STD 12 - Electromagnetic waves PYQs: JEE Mains Physics

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1. 1. A displacement current of \(4.0\) A can be set up in the space between two parallel plates of \(6\) \(\mu\)F capacitor. The rate of change of potential difference across the plates of the capacitor is nearly \(\alpha \times 10^6\) V/s. The value of \(\alpha\) is __________. 2026 Easy
2. 2. A laser beam has intensity of \( 4.0\times10^{14} W/m^{2} \). The amplitude of magnetic field associated with beam is__________ T. (Take \( \epsilon_{0}=8.85\times10^{-12} C^{2}/Nm^{2} \) and \( c=3\times10^{8} m/s \)) 2026 Easy
3. 3. A magnetic field vector in an electromagnetic wave is represented by \(\vec{B}=B_0\sin\left(2\pi vt-\dfrac{2\pi x}{\lambda}\right)\hat{j}\). Its associated electric field vector is ______. 2026 Medium
4. 4. A plane electromagnetic wave is moving in free space with velocity \(c =3 \times 10^8 m / s\) and its electric field is given as \(\overrightarrow{ E }=54 \sin ( kz -\omega t ) \hat{ j } V / m\), where \(\hat{j}\) is the unit vector along \(y\)-axis. The magnetic field vector \(\overrightarrow{ B }\) of the wave is : 2026 Hard
5. 5. A point light source emits E.M. waves in free space. A detector, placed at a distance of \(L\) m, measures the intensity as \(I_o\). The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as \(45°\). The measured intensity at new location will be _______. 2026 Easy
6. 6. An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, \(\sigma=10 mho / m\). The ratio of maximum conducting current density to maximum displacement current density is _________ .
   \(\left[\right.\) Take \(\left.\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 Nm ^2 / C ^2\right]\) 2026 Hard
7. 7. An electromagnetic wave travelling in \(x\)-direction is described by field equation \(E_y = 300\sin\omega\left(t - \dfrac{x}{c}\right)\). If the electron is restricted to move in \(y\)-direction only with speed of \(1.5 \times 10^6\) m/s then ratio of maximum electric and magnetic forces acting on the electron is _______. 2026 Medium
8. 8. An electromagnetic wave travels in free space along the \(x\)-direction. At a particular point in space and time, \(\vec{B} = 2 \times 10^{-7} \hat{j}\) T is associated with this wave. The value of corresponding electric field \(\vec{E}\) at this point is _______ V/m. 2026 Medium
9. 9. For an electromagnetic wave propagating through vacuum, \(\vec{k}\), \(\vec{E}\) and \(\omega\) represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by : 2026 Medium
10. 10. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A): The electromagnetic wave exerts pressure on the surface on which they are allowed to fall.
    Reason (R): There is no mass associated with the electromagnetic waves.
    In the light of the above statements, choose the correct answer from the options given below : 2026 Medium
11. 11. Match List-I with List-II.

    List-I (Relation)		List-II (Law)
    A.	\(\oint \overrightarrow{ E } \cdot \overrightarrow{ d } l =-\frac{ d }{ dt } \oint \overrightarrow{ B } \cdot \overrightarrow{ d a}\)	I.	Ampere's circuital law.
    B.	\(\oint\) B. \(\vec{d} l=\mu_0\left(1+\epsilon_0 \frac{d \phi_E}{d t}\right)\)	II.	Faraday's laws of electromagnetic induction.
    C.	\(\oint \overrightarrow{ E } . \overrightarrow{ d a}=\frac{1}{\epsilon_0} \int \rho dv\)	III.	Ampere-Maxwell law
    D.	\(\oint \overrightarrow{ B } \cdot \overrightarrow{ d } l =\mu_0 I\)	IV.	Gauss's law of electrostatics

    Choose the correct answer from the options given below : 2026 Easy
12. 12. Match the List-I with List-II
    

