Properties of Electromagnetic Waves PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 123 questions

51. 51. An electric bulb is rated as \(200 \,W\). What will be the peak magnetic field (\(\times 10^{-8}\, T\)) at \(4\, m\) distance produced by the radiations coming from this bulb\(?\) Consider this bulb as a point source with \(3.5 \%\) efficiency. 2022 Hard
52. 52. An \(EM\) wave propagating in \(x\)-direction has a wavelength of \(8\,mm\). The electric field vibrating \(y\) direction has maximum magnitude of \(60\,Vm ^{-1}\). Choose the correct equations for electric and magnetic fields if the \(EM\) wave is propagating in vacuum 2022 Medium
53. 53. 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 2022 Medium
54. 54. Identify the correct statements from the following descriptions of various properties of electromagnetic waves. \(A\). In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field. \(B.\) The energy in electromagnetic wave is divided equally between electric and magnetic fields. \(C.\) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave. \(D.\) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other. \(E.\) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light. Choose the most appropriate answer from the options given below: 2022 Medium
55. 55. If electric field intensity of a uniform plane electro magnetic wave is given as \(E =-301.6 \sin ( kz -\omega t ) \hat{a}_{ x }+452.4 \sin ( kz -\omega t )\) \(\hat{a}_{y} \frac{V}{m}\) Then, magnetic intensity \(H\) of this wave in \(Am ^{-1}\) will be [Given: Speed of light in vacuum \(c =3 \times 10^{8} ms ^{-1}\), permeability of vacuum \(\mu_{0}=4 \pi \times 10^{-7} NA ^{-2}\) ] 2022 Medium
56. 56. Light wave traveling in air along \(x\)-direction is given by \(E _{ y }=540 \sin \pi \times 10^{4}( x - ct ) Vm ^{-1}\). Then, the peak value of magnetic field of wave will be \(\dots \times 10^{-7}\,T\) (Given \(c =3 \times 10^{8}\,ms ^{-1}\) ) 2022 Easy
57. 57. Nearly \(10 \%\) of the power of a \(110\,W\) light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of \(1\, m\) from the bulb to a distance of \(5\,m\) is \(a \times 10^{-2}\,W / m ^{2}\). The value of ' \(a\) ' will be. 2022 Medium
58. 58. Sun light falls normally on a surface of area \(36\,cm ^{2}\) and exerts an average force of \(7.2 \times 10^{-9}\,N\) within a time period of \(20\) minutes. Considering a case of complete absorption, the energy flux of incident light is. 2022 Medium
59. 59. The electric field in an electromagnetic wave is given by \(E =56.5 \sin \omega( t - x / c ) \;NC ^{-1}\). Find the intensity of the wave if it is propagating along \(x-\)axis in the free space. (Given \(\left.\varepsilon_{0}=8.85 \times 10^{-12} \;C ^{2} N ^{-1} m ^{-2}\right)\) 2022 Medium
60. 60. The electromagnetic waves travel in a medium at a speed of \(2.0 \times 10^{8}\, m / s\). The relative permeability of the medium is \(1.0.\) The relative permittivity of the medium will be 2022 Medium
61. 61. The intensity of the light from a bulb incident on a surface is \(0.22 \,W / m ^{2}\). The amplitude of the magnetic field in this light-wave is_______ \(\times 10^{-9} \,T\). (Given : Permittivity of vacuum \(\epsilon_{0}=8.85 \times 10^{-12} \,C ^{2} N ^{-1} m ^{-2}\), speed of light in vacuum \(c =3 \times 10^{8} \,ms ^{-1}\) ) 2022 Medium
62. 62. The magnetic field of a plane electromagnetic wave is given by \(\overrightarrow{ B }=2 \times 10^{-8} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ j } T\) The amplitude of the electric field would be. 2022 Medium
63. 63. The oscillating magnetic field in a plane electromagnetic wave is given by \(B _{ y }=5 \times 10^{-6} \sin\) \(1000\,\pi\left(5 x -4 \times 10^{8} t \right) T\). The amplitude of electric field will be. 2022 Medium
64. 64. A light beam is described by \(E=800 \sin \omega\left(t-\frac{x}{c}\right)\) An electron is allowed to move normal to the propagation of light beam with a speed of \(3 \times 10^{7}\;{ms}^{-1}\). What is the maximum magnetic force exerted on the electron ? 2021 Medium
65. 65. A linearly polarized electromagnetic wave in vacuum is \(E=3.1 \cos \left[(1.8) z-\left(5.4 \times 10^{6}\right) {t}\right] \hat{\text { i }}\, {N} / {C}\) is incident normally on a perfectly reflecting wall at \(z=a\). Choose the correct option 2021 Medium
66. 66. A plane electromagnetic wave of frequency \(100\, MHz\) is travelling in vacuum along the \(x -\) direction. At a particular point in space and time, \(\overrightarrow{ B }=2.0 \times 10^{-8} \hat{ k } T\). (where, \(\hat{ k }\) is unit vector along \(z-\)direction) What is \(\overrightarrow{ E }\) at this point ? 2021 Medium
67. 67. A plane electromagnetic wave of frequency \(500\, MHz\) is travelling in vacuum along \(y-\)direction. At a particular point in space and time, \(\overrightarrow{ B }=8.0 \times 10^{-8} \hat{ z } \;T\). The value of electric field at this point is (speed of light \(\left.=3 \times 10^{8}\, ms ^{-1}\right)\) \(\hat{ x }, \hat{ y }, \hat{ z }\) are unit vectors along \(x , y\) and \(z\) direction. 2021 Medium
68. 68. A plane electromagnetic wave propagating along y-direction can have the following pair of electric field \((\vec{E} )\) and magnetic field \((\overrightarrow{ B })\) components. 2021 Medium
69. 69. A plane electromagnetic wave with frequency of \(30 {MHz}\) travels in free space. At particular point in space and time, electric field is \(6 {V} / {m}\). The magnetic field at this point will be \({x} \times 10^{-8} {T}\). The value of \({x}\) is ..... . 2021 Medium
70. 70. A radiation is emitted by \(1000\, W\) bulb and it generates an electric field and magnetic field at \(P\), placed at a distance of \(2\, m\). The efficiency of the bulb is \(1.25 \%\). The value of peak electric field at \(P\) is \(x \times 10^{-1} \,V / m\). Value of \(x\) is. (Rounded-off to the nearest integer) [Take \(\varepsilon_{0}=8.85 \times 10^{-12} C ^{2} N ^{-1} m ^{-2}, c =3 \times 10^{8}\) \(ms ^{-1}\) ] 2021 Hard
71. 71. An electromagnetic wave of frequency \(3\, GHz\) enters a dielectric medium of relative electric permittivity \(2.25\) from vacuum. The wavelength of this wave in that medium will be \(.......\,\times 10^{-2} \, cm\) 2021 Hard
72. 72. An electromagnetic wave of frequency \(5\, GHz ,\) is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are \(2 .\) Its velocity in this medium is \(\times 10^{7}\, m / s\) 2021 Hard
73. 73. Electric field in a plane electromagnetic wave is given by \({E}=50 \sin \left(500 {x}-10 \times 10^{10} {t}\right) \,{V} / {m}\) The velocity of electromagnetic wave in this medium is : (Given \({C}=\) speed of light in vacuum) 2021 Medium
74. 74. Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by \({E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .\) The dielectric constant of the medium is equal to : (Take \(\mu_{{r}}=1\) ) 2021 Hard
75. 75. For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric \(\left( U _{ e }\right)\) and magnetic \(\left( U _{ m }\right)\) fields is 2021 Medium
76. 76. In an electromagnetic wave the electric field vector and magnetic field vector are given as \(\vec{E}=E_{0} \hat{i}\) and \(\vec{B}=B_{0} \hat{k}\) respectively. The direction of propagation of electromagnetic wave is along. 2021 Medium
77. 77. Intensity of sunlight is observed as \(0.092\, {Wm}^{-2}\) at a point in free space. What will be the peak value of magnetic field at that point? \(\left(\sigma_{0}=8.85 \times 10^{-12}\, {C}^{2} \,{N}^{-1} \,{m}^{-2}\right.\) ) 2021 Medium
78. 78. The electric field in a plane electromagnetic wave is given by \(\overrightarrow{{E}}=200 \cos \left[\left(\frac{0.5 \times 10^{3}}{{m}}\right) {x}-\left(1.5 \times 10^{11} \frac{{rad}}{{s}} \times {t}\right)\right] \frac{{V}}{{m}} \hat{{j}}\) If this wave falls normally on a perfectly reflecting surface having an area of \(100 \;{cm}^{2}\). If the radiation pressure exerted by the \(E.M.\) wave on the surface during a \(10\, minute\) exposure is \(\frac{{x}}{10^{9}} \frac{{N}}{{m}^{2}}\). Find the value of \({x}\). 2021 Hard
79. 79. The electric field in an electromagnetic wave is given by \({E}=\left(50\, {NC}^{-1}\right) \sin \omega({t}-{x} / {c})\) The energy contained in a cylinder of volume \({V}\) is \(5.5 \times 10^{-12} \, {J}\). The value of \({V}\) is \(......{cm}^{3}\) \(\left(\right.\) given \(\left.\in_{0}=8.8 \times 10^{-12} \,{C}^{2} {N}^{-1} {m}^{-2}\right)\) 2021 Hard
80. 80. The magnetic field vector of an electromagnetic wave is given by \({B}={B}_{o} \frac{\hat{{i}}+\hat{{j}}}{\sqrt{2}} \cos ({kz}-\omega {t})\); where \(\hat{i}, \hat{j}\) represents unit vector along \({x}\) and \({y}\)-axis respectively. At \(t=0\, {s}\), two electric charges \(q_{1}\) of \(4\, \pi\) coulomb and \({q}_{2}\) of \(2 \,\pi\) coulomb located at \(\left(0,0, \frac{\pi}{{k}}\right)\) and \(\left(0,0, \frac{3 \pi}{{k}}\right)\), respectively, have the same velocity of \(0.5 \,{c} \hat{{i}}\), (where \({c}\) is the velocity of light). The ratio of the force acting on charge \({q}_{1}\) to \({q}_{2}\) is :- 2021 Hard
81. 81. A particle of mass \(\mathrm{m}\) and charge \(\mathrm{q}\) has an initial velocity \(\overline{\mathrm{v}}=\mathrm{v}_{0} \hat{\mathrm{j}} .\) If an electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{i}}\) and magnetic field \(\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{\mathrm{i}}\) act on the particle, its speed will double after a time: 2020 Medium
82. 82. A plane electromagnetic wave, has frequency of \(2.0 \times 10^{10}\, Hz\) and its energy density is \(1.02 \times 10^{-8}\, J / m ^{3}\) in vacuum. The amplitude of the magnetic field of the wave is close to\(....nT\) \(\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{\circ} \frac{ Nm ^{2}}{ C ^{2}}\right.\) and speed of \(1 ight\) \(\left.=3 \times 10^{8}\, ms ^{-1}\right)\) 2020 Hard
83. 83. A plane electromagnetic wave is propagating along the direction \(\frac{\hat{i}+\hat{j}}{\sqrt{2}},\) with its polarization along the direction \(\hat{\mathrm{k}}\). The correct form of the magnetic field of the wave would be (here \(\mathrm{B}_{0}\) is an appropriate constant) 2020 Medium
84. 84. A plane electromagnetic wave of frequency \(25\; \mathrm{GHz}\) is propagating in vacuum along the \(z-\)direction. At a particular point in space and time, the magnetic field is given by \(\overrightarrow{\mathrm{B}}=5 \times 10^{-8} \hat{\mathrm{j}}\; \mathrm{T}\). The corresponding electric field \(\overrightarrow{\mathrm{E}}\) is (speed of light  \(\mathrm{c}=3 \times 10^{8}\; \mathrm{ms}^{-1})\) 2020 Easy
85. 85. An electron is constrained to move along the \(y-\)axis with a speed of \(0.1\, c\) (c is the speed of light) in the presence of electromagnetic wave, whose electric field is \(\overrightarrow{ E }=30 \hat{ j } \sin \left(1.5 \times 10^{7} t -5 \times 10^{-2} x \right)\, V / m\) The maximum magnetic force experienced by the electron will be: (given \(c=3 \times 10^{8}\, ms ^{-1}\) and electron charge \(\left.=1.6 \times 10^{-19} C \right)\) 2020 Medium
86. 86. For a plane electromagnetic wave, the magnetic field at a point \(x\) and time \(t\) is \(\overrightarrow{ B }( x , t )=\left[1.2 \times 10^{-7} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ k }\right] T\) The instantaneous electric field \(\overrightarrow{ E }\) corresponding to \(\overrightarrow{ B }\) is : (speed of light \(\left.c=3 \times 10^{8} ms ^{-1}\right)\) 2020 Medium
