EM Waves — JEE Main PYQs

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
${\mathrm{E}}_{\mathrm{y}}=20\sin \left(3\times 10^6\mathrm{x}-4.5\times 10^{14}\mathrm{t}\right)\mathrm{V}/\mathrm{m}$
(where $\mathrm{x},\mathrm{t}$ and ot …

A laser beam has intensity of $4.0\times 10^{14}\mathrm{W}/{\mathrm{m}}^2$. The amplitude of magnetic field associated with beam is ______ T. (Take ${ϵ}_0=8.85\times 10^{-12}{\mathrm{C}}^2/{\mathrm{Nm}}^2$ and $\mathrm{c}=3\times 10^8\mathrm{m}/\mathrm{s}$)

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma =10\mathrm{mho}/\mathrm{m}$. The ratio of maximum conducting current density to maximum displacement current density is ____ .

$[$ Take …

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
The average power of the electromagnetic wave is $\left(\frac{1}{\alpha }\right)$ W/m${}^2$. T …

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k=3$ and permeability of $\mu =2{\mu }_0$, is (${\mu }_0=$ permeability of vacuum)

The electric field of an electromagnetic wave travelling through a medium is given by
$\vec{E}(x,t)=25\sin \left(2.0\times 10^{15}t-10^{7}x\right)\hat{n}$
then the refractive index of the medium is ______.
(All given measurement are in SI units)

A plane electromagnetic wave is moving in free space with velocity c $=3\times 10^8\mathrm{m}/\mathrm{s}$ and its electric field is given as $\overrightarrow{\mathrm{E}}=54\sin (\mathrm{kz}-\omega \mathrm{t})\hat{\mathrm{j}}\mathrm{V}/\mathrm{m}$, where …

Which one of the following is not a measurable quantity?

The electric field a plane electromagnetic wave is given by :
${\mathrm{E}}_{\mathrm{y}}=69\sin \left[0.6\times 10^3\mathrm{x}-1.8\times 10^{11}\mathrm{t}\right]\mathrm{V}/\mathrm{m}$.
The expression for magnetic field associated with this electromagnetic wave is ___ …

An electromagnetic wave travels in free space along the $x$-direction. At a particular point in space and time, $\overrightarrow{\mathrm{B}}=2\times 10^{-7}\hat{\mathrm{j}}\mathrm{T}$ is associated with this wave. The value of corresponding electric field …

A magnetic field vector in an electromagnetic wave is represented by, $\overrightarrow{\mathrm{B}}={\mathrm{B}}_0\sin \left(2\pi \mathrm{vt}-\frac{2\pi \mathrm{x}}{\lambda }\right)\hat{\mathrm{j}}$. 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 $6\mu \mathrm{F}$ 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 …

A point light source emits E.M. waves in free space. A detector, placed at a distance of L m, measures the intensity as ${\mathrm{I}}_0$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as …

For an electromagnetic wave propagating through vacuum, $\overrightarrow{k}$, $\overrightarrow{E}$ and $\omega$ represent propagation vector, electric field and angular frequency, respectively. The magnetic field associated with this wave is represented by:

An electromagnetic wave travelling in x-direction is described by field equation ${\mathrm{E}}_{\mathrm{y}}=300\sin \omega \left(\mathrm{t}-\frac{\mathrm{x}}{\mathrm{c}}\right)$. If the electron is restricted to move in y-direction only with speed of …

A parallel plate capacitor of area $\mathrm{A}=16{\mathrm{cm}}^2$ and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area ${\mathrm{A}}_0=3.2{\mathrm{cm}}^2$ inside the capacitor and parallel to the plates. At an ins …

The electric field of an electromagnetic wave in free space is
$\overrightarrow{\mathrm{E}}=57\cos \left[7.5\times 10^6\mathrm{t}-5\times 10^{-3}(3\mathrm{x}+4\mathrm{y})\right]$
$(4\hat{\mathrm{i}}-3\hat{\mathrm{j}})\mathrm{N}/\mathrm{C}$.
The associated magnetic fi …

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 inter …

A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, $\overrightarrow{\mathrm{E}}$ and magnetic field, $\overrightarrow{\mathrm{B}}$ vectors associated with the wave in Cartesian frame are :

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

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 o …

Arrange the following in the ascending order of wavelength ( $\lambda$ ) :
(A) Microwaves $\left({\lambda }_1\right)$
(B) Ultraviolet rays ( ${\lambda }_2$ )
(C) Infrared rays ( ${\lambda }_3$ )
(D) X-rays $\left({\lambda }_4\right)$

Choose the most appropriate answer from the optio …

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

The unit of $\sqrt{\frac{2I}{{ϵ}_{0}c}}$ is :
(I = intensity of an electromagnetic wave, $\mathrm{c}:$ speed of light)

In the given electromagnetic wave ${\mathrm{E}}_{\mathrm{y}}=600\sin (\omega \mathrm{t}-\mathrm{kx}){\mathrm{Vm}}^{-1}$, intensity of the associate light beam is (in $\mathrm{W}/{\mathrm{m}}^2$: $($ Given …

Arrange the following in the ascending order of wavelength:
(A) Gamma rays (${\lambda }_1$)
(B) x-ray $\left({\lambda }_2\right)$
(C) Infrared waves (${\lambda }_3$)
(D) Microwaves $\left({\lambda }_4\right)$

Choose the most appropriate answer from the options given below :

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

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 :

Average force exerted on a non-reflecting surface at normal incidence is $2.4\times 10^{-4}\mathrm{N}$. If $360\mathrm{W}/{\mathrm{cm}}^2$ 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 Vm${}^{-1}$, the equation for magnetic field is:

The magnetic field in a plane electromagnetic wave is ${\mathrm{B}}_{\mathrm{y}}=\left(3.5\times 10^{-7}\right)\sin \left(1.5\times 10^3\mathrm{x}+0.5\times 10^{11}\mathrm{t}\right)\mathrm{T}$. The corresponding electric field will be

An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity $6\times 10^8\mathrm{W}/{\mathrm{m}}^2$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space …

A plane electromagnetic wave of frequency 35 MHz travels in free space along the 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:

A plane electromagnetic wave propagating in x-direction is described by
${\mathrm{E}}_{\mathrm{y}}=\left(200{\mathrm{Vm}}^{-1}\right)\sin \left[1.5\times 10^7\mathrm{t}-0.05\mathrm{x}\right]$;
The intensity of the wave is :
(Use …

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 …

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 :

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

The electric field of an electromagnetic wave in free space is represented as $\vec{E}=E_0\cos (\omega t-kz)\hat{i}$.

The corresponding magnetic induction vector will be :

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 …

A TV transmitting antenna is 98 m high and the receiving antenna is at the ground level. If the radius of the earth is 6400 km, the surface area covered by the transmitting antenna is approximately:

The energy density associated with electric field $\vec{E}$ and magnetic field $\overrightarrow{\mathrm{B}}$ of an electromagnetic wave in free space is given by (${ϵ}_0$ - permittivity of free space, ${\mu }_0$ - permeability of free space)

The amplitude of magnetic field in an electromagnetic wave propagating along y -axis is $6.0\times 10^{-7}\mathrm{T}$. The maximum value of electric field in the electromagnetic wave is:

The energy of an electromagnetic wave contained in a small volume oscillates with

The electric field in an electromagnetic wave is given as $\vec{E}=20\sin \omega \left(t-\frac{x}{c}\right)\vec{j}{\mathrm{NC}}^{-1}$, where $\omega$ and $c$ are the angular frequency and the velocity of the electromagnetic wave. The total energy contained in a volume of cross-s …

A transmitting antenna is kept on the surface of the earth. The minimum height of receiving antenna required to receive the signal in line of sight at 4 km distance from it is $\mathrm{x}\times 10^{-2}\mathrm{m}$. The value of x is (Let. radius of earth …

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 energeti …

The source of time varying magnetic field may be
(A) a permanent magnet
(B) an electric field changing linearly with time
(C) direct current
(D) a decelerating charge particle
(E) an antenna fed with a digital signal

Choose the correct answer from the options given below:

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z -axis and magnetic field is along the positive x -axis. Then the direction of propagation of electromagnetic wave is: