||\vec{B}\times \vec{E}$

B)
$\vec{X}||\vec{E}$ and $\vec{k}||\vec{E}\times \vec{B}$

C)
$\vec{X}||\vec{B}$ and $\vec{k}||\vec{E}\times \vec{B}$

D)
$\vec{X}||\vec{E}$ and $\vec{k}||\vec{B}\times \vec{E}$

• question_answer8) An electromagnetic wave with frequency co 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        [JEE ONLINE 19-05-2012]

A)
$\overset{\to }{\mathop{E}}\,=-{{E}_{0}}\cos \left( \omega t+\frac{2\pi }{\lambda }y \right)\hat{x}$

B)
$\overset{\to }{\mathop{E}}\,={{E}_{0}}\cos \left( \omega t-\frac{2\pi }{\lambda }y \right)\hat{x}$

C)
$\overset{\to }{\mathop{E}}\,={{E}_{0}}\cos \left( \omega t-\frac{2\pi }{\lambda }y \right)\hat{z}$

D)
$\overset{\to }{\mathop{E}}\,=-{{E}_{0}}\cos \left( \omega t+\frac{2\pi }{\lambda }y \right)\hat{z}$

• question_answer9) A radio transmitter transmits at 830 kHz. At a certain distance from the transmitter magnetic field has amplitude $4.82\times {{10}^{-11}}T.$The electric field and the wavelength are respectively[JEE ONLINE 26-05-2012]

A)
0.014N/C, 36m

B)
0.14N/C, 36m

C)
0.14N/C, 360m

D)
0.014N/C, 360m

• question_answer10) The frequency of X-rays; $\gamma \text{-}$rays and ultraviolet rays are respectively a, b and c then [JEE ONLINE 26-05-2012]

A)
$a<b;b>c$

B)
$a>b;b>c$

C)
$a<b<c$

D)
$a=b=c$

• question_answer11) The magnetic field in a travelling electromagnetic wave has a peak value of 20 $nT$. The peak value of electric field strength is:                                             [JEE MAIN 2013]

A)
$\frac{3V}{m}$

B)
$\frac{6V}{m}$

C)
$\frac{9V}{m}$

D)
$\frac{12V}{m}$

• question_answer12) Photons of an electromagnetic radiation has an energy 11 keV each. To which region of electromagnetic spectrum does it belong?                                  [JEE ONLINE 09-04-2013]

A)
X-ray region

B)
Ultra violet region

C)
Infrared region

D)
Visible region

• question_answer13) A plane electromagnetic wave in a non-magnetic dielectric medium is given by $\overset{\to }{\mathop{\operatorname{E}}}\,={{\overset{\to }{\mathop{\operatorname{E}}}\,}_{0}}$$(4\times {{10}^{-7}}x-50t)$ with distance being in meter and time in seconds. The dielectric constant of the medium is:      [JEE ONLINE 22-04-2013]

A)
2.4

B)
5.8

C)
8.2

D)
4.8

• question_answer14) Select the correct statement form the following:                    [JEE ONLINE 23-04-2013]

A)
Electromagnetic waves cannot travel in vacuum

B)
Electromagnetic waves are longitudinal waves

C)
Electromagnetic waves are produced by charge moving with uniform velocity.

D)
Electromagnetic waves carry both energy and momentum as they processes through space.

Match List  I (Electromagnetic wave type) with List  II (Its association/application) and select the correct option from the choices given below the lists:         [JEE MAIN 2014]
 List I List-II Infrared waves (i) To treat muscular strain Radio waves (ii) For broadcasting X-rays (iii) To detect fracture of bones Ultraviolet rays (iv) Absorbed by the ozone layer of the atmosphere

A)
A-(iii),  B-(ii),   C-(i),    D-(iv)

B)
A-(i),    B-(ii),   C-(iii),  D-(iv)

C)
A-(iv),  B-(iii),  C-(ii),   D-(i)

D)
A-(i),    B-(ii),   C-(iv),  D-(iii)

• question_answer16) During the propagation of electromagnetic waves in a medium:                   [JEE MAIN 2014]

A)
Electric energy density is equal to the magnetic energy density.

B)
Both electric and magnetic energy densities are zero.

C)
Electric energy density is double of the magnetic energy density.

D)
Electric energy density is half of the magnetic density.

Match List I (Wavelength range of electromagnetic spectrum) with List II (Method of production of these waves) and select the correct option from the options given below the lists.
 List I List II (1) 700 nm to 1 mn (i) Vibration of atoms and molecules. (2) 1 nm to 400 nm (ii) Inner shell electrons in atoms moving from one energy level to a lower level. (3)$<{{10}^{-3}}nm$ (iii) Radioactive decay of the nucleus. (4) 1 mm to 0.1 m (iv) Magnetron valve.
[JEE ONLINE 09-04-2014]

A)
(1)-(iv), (2)-(iii), (3)-(ii), (4)-(i)

B)
(1)-(iii), (2)-(iv), (3)-(i), (4)-(ii)

C)
(1)-(ii), (2)-(iii), (3)-(iv), (4)-(i)

D)
(1)-(i), (2)-(ii), (3)-(iii), (4)-(iv)

• question_answer18) An electromagnetic wave of frequency  $1\times {{10}^{14}}$ hertz is propagating along z-axis. The amplitude of electric field is 4 V/m. If ${{\varepsilon }_{0}}=8.8\times {{10}^{-12}}{{C}^{2}}/N-{{m}^{2}},$then average energy density of electric field will be:          [JEE ONLINE 11-04-2014]

A)
$35.2\times {{10}^{-10}}J/{{m}^{3}}$

B)
$35.2\times {{10}^{-11}}J/{{m}^{3}}$

C)
$35.2\times {{10}^{-12}}J/{{m}^{3}}$

D)
$35.2\times {{10}^{-13}}J/{{m}^{3}}$

Match the List-I (Phenomenon associated with electromagnetic radiation) with List-II (Part of electromagnetic spectrum) and select the correct code from the choices given below this lists:      [JEE ONLINE 11-04-2014]
 (I) Doublet of sodium Visible radiation (II) Wavelength corresponding to temperature associated with the isotropic radiation filling all space Microwave (III) Wavelength emitted by Atomic hydrogen in Interstellar space Short radio wave (IV) Wavelength of radiation arising from two close energy levels in hydrogen X-rays

A)
(I)-, (II)-, (III)-, (IV)-

B)
(I)-, (II)-, (III)-, (IV)-

C)
(I)-, (II)-, (III)-, (IV)-

D)
(I)-, (II)-, (III)-, (IV)-

• question_answer20) 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:                              [JEE ONLINE 12-04-2014]

A)
1.34 V/m

B)
2.68 V/m

C)
4.02 V/m

D)
5.36 V/m

• question_answer21) If microwaves, X rays, infrared, gamma rays, ultra-violet, radio waves and visible parts of the electromagnetic spectrum by are denoted M, X, I, G, U, R and V then which of the following is the arrangement in ascending order of wavelength? [JEE ONLINE 19-04-2014]

A)
R, M, I, V, U, X and G

B)
M, R, V, X, U, G and I

C)
G, X, U, V, I, M and R

D)
I, M, R, U, V, X and G

• question_answer22) A red LED emits light at 0.1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1m from the diode is:                                    [JEE MAIN 2015]

A)
5.48 V/m

B)
7.75 V/m

C)
1.73 V/m

D)
2.45 V/mions /

• question_answer23) An electromagnetic wave travelling in the x-direction has frequency of $2\times {{10}^{14}}Hz$and electric field amplitude of $27V{{m}^{-1}}.$From the options given below, which one describes the magnetic field for this wave? [JEE ONLINE 10-04-2015]

A)
$\overset{\to }{\mathop{B}}\,(x.t)=(9\times {{10}^{-8}}T)\hat{i}$$\sin \left[ 2\pi (1.5\times {{10}^{-8}}x-2\times {{10}^{14}}t) \right]$

B)
$\overset{\to }{\mathop{B}}\,(x,t)=(3\times {{10}^{-8}}T)\hat{j}$ $\sin \left[ 1.5\times {{10}^{-6}}x-2\times {{10}^{14}}t) \right]$

C)
$\overset{\to }{\mathop{B}}\,(x,t)=(3\times {{10}^{-8}}T)\hat{j}$$\sin \left[ 2\pi (1.5\times {{10}^{-8}}x-2\times {{10}^{14}}t) \right]$

D)
None of these

• question_answer24) For plane electromagnetic waves propagating in the z direction, which one of the following combination gives the correct possible direction for $\overset{\to }{\mathop{E}}\,$and $\overset{\to }{\mathop{B}}\,$field respectively? [JEE MAIN 11-04-2015]

A)
$\left( \hat{i}+2\hat{j} \right)$and$\left( 2\hat{i}-\hat{j} \right)$

B)
$\left( -2\hat{i}-3\hat{j} \right)$and$\left( 3\hat{i}-2\hat{j} \right)$

C)
$\left( 2\hat{i}+3\hat{j} \right)$and$\left( \hat{i}+2\hat{j} \right)$

D)
$\left( 3\hat{i}+4\hat{j} \right)$and$\left( 4\hat{i}-3\hat{j} \right)$

• question_answer25)  Arrange the following electromagnetic radiations per quantum in the order of increasing energy :-      [JEE MAIN - I 3-4-2016] A : Blue light                B : Yellow light C : Xray                     D : Radio wave

A)
B, A, D, C

B)
D, B, A, C

C)
A, B, D, C

D)
C, A, B, D

• question_answer26) Microwave oven acts on the principle of:                             [JEE ONLINE 09-04-2016]

A)
giving rotational energy to water molecules

B)
giving vibrational energy to water molecules

C)
giving translational energy to water molecules

D)
transferring electrons from lower to higher energy levels in water molecule

• question_answer27) Consider an electromagnetic wave propagating in vacuum. Choose the correct statement:            [JEE ONLINE 10-04-2016]

A)
For an electromagnetic wave propagating in +y direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( x,t \right)\hat{z}$and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{z}}\left( x,t \right)\hat{y}$

B)
For an electromagnetic wave propagating in +y direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( x,t \right)\hat{y}$and he magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{yz}}\left( x,t \right)\hat{z}$

C)
For an electromagnetic wave propagating in +x direction the electric field is             $\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( y,z,t \right)\left( \hat{y}+\hat{z} \right)$ and the magnetic field is $\overrightarrow{B}=\frac{1}{\sqrt{2}}{{B}_{yz}}\left( y,z,t \right)\left( \hat{y}+\hat{z} \right)$

D)
For an electromagnetic wave propagating in +x direction the electric field is $\overrightarrow{E}=\frac{1}{\sqrt{2}}{{E}_{yz}}\left( x,t \right)\left( \hat{y}-\hat{z} \right)$ and eh magnetic field is $B=\frac{1}{\sqrt{2}}{{B}_{yz}}\left( x,t \right)\left( \hat{y}+\hat{z} \right)$

• question_answer28) Magnetic field in a plane electromagnetic wave is given by$\vec{B}={{B}_{0}}\sin (kx+\omega t)\hat{j}T$ Expression for corresponding electric field will be                    [JEE Online 08-04-2017]

A)
$\vec{E}=-{{B}_{0}}c\sin (kx+\omega t)\hat{k}V/m$

B)
$\vec{E}={{B}_{0}}c\sin (kx-\omega t)\hat{k}V/m$

C)
$\vec{E}={{B}_{0}}c\sin (kx+\omega t)\hat{k}V/m$

D)
$\vec{E}=\frac{{{B}_{0}}}{c}\sin \,(kx+\omega t)\hat{k}V/m$

• question_answer29) The electric field component of a monochromatic radiation is given by $\vec{E}=2{{E}_{0}}\hat{i}\,\cos kz\,\cos \omega t$ Its magnetic field $\vec{B}$  [JEE Online 09-04-2017]

A)
$\frac{2{{E}_{0}}}{c}\hat{j}\,\sin kz\,\sin \omega t$

B)
$\frac{2{{E}_{0}}}{c}\hat{j}\cos kz\,\cos \omega t$

C)
$\frac{2{{E}_{0}}}{c}\hat{j}\sin kz\,\cos \omega t$

D)
$-\frac{2{{E}_{0}}}{c}\hat{j}\sin kz\,\sin \omega t$

• question_answer30) An EM wave from air enters a medium. The electric fields are ${{\overset{\to }{\mathop{\text{E}}}\,}_{1}}={{E}_{01}}\,\,\widehat{x}\cos \left[ 2\pi v\left( \frac{z}{c}-t \right) \right]$ in air and ${{\overset{\to }{\mathop{\text{E}}}\,}_{2}}={{E}_{02}}\,\,\widehat{x}\cos [k(2z-ct)]$ in medium, where the wave number $k$ and frequency $v$ refer to their values in air. The medium is non-magnetic. If ${{\in }_{{{r}_{1}}}}$ and ${{\in }_{{{r}_{2}}}}$refer to relative permittivitys of air and medium respectively, which of the following options is correct? [JEE Main Online 08-04-2018]

A)
$\frac{{{\in }_{{{r}_{1}}}}}{{{\in }_{{{r}_{2}}}}}=\frac{1}{4}$

B)
$\frac{{{\in }_{{{r}_{1}}}}}{{{\in }_{{{r}_{2}}}}}=\frac{1}{2}$

C)
$\frac{{{\in }_{{{r}_{1}}}}}{{{\in }_{{{r}_{2}}}}}=4$

D)
$\frac{{{\in }_{{{r}_{1}}}}}{{{\in }_{{{r}_{2}}}}}=2$

• question_answer31) A monochromatic beam of light has a frequency $v=\frac{3}{2\pi }\times {{10}^{12}}Hz$ and is propagating along the direction$\frac{\widehat{i}+\widehat{j}}{\sqrt{2}}$. It is polarized along $\widehat{k}$ the direction. The acceptable form for the magnetic field is: [JEE Online 15-04-2018]

A)
$k\frac{{{E}_{0}}}{C}\left( \frac{\widehat{i}-\widehat{j}}{\sqrt{2}} \right)\cos \left[ {{10}^{4}}\left( \frac{\widehat{i}-\widehat{j}}{\sqrt{2}} \right).\overrightarrow{r}-(3\times {{10}^{12}})t \right]$

B)
$\frac{{{E}_{0}}}{C}\left( \frac{\widehat{i}-\widehat{j}}{\sqrt{2}} \right)\cos \left[ {{10}^{4}}\left( \frac{\widehat{i}+\widehat{j}}{\sqrt{2}} \right).\overrightarrow{r}-(3\times {{10}^{12}})t \right]$

C)
$\frac{{{E}_{0}}}{C}\widehat{k}\cos \left[ {{10}^{4}}\left( \frac{\widehat{i}+\widehat{j}}{\sqrt{2}} \right).\overrightarrow{r}+(3\times {{10}^{12}})t \right]$

D)
$\frac{{{E}_{0}}}{C}\frac{\left( \widehat{i}+\widehat{j}+\widehat{k} \right)}{\sqrt{3}}\cos \left[ {{10}^{4}}\left( \frac{\widehat{i}+\widehat{j}}{\sqrt{2}} \right).\overrightarrow{r}+(3\times {{10}^{12}})t \right]$

• question_answer32) A plane polarized monochromatic EM wave is travelling a vacuum along z direction such that at $t={{t}_{1}}$ it is found that the electric field is zero at a spatial point ${{z}_{1}}$. The next zero that occurs in its neighbourhood is at ${{z}_{2}}$. The frequency of the electromagnetic wave is: [JEE Online 15-04-2018 (II)]

A)
$\frac{3\times {{10}^{8}}}{|{{z}_{2}}-{{z}_{1}}|}$

B)
$\frac{6\times {{10}^{8}}}{|{{z}_{2}}-{{z}_{1}}|}$

C)
$\frac{1.5\times {{10}^{8}}}{|{{z}_{2}}-{{z}_{1}}|}$

D)
$\frac{1}{{{t}_{1}}+\frac{|{{z}_{2}}-{{z}_{1}}|}{3\times {{10}^{8}}}}$

• question_answer33) A plane electromagnetic wave of wavelength$\lambda$ has an intensity $I.$ It is propagating along the positive$Y-direction.$ The allowed expressions for the electric and magnetic fields are given by

A)
$\vec{E}=\sqrt{\frac{I}{{{\varepsilon }_{0}}C}}\cos \left[ \frac{2\pi }{\lambda }(y-ct) \right]\hat{i};\vec{B}=\frac{1}{c}E\hat{k}$

B)
$\vec{E}=\sqrt{\frac{I}{{{\varepsilon }_{0}}C}}\cos \left[ \frac{2\pi }{\lambda }(y-ct) \right]\hat{k};\vec{B}=-\frac{1}{c}E\hat{i}$

C)
$\vec{E}=\sqrt{\frac{2I}{{{\varepsilon }_{0}}C}}\cos \left[ \frac{2\pi }{\lambda }(y-ct) \right]\hat{k};\vec{B}=+\frac{1}{c}E\hat{i}$

D)
$\vec{E}=\sqrt{\frac{2I}{{{\varepsilon }_{0}}C}}\cos \left[ \frac{2\pi }{\lambda }(y+ct) \right]\hat{k};\vec{B}=\frac{1}{c}E\hat{i}$

• question_answer34) A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time,$\overrightarrow{E}=6.3\text{ }\overrightarrow{j}\text{ }V/m$. The corresponding magnetic field B, at that point will be- [JEE Main 09-Jan-2019 Morning]

A)
$18.9\times {{10}^{-8}}\text{ }\widehat{k}T$

B)
$2.1\times {{10}^{-8}}\text{ }\widehat{k}T$

C)
$18.9\times {{10}^{8}}\text{ }\widehat{k}T$

D)
$6.3\times {{10}^{-8}}\text{ }\widehat{k}T$

• question_answer35) The energy associated with electric field is (${{U}_{E}}$) and with magnetic field is (${{U}_{B}}$) for an electromagnetic wave in free space. Then: [JEE Main 09-Jan-2019 Evening]

A)
${{U}_{E}}<{{U}_{B}}$

B)
${{U}_{E}}=\,\frac{{{U}_{B}}}{2}$

C)
${{U}_{E}}={{U}_{B}}$

D)
${{U}_{E}}>{{U}_{B}}$

• question_answer36) If the magnetic field of a plane electromagnetic wave is given by (the speed of light $=~\,3~\times ~{{10}^{8}}m/s)$ $B\,=\,100\times {{10}^{-6}}\,\sin \,\left[ 2\pi \times 2\times {{10}^{15}}\left( t-\frac{x}{c} \right) \right]$then the maximum electric field associated with it is  [JEE Main 10-Jan-2019 Morning]

A)
$4.5\times {{10}^{4}}\,N/C$

B)
$4\times {{10}^{4}}\,N/C$

C)
$6\times {{10}^{4}}\,N/C$

D)
$3\times {{10}^{4}}\,N/C$

• question_answer37) The electric field of a plane polarized electromagnetic wave in free space at time  $t=0$ is given by an expression $\overrightarrow{E}\left( x,y \right)=10\widehat{j}\text{ }cos\left[ \left( 6x+8z \right) \right]$. The magnetic field $\overrightarrow{B}\left( x,\text{ }z,\text{ }t \right)$ is given by - (c is the velocity of light) [JEE Main 10-Jan-2019 Evening]

A)
$\frac{1}{c}(6\widehat{k}+8\widehat{i})\,cos[(6x+8z-10ct)]$

B)
$\frac{1}{c}(6\widehat{k}-8\widehat{i})\,cos[(6x+8z-10ct)]$

C)
$\frac{1}{c}(6\widehat{k}+8\widehat{i})\,cos[(6x-8z+10ct)]$

D)
$\frac{1}{c}(6\widehat{k}-8\widehat{i})\,cos[(6x+8z+10ct)]$

• question_answer38) A 27 mW laser beam has a cross-sectional area of$10\text{ }m{{m}^{2}}$. The magnitude of the maximum electric field in this electromagnetic wave is given by [Given permittivity of space${{\varepsilon }_{0}}=9\times {{10}^{-12}}$ SI units, speed of light $c=3\times {{10}^{8}}m/s$] [JEE Main 11-Jan-2019 Evening]

A)
2 kV/m

B)
0.7 kV/m

C)
1 kV/m

D)
1.4 kV/m

• question_answer39) The mean intensity of radiation on the surface of the Sun is about ${{10}^{8}}W/{{m}^{2}}$. The rms value of the corresponding magnetic field is closest to [JEE Main 12-Jan-2019 Evening]

A)
${{10}^{-2}}T$

B)
$1T$

C)
${{10}^{-4}}T$

D)
${{10}^{2}}T$

• question_answer40) A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is $E=6V{{m}^{-1}}$ along y-direction. Its corresponding magnetic field component, B would be :      [JEE Main 8-4-2019 Morning]

A)
$6\times {{10}^{-8}}T$ along z-direction

B)
$6\times {{10}^{-8}}T$ along x-direction

C)
$2\times {{10}^{-8}}T$ along z-direction

D)
$2\times {{10}^{-8}}T$ along y-direction

• question_answer41) A circuit connected to an ac source of emf $e={{e}_{0}}\sin (100t)$with t in seconds, gives a phase difference of$\frac{\pi }{4}$ between the emf e and current i. Which of the following circuits will exhibit this? [JEE Main 8-4-2019 Afternoon]

A)
RC circuit with $R=1k\Omega$and $C=1\mu F$

B)
RL circuit with $R=1k\Omega$ and L = 1mH

C)
RL circuit with $R=1k\Omega$ and L = 10 mH

D)
RC circuit with $R=1k\Omega$ and $C=10\mu F$

• question_answer42) The magnetic field of an electromagnetic wave is given by :- $\vec{B}=1.6\times {{10}^{-6}}\cos \left( 2\times {{10}^{7}}z+6\times {{10}^{15}}t \right)\left( 2\hat{i}+\hat{j} \right)\frac{Wb}{{{m}^{2}}}$The associated electric field will be :-             [JEE Main 8-4-2019 Afternoon]

A)
$\vec{E}=4.8\times {{10}^{2}}\cos \left( 2\times {{10}^{7}}z+6\times {{10}^{15}}t \right)\left( \hat{i}-2\hat{j} \right)\frac{V}{m}$

B)
$\vec{E}=4.8\times {{10}^{2}}\cos \left( 2\times {{10}^{7}}z-6\times {{10}^{15}}t \right)\left( 2\hat{i}+\hat{j} \right)\frac{V}{m}$

C)
$\vec{E}=4.8\times {{10}^{2}}\cos \left( 2\times {{10}^{7}}z-6\times {{10}^{15}}t \right)\left( -2\hat{j}+\hat{i} \right)\frac{V}{m}$

D)
$\vec{E}=4.8\times {{10}^{2}}\cos \left( 2\times {{10}^{7}}z+6\times {{10}^{15}}t \right)\left( -\hat{i}+2\hat{j} \right)\frac{V}{m}$

• question_answer43) The electric field of light wave is given as $\vec{E}={{10}^{-3}}\cos \left( \frac{2\pi x}{5\times {{10}^{-7}}}-2\pi \times 6\times {{10}^{14}}t \right)$$\hat{x}\frac{N}{C}.$This light falls on a metal plate of work function 2eV. The stopping potential of the photo-electrons is : Given, E (in eV) $=\frac{12375}{\lambda (in{\AA})}$      [JEE Main 9-4-2019 Morning]

A)
0.48 V

B)
2.0 V

C)
2.48 V

D)
0.72 V

• question_answer44)  The magnetic field of a plane electromagnetic wave is given by : $\vec{B}={{B}_{0}}\hat{i}[cos(kz-\omega t)]+{{B}_{1}}\hat{j}\cos (kz+\omega t)$ where ${{B}_{0}}=3\times {{10}^{-5}}T$ and ${{B}_{1}}=2\times {{10}^{-6}}T.$ The rms  value of the force experienced by a stationary charge $Q={{10}^{-4}}C$at $z=0$is closest to :         [JEE Main 9-4-2019 Morning]

A)
$0.9\text{ }N$

B)
$0.1\text{ }N$

C)
$3\times {{10}^{2}}N$

D)
$0.6N$

• question_answer45)  The electric field of a plane electromagnetic wave is given by $\vec{E}={{E}_{0}}\hat{i}\cos (kz)cos(\omega t)$ The corresponding magnetic field $\vec{B}$is then given by:      [JEE Main 10-4-2019 Morning]

A)
$\vec{B}=\frac{{{E}_{0}}}{C}\hat{j}\sin (kz)cos(\omega t)$

B)
$\vec{B}=\frac{{{E}_{0}}}{C}\hat{j}\sin (kz)sin(\omega t)$

C)
$\vec{B}=\frac{{{E}_{0}}}{C}\hat{k}\sin (kz)cos(\omega t)$

D)
$\vec{B}=\frac{{{E}_{0}}}{C}\hat{j}\sin (kz)sin(\omega t)$

• question_answer46) The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz is : [JEE Main 10-4-2019 Afternoon]

A)

B)

C)

D)

• question_answer47) An electromagnetic wave is represented by the electric field $\vec{E}={{E}_{0}}\hat{n}\sin [\omega t+(6y-8z)]$. Taking unit vectors in x, y and z directions to be $\hat{i}.\hat{j},\hat{k},$the direction of propagation $\hat{s},$ is: [JEE Main Held on 12-4-2019 Morning]

A)
$\hat{s}=\frac{4\hat{j}-3\hat{k}}{5}$

B)
$\hat{s}=\frac{3\hat{j}-4\hat{j}}{5}$

C)
$\hat{s}=\left( \frac{-3\hat{j}+4\hat{k}}{5} \right)$

D)
$\hat{s}=\frac{-4\hat{j}+3\hat{j}}{5}$

• question_answer48)  Consider the LR circuit shown in the figure. If the switch S is closed at t = 0 then the amount of charge that passes through the battery between t = 0 and $t=\frac{L}{R}$is [JEE Main 12-4-2019 Afternoon]

A)
$\frac{EL}{7.3{{R}^{2}}}$

B)
$\frac{EL}{2.7{{R}^{2}}}$

C)
$\frac{7.3EL}{{{R}^{2}}}$

D)
$\frac{2.7EL}{{{R}^{2}}}$

• question_answer49) A plane electromagnetic wave having a frequency v = 23.9 GHz propagates along the positive z-direction in free space. The peak value of the electric field is 60 V/m. Which among the following is the acceptable magnetic field component in the electromagnetic wave? [JEE Main 12-4-2019 Afternoon]

A)
$\vec{B}=2\times {{10}^{7}}\sin (0.5\times {{10}^{3}}z+1.5\times {{10}^{11}}t)\hat{i}$

B)
$\vec{B}=2\times {{10}^{-7}}\sin (1.5\times {{10}^{2}}x+0.5\times {{10}^{11}}t)\hat{j}$

C)
$\vec{B}=2\times {{10}^{-7}}\sin (0.5\times {{10}^{3}}z-1.5\times {{10}^{11}}t)\hat{i}$

D)
$\vec{B}=60\sin (0.5\times {{10}^{3}}x+1.5\times {{10}^{11}}t)\hat{k}$

• question_answer50) If the magnetic field in a plane electromagnetic wave is given by $\overline{B}=3\times {{10}^{-8}}\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{j}T$, then what will be expression for electric field? [JEE MAIN Held on 07-01-2020 Morning]