    	List-I		List-II
    A	Radio-wave	I	is produced by Magnetron value
    B	Micro-wave	II	Due to change in the vibrational modes of atoms
    C	Infrared-wave	II	Due to inner shell electrons moving from higher energy level to lower energy level
    D	X-ray	IV	Due to rapid acceleration of electrons

    Choose the correct answer from the options given below: 2026 Hard
13. 13. The dimensional formula of \(\dfrac{1}{2}\epsilon_0 E^2\) (\(\epsilon_0\) = permittivity of vacuum and \(E\) = electric field) is \(M^a L^b T^c\). The value of \(2a - b + c = \) _______. 2026 Medium
14. 14. The electric field a plane electromagnetic wave is given by :
    \(E _y=69 \sin \left[0.6 \times 10^3 x -1.8 \times 10^{11} t \right] V / m\).
    The expression for magnetic field associated with this electromagnetic wave is _________ T. 2026 Hard
15. 15. The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
    \(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right) V / m\)
    (where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is __________ .
    (speed of light in free space is \(3 \times 10^8 m / s\) ) 2026 Easy
16. 16. The electric field of an electromagnetic wave travelling through a medium is given by \(\overline{E}(x,t) = 25\ sin(2.0 \times 10^{15}t - 10^{7}x)\hat{n}\) then the refractive index of the medium is ___________.
    (All given measurement are in SI units) 2026 Hard
17. 17. The equation of the electric field of an electromagnetic wave propagating through free space is given by :
    E \(=\sqrt{377} \sin \left(6.27 \times 10^3 t -2.09 \times 10^{-5} x \right)\) N/C
    he average power of the electromagnetic wave is\(\left(\frac{1}{\alpha}\right) W / m ^2\). The value of \(\alpha\) is ___________
    \(\left(\right.\) Take \(\sqrt{\frac{\mu_0}{\varepsilon_0}}=377\) in SI units \()\) 2026 Medium
18. 18. The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant k=3 and permeability \(\mu=2\mu_{0}\), is
    ( \(\mu_0=\) permeability of vacuum) 2026 Easy
19. 19. A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is \(7 \times 10^8 \mathrm{~V} / \mathrm{s}\) then the integer value of the distance between the parallel plates is \(\left(\right.\) Take, \(\left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right)\) ________ \(\mu \mathrm{m}\). 2025 Medium
20. 20. A plane electromagnetic wave of frequency 20 MHz travels in free space along the \(+x\) direction. At a particular point in space and time, the electric field vector of the wave is \(\mathrm{E}_y=9.3 \mathrm{Vm}^{-1}\). Then, the magnetic field vector of the wave at that point is: 2025 Medium
21. 21. A plane electromagnetic wave propagates along the \(+x\) direction in free space. The components of the electric field, \(\vec{E}\) and magnetic field, \(\vec{B}\) vectors associated with the wave in Cartesian frame are 2025 Easy
22. 22. A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance \(2.5 \mu \mathrm{~F}\). The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _____ \(\mathrm{Vs}^{-1}\). 2025 Hard
23. 23. Due to presence of an em-wave whose electric component is given by \(\mathrm{E}=100 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{NC}^{-1}\), a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as 2025 Medium
24. 24. If an optical medium possesses a relative permeability of \(\frac{10}{\pi}\) and relative permittivity of \(\frac{1}{0.0885}\), then the velocity of light is greater in vacuum than that in this medium by ________ times.
    \(\left(\mu_0=4 \pi \times 10^{-7} \mathrm{H} / \mathrm{m}, \epsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right.\)
    \(\left.\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)\) 2025 Easy
25. 25. The electric field of an electromagnetic wave in free space is \(\overrightarrow{\mathrm{E}}=57 \cos \left[7.5 \times 10^6 \mathrm{t}-5 \times 10^{-3}(3 x+4 y)\right](4 \hat{i}-3 \hat{j}) N / C\). The associated magnetic field in Tesla is _______. 2025 Medium
26. 26. The magnetic field of an E.M. wave is given by \(\overrightarrow{\mathrm{B}}=\left(\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}\right) 30 \sin \left[\omega\left(\mathrm{t}-\frac{z}{\mathrm{c}}\right)\right]\) (S.I. Units).
    The corresponding electric field in S.I. units is : 2025 Easy
27. 27. A plane electromagnetic wave of frequency \(35\  \mathrm{MHz}\) travels in free space along the \(\mathrm{X}\)-direction. At a particular point (in space and time) \(\overrightarrow{\mathrm{E}}=9.6\  \hat{\mathrm{j}} \mathrm{V} / \mathrm{m}\). The value of magnetic field at this point is _______. 2024 Hard
28. 28. A plane electromagnetic wave propagating in \(\mathrm{x}\)-direction is described by \(\mathrm{E}_{\mathrm{y}}=\left(200\  \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 \mathrm{t}-0.05\  \mathrm{x}\right] \text {; }\) The intensity of the wave is :(Use \(\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\) ) 2024 Hard
29. 29. A plane EM wave is propagating along \(\mathrm{x}\) direction. It has a wavelength of \(4 \mathrm{~mm}\). If electric field is in y direction with the maximum magnitude of \(60 \mathrm{Vm}^{-1}\), the equation for magnetic field is _______. 2024 Hard
30. 30. An alternating voltage of amplitude \(40 \mathrm{~V}\) and frequency \(4 \mathrm{kHz}\) is applied directly across the capacitor of \(12 \mu \mathrm{F}\). The maximum displacement current between the plates of the capacitor is nearly _______. 2024 Hard
31. 31. Arrange the following in the ascending order of wavelength : \((A)\) Gamma rays \(\left(\lambda_1\right)\) \((B)\) x-ray \(\left(\lambda_2\right)\) \((C)\) Infrared waves \(\left(\lambda_3\right)\) \((D)\) Microwaves \(\left(\lambda_4\right)\) Choose the most appropriate answer from the options given below : 2024 Hard
32. 32. Electromagnetic waves travel in a medium with speed of \(1.5 \times 10^8 \mathrm{~ms}^{-1}\). The relative permeability of the medium is \(2.0\) . The relative permittivity will be _______. 2024 Hard
33. 33. Given below are two statements:
    Statement \(I\): Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields.
    Statement \(II\): When electromagnetic waves strike a surface, a pressure is exerted on the surface.
    In the light of the above statements, choose the most appropriate answer from the options given below: 2024 Hard
34. 34. If frequency of electromagnetic wave is \(60 \mathrm{MHz}\) and it travels in air along \(\mathrm{z}\) direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in \(\mathrm{m}\) ) is _______. 2024 Hard
35. 35. In a plane \(EM\) wave, the electric field oscillates sinusoidally at a frequency of \(5 \times 10^{10} \mathrm{~Hz}\) and an amplitude of \(50 \mathrm{Vm}^{-1}\). The total average energy density of the electromagnetic field of the wave is _______. [Use \(\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\) ] 2024 Hard
36. 36. In the given electromagnetic wave \(E_y=600 \sin (\omega t-k x) \mathrm{Vm}^{-1}\), intensity of the associated light beam is what? (in \(\mathrm{W} / \mathrm{m}^2\) ); (Given \(\epsilon_0=\) \(\left.9 \times 10^{-12} \mathrm{C}^{-2} \mathrm{~N}^{-1} \mathrm{~m}^{-2}\right)\) 2024 Hard
37. 37. Maatch Liat \(I\) List \(II\) Chose the correct answer from the options given below
    2024 Hard
38. 38. Match List-\(I\) with List-\(II\) :-

    List - \(I\) (EM-Wave)	List - \(II\) (Wavelength) (Range)
    \((A)\) infra-red	\((i)\) \(<10^{-3} \mathrm{~nm}\)
    \((B)\) Ultraviolet	\((ii)\) \(400 \mathrm{~nm}\) to \(1 \mathrm{~nm}\)
    \((C)\) X-rays	\((iii)\) \(1 \mathrm{~mm}\) to \(700 \mathrm{~nm}\)
    \((D)\) Gamma rays	\((iv)\) \(1 \mathrm{~nm}\) to \(10^{-3} \mathrm{~nm}\)

    Choose the correct answer from the options given below: 2024 Hard
39. 39. Match List\(-I\) with List\(-II\).

    List\(-I\)	List\(-II\)
    \(A\). Gauss's Law in Electrostatics	\(I\). \(\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}\)
    \(B\). Faraday's Law	\(II\). \(\oint \overrightarrow{ B } \cdot d \overrightarrow{ A }=0\)
    \(C\). Gauss's Law in Magnetism	\(III\). \(\oint \vec{B} \cdot d \vec{l}=\mu_0 i_C+\mu_0 \in_0 \frac{d \phi_E}{d t}\)
    \(D\). Ampere-Maxwell Law	\(IV\). \(\oint \overrightarrow{ E } \cdot d \overrightarrow{ s }=\frac{ q }{\epsilon_0}\)

    Choose the correct answer from the options given below: 2024 Medium
40. 40. 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) _______. 2024 Hard
41. 41. The electric field of an electromagnetic wave in free space is represented as \(\vec{E}=E_0 \cos (\omega t-k z) \hat{i}\). The corresponding magnetic induction vector will be _______. 2024 Hard
42. 42. The magnetic field in a plane electromagnetic wave is \(\mathrm{B}_y=\left(3.5 \times 10^{-7}\right) \sin \left(1.5 \times 10^3 \mathrm{x}+0.5\right.\) \(\left.\times 10^{11} \mathrm{t}\right) \mathrm{T}\). The corresponding electric field will be _______. 2024 Hard
43. 43. A plane electromagnetic wave of frequency \(20\,MHz\) propagates in free space along \(x\)-direction. At a particular space and time, \(\overrightarrow{ E }=6.6 \hat{ j } V / m\). What is \(\overrightarrow{ B }\) at this point? 2023 Medium
44. 44. A point source of \(100\,W\) emits light with \(5 \%\) efficiency. At a distance of \(5\,m\) from the source, the intensity produced by the electric field component is : 2023 Medium
45. 45. All electromagnetic wave is transporting energy in the negative \(z\) direction. At a certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of the magnetic field of the wave at that point and instant? 2023 Easy
46. 46. For the plane electromagnetic wave given by \(\mathrm{E}=\mathrm{E}_0 \sin (\omega \mathrm{t}-\mathrm{kx})\) and \(\mathrm{B}=\mathrm{B}_0 \sin (\omega \mathrm{t}-\mathrm{kx})\), the ratio of average electric energy density to average magnetic energy density is 2023 Medium
47. 47. Given below are two statement: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R.\) Assertion \(A:\) \(EM\) waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology. Reason \(R\) : Infrared \(EM\) waves are more energetic than microwaves, (used in Radar) In the light of given statements, choose the correct answer from the options given below: 2023 Medium
48. 48. Given below are two statements: Statement \(I\) : Electromagnetic waves are not deflected by electric and magnetic field. Statement \(II\) : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as \(E _0=\sqrt{\frac{\mu_0}{\varepsilon_0}} B_0\) In the light of the above statements, choose the correct answer from the options given below: 2023 Medium
49. 49. If a source of electromagnetic radiation having power \(15 kW\) produces \(10^{16}\) photons per second, the radiation belongs to a part of spectrum is.(Take Planck constant \(h =6 \times 10^{-34}\,Js\) ) 2023 Easy
50. 50. If \(\vec{E}\) and \(\vec{K}\) represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by : \((\omega-\) angular frequency) : 2023 Medium

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