87. 87. If the magnetic field in a plane electromagnetic wave is given by \(\overrightarrow{\mathrm{B}}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{j}}\; \mathrm{T}\) then what will be expression for electric field? 2020 Easy
88. 88. In a plane electromagnetic wave, the directions of electric field and magnetic field are represented by \(\hat{ k }\) and \(2 \hat{ i }-2 \hat{ j },\) respectively What is the unit vector along direction of propagation of the wave. 2020 Medium
89. 89. Suppose that intensity of a laser is \(\left(\frac{315}{\pi}\right)\, W / m ^{2} .\) The \(rms\) electric field, in units of \(V / m\) associated with this source is close to the nearest integer is \(\left(\epsilon_{0}=8.86 \times 10^{-12} C ^{2} Nm ^{-2} ; c =3 \times 10^{8} ms ^{-1}\right)\) 2020 Medium
90. 90. The electric field of a plane electromagnetic wave is given by \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \cos (\mathrm{kz}+\omega \mathrm{t})\) At \(\mathrm{t}=0,\) a positively charged particle is at the point \((\mathrm{x}, \mathrm{y}, \mathrm{z})=\left(0,0, \frac{\pi}{\mathrm{k}}\right) .\) If its instantaneous velocity at \((t=0)\) is \(v_{0} \hat{\mathrm{k}},\) the force acting on it due to the wave is 2020 Hard
91. 91. The electric field of a plane electromagnetic wave is given by \(\overrightarrow{ E }= E _{0}(\hat{ x }+\hat{ y }) \sin ( kz -\omega t )\) Its magnetic field will be given by 2020 Medium
92. 92. The electric field of a plane electromagnetic wave propagating along the \(x\) direction in vacuum is \(\overrightarrow{ E }= E _{0} \hat{ j } \cos (\omega t - kx )\). The magnetic field \(\overrightarrow{ B },\) at the moment \(t =0\) is : 2020 Hard
93. 93. The electric fields of two plane electromagnetic plane waves in vacuum are given by \(\overrightarrow{\mathrm{E}}_{1}=\mathrm{E}_{0} \hat{\mathrm{j}} \cos (\omega \mathrm{t}-\mathrm{kx})\) and \(\overrightarrow{\mathrm{E}}_{2}=\mathrm{E}_{0} \hat{\mathrm{k}} \cos (\omega \mathrm{t}-\mathrm{ky})\) At \(t=0,\) a particle of charge \(q\) is at origin with a velocity \(\overrightarrow{\mathrm{v}}=0.8 \mathrm{c} \hat{\mathrm{j}}\) (\(c\) is the speed of light in vacuum). The instantaneous force experienced by the particle is  2020 Hard
94. 94. The magnetic field of a plane electromagnetic Wave is \(\overrightarrow{ B }=3 \times 10^{-8} \sin [200 \pi( y + ct )] \hat{ i }\, T\) Where \(c=3 \times 10^{8} \,ms ^{-1}\) is the speed of light. The corresponding electric field is 2020 Hard
95. 95. A \(27\, mW\) lager beam has a cross -sectional area of \(10\, mm^2\). The magnitude of the maximum electric field in this electromagnetic wave is given by:........\(kV/m\) [Given permittivity of space \({ \in _0} = 9 \times {10^{ - 12}}\, SI\, units\), speed of light \(c = 3 \times 10^8\, m/s\)] 2019 Medium
96. 96. A light wave is incident normally on a glass slab of refractive index \(1.5\). If \(4\%\) of light gets reflected and the amplitude of the electric field of the incident light is \(30\, V/m\), then the amplitude of the electric field for the wave propagating in the glass medium will be.......\( V/m\) 2019 Hard
97. 97. A plane electromagnetic wave having a frequency \(n = 23.9\, GHz\) 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? 2019 Medium
98. 98. 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, \(\vec E = 6.3\,\hat j\,V/m\) . The corresponding magnetic field \(\vec B\), at that point will be 2019 Easy
99. 99. 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 \(E =6\; Vm^{-1}\) along \(y -\) direction. Its corresponding magnetic filed component, \(B\) would be 2019 Medium
100. 100. An electromagnetic wave is represented by the electric field \(\vec E = {E_0}\hat n\,\sin \,\left[ {\omega t + \left( {6y - 8z} \right)} \right]\). Taking unit vectors in \(x, y\) and \(z\) directions to be \(\hat i,\hat j,\hat k\) ,the direction of propogation \(\hat s\), is 2019 Medium

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