A)
$\vec{E}=\left( 60\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{k}V/m \right)$

B)
$\vec{E}=\left( 3\times {{10}^{-8}}\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{i}V/m \right)$

C)
$\vec{E}=\left( 9\sin (1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{k}V/m \right)$

D)
$\vec{E}=\left( 3\times {{10}^{-8}}sin(1.6\times {{10}^{3}}x+48\times {{10}^{10}}t)\hat{j}V/m \right)$

• question_answer51)  The electric field of a plane electromagnetic wave is given by $\vec{E}={{E}_{0}}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\,\cos \,(kz+\omega t)$ At t = 0, a positively charged particle is at the point $(x,y,z)\,=\,\left( 0,0,\,\frac{\pi }{k} \right)$. If its instantaneous velocity at (t = 0) is${{v}_{0}}\,\hat{k},$, the force acting on it due to the wave is: [JEE MAIN Held on 07-01-2020 Evening]

A)
Antiparallel to $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$

B)
Zero

C)
Parallel to $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$

D)
Parallel to $\hat{k}$

• question_answer52) The critical angle of medium for a specific wavelength, if the medium has relative permittivity 3 and relative permeability$\frac{4}{3}$ for this wavelength, will be [JEE MAIN Held On 08-01-2020 Morning]

A)
$60{}^\circ$

B)
$45{}^\circ$

C)
$15{}^\circ$

D)
$30{}^\circ$

• question_answer53) A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by$\vec{B}=5\times {{10}^{-8}}\hat{j}\text{ }T$. The corresponding electric field $\vec{E}$ is (speed of light $c=3\times {{10}^{8}}\text{ }m{{s}^{1}}$)  [JEE MAIN Held on 08-01-2020 Evening]

A)
$-1.66\times {{10}^{-16}}\hat{i}\text{ }V/m$

B)
$1.66\times {{10}^{-16}}\hat{i}\text{ }V/m$

C)
$-15\text{ \hat{i} }V/m$

D)
$15\,\,\hat{i}\,\,V/m$

• question_answer54)  The electric fields of two plane electromagnetic plane waves in vacuum are given by ${{\vec{E}}_{1}}={{E}_{0}}\hat{j}\cos \left( \omega t-kx \right)$ and       ${{\vec{E}}_{2}}={{E}_{0}}\hat{k}\cos \left( \omega t-ky \right)$ At t = 0, a particle of chcarge q is at origin with a velocity $\vec{v}=0.8c\hat{j}$ (c is the speed of light in vaccum). The instantaneous force experienced by the particle is: [JEE MAIN Held on 09-01-2020 Morning]

A)
${{E}_{0}}q\left( 0.4\hat{i}-3\hat{j}+0.8\hat{k} \right)$

B)
${{E}_{0}}q\left( -\,0.8\hat{i}+\hat{j}+\hat{k} \right)$

C)
${{E}_{0}}q\left( 0.8\hat{i}+\hat{j}+0.2\hat{k} \right)$

D)
${{E}_{0}}q\left( 0.8\hat{i}-\hat{j}+0.4\hat{k} \right)$

• question_answer55) A plane electromagnetic wave is propagating along the direction $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$, with its polarization along the direction $\hat{k}$. The correct form of the magnetic field of the wave would be (here ${{B}_{0}}$is an appropriate constant) [JEE MAIN Held on 09-01-2020 Evening]

A)
${{B}_{0}}\frac{\hat{i}-\hat{j}}{\sqrt{2}}\cos \left( \omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}} \right)$

B)
${{B}_{0}}\hat{k}\cos \left( \omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}} \right)$

C)
${{B}_{0}}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\cos \left( \omega t-k\frac{\hat{i}+\hat{j}}{\sqrt{2}} \right)$

D)
${{B}_{0}}\frac{\hat{j}-\hat{i}}{\sqrt{2}}\cos \left( \omega t+k\frac{\hat{i}+\hat{j}}{\sqrt{2}} \right)$