Electromagnetic Waves — JEE Main PYQs

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.

A magnetic field vector in an electromagnetic wave is represented by $\vec{B} = B_0 \sin\left(2\pi\nu t - \frac{2\pi x}{\lambda}\right)\hat{j}$. Its associated electric field vector is _________.

A displacement current of 4.0 A can be set up in the space between two parallel plates of $6 \text{ } \mu\text{F}$ 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 ________.

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 :

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 ________.

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 :

A monochromatic source of light operating at $15\,\text{kW}$ emits $2.5 \times 10^{22}$ photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ________. (Take $h = 6.6 \times 10^{-34}\,\text{J.s}$ and $c = 3 \times 10^8\,\text{m/s}$).

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2m away from it, is

If an optical medium possesses a relative permeability of $\dfrac{10}{\pi}$ and relative permittivity of $\dfrac{1}{0.0885}$, then the velocity of light is greater in vacuum than that in this medium by __________ times.

($\mu_0 = 4\pi \times 10^{-7} \mathrm{~H/m}$, $\epsilon_0 = 8.85 \times 10^{-12} \mathrm{~F/m}$, $\mathrm{c} = 3 \times 10^{8} \mathrm{~m/s}$)

The unit of $\sqrt{\dfrac{2I}{\epsilon_0 c}}$ is :

(I = intensity of an electromagnetic wave, c : speed of light)

The electric field of an electromagnetic wave in free space is $$\vec{E} = 57 \cos\left[7.5\times10^{6}\,\mathrm{t} - 5\times10^{-3}\left(3x+4y\right)\right]\left(4\hat{i}-3\hat{j}\right)\ \mathrm{N/C}.$$ The associated magnetic field in Tesla is

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 $E_y = 9.3~\mathrm{Vm^{-1}}$. Then, the magnetic field vector of the wave at that point is

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 __________ $\mathrm{Vs^{-1}}$.

Arrange the following in the ascending order of wavelength ($\lambda$) :

(A) Microwaves ($\lambda_1$)

(B) Ultraviolet rays ($\lambda_2$)

(C) Infrared rays ($\lambda_3$)

(D) X-rays ($\lambda_4$)

Choose the most appropriate answer from the options given below :

Due to presence of an em-wave whose electric component is given by $E = 100 \sin(\omega t - kx)\ \mathrm{NC^{-1}}$, 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

The magnetic field of an E.M. wave is given by $\vec{B} = \left(\dfrac{\sqrt{3}}{2}\hat{i} + \dfrac{1}{2}\hat{j}\right)30\sin\left[\omega\left(t - \dfrac{z}{c}\right)\right]$ (S.I. Units).

The corresponding electric field in S.I. units is :

The electric field in an electromagnetic wave is given by $\vec{\mathrm{E}} = \hat{i}~40 \cos\omega\left(\mathrm{t} - \frac{z}{c}\right)~\mathrm{N\,C^{-1}}$. The magnetic field induction of this wave is (in SI unit) :

Arrange the following in the ascending order of wavelength:

A. Gamma rays ($\lambda_1$) B. x - rays ($\lambda_2$) C. Infrared waves ($\lambda_3$) D. Microwaves ($\lambda_4$)

Choose the most appropriate answer from the options given below

An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of $12\ \mu\mathrm{F}$. The maximum displacement current between the plates of the capacitor is nearly :

Match List-I with List-II :

List-I (EM-Wave)	List-II (Wavelength Range)
(A) Infra-red	(I) $< 10^{-3}$ nm
(B) Ultraviolet	(II) 400 nm to 1 nm
(C) X-rays	(III) 1 mm to 700 nm
(D) Gamma rays	(IV) 1 nm to $10^{-3}$ nm

Choose the correct answer from the options given below :

Electromagnetic waves travel in a medium with speed of $1.5\times10^{8}\ \mathrm{m\ s^{-1}}$. The relative permeability of the medium is 2.0. The relative permittivity will be:

In the given electromagnetic wave $E_y = 600 \sin(\omega t - kx)\ \mathrm{Vm^{-1}}$, intensity of the associated light beam is (in $\mathrm{W/m^2}$) : (Given $\epsilon_0 = 9 \times 10^{-12}\ \mathrm{C^2 N^{-1} m^{-2}}$)

Average force exerted on a non-reflecting surface at normal incidence is $2.4 \times 10^{-4}$ N. If $360\ \mathrm{W/cm^2}$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:

A plane EM wave is propagating along $x$ direction. It has a wavelength of 4 mm. If electric field is in $y$ direction with the maximum magnitude of $60\ \mathrm{Vm^{-1}}$, the equation for magnetic field is :

The magnetic field in a plane electromagnetic wave is $\mathrm{B_y} = (3.5\times10^{-7})\sin(1.5\times10^3 x + 0.5\times10^{11} t)$ T. The corresponding electric field will be :

A parallel plate capacitor has a capacitance C = 200 pF. It is connected to 230 V ac supply with an angular frequency 300 rad/s. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

If frequency of electromagnetic wave is 60 MHz and it travels in air along $z$ direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in m) is :

A plane electromagnetic wave propagating in $x$-direction is described by

$E_y = (200\ \mathrm{Vm^{-1}})\ \sin[1.5 \times 10^7 t - 0.05\ x]$; The intensity of the wave is :

(Use $\epsilon_0 = 8.85 \times 10^{-12}\ \mathrm{C^2 N^{-1} m^{-2}}$)

Match List I with List II

	LIST I		LIST II
A.	$\oint \vec{B} \cdot \vec{dl} = \mu_o i_c + \mu_o \varepsilon_o \dfrac{d\phi_E}{dt}$	I.	Gauss' law for electricity
B.	$\oint \vec{E} \cdot \vec{dl} = \dfrac{d\phi_B}{dt}$	II.	Gauss' law for magnetism
C.	$\oint \vec{E} \cdot \vec{dA} = \dfrac{Q}{\varepsilon_o}$	III.	Faraday law
D.	$\oint \vec{B} \cdot \vec{dA} = 0$	IV.	Ampere - Maxwell law

Choose the correct answer from the options given below:

The electric field of an electromagnetic wave in free space is represented as $\vec{\mathrm{E}} = \mathrm{E}_0 \cos(\omega t - kz)\,\hat{i}$. The corresponding magnetic induction vector will be :

Match List I with List II

	List I		List II
A.	Gauss's law of magnetostatics	I.	$\oint \vec{E} \cdot \vec{da} = \dfrac{1}{\varepsilon_o} \int \rho \, dV$
B.	Faraday's law of electro magnetic induction	II.	$\oint \vec{B} \cdot \vec{da} = 0$
C.	Ampere's law	III.	$\int \vec{E} \cdot \vec{dl} = \dfrac{-d}{dt} \int \vec{B} \cdot \vec{da}$
D.	Gauss's law of electrostatics	IV.	$\oint \vec{B} \cdot \vec{dl} = \mu_0 I$

Choose the correct answer from the options given below:

If the total energy transferred to a surface in time $t$ is $6.48 \times 10^5\ J$, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5 \times 10^{10}$ Hz and an amplitude of $50\ \mathrm{Vm^{-1}}$. The total average energy density of the electromagnetic field of the wave is : [Use $\varepsilon_0 = 8.85 \times 10^{-12}\ \mathrm{C^2/Nm^2}$]

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: