EM Waves — JEE Main PYQs

To radiate EM signal of wavelength $\lambda$ with high efficiency, the antennas should have a minimum size equal to :

The height of transmitting antenna is 180 m and the height of the receiving antenna is 245 m. The maximum distance between them for satisfactory communication in line of sight will be :
(given $R=6400$ km)

Match List I with List II of Electromagnetic waves with corresponding wavelength range :

List I
(A) Microwave
(B) Ultraviolet
(C) X-Ray
(D) Infra-red

List II
(I) 400 nm to 1 nm
(II) 1 nm to $10^{-3}\mathrm{nm}$
(III) 1 mm to 700 nm
(IV) 0.1 m to 1 mm

Choose the correct answe …

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

A plane electromagnetic wave of frequency 20 MHz propagates in free space along x-direction. At a particular space and time, $\overrightarrow{\mathrm{E}}=6.6\hat{\mathrm{j}}\mathrm{V}/\mathrm{m}$. What is $\overrightarrow{\mathrm{B}}$ at this point?

Which of the following frequencies does not belong to FM broadcast.

If $\overrightarrow{\mathrm{E}}$ and $\overrightarrow{\mathrm{K}}$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by : ( $\omega$ angular frequency) :

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
${\mathrm{E}}_{\mathrm{x}}={\mathrm{E}}_0\sin (\mathrm{kz}-\omega \mathrm{t})$
${\mathrm{B}}_{\mathrm{y}}={\mathrm{B}}_0\sin (\mathrm{kz}-\omega \mathrm{t})$
Then th …

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?

Which of the following are true?
(A) Speed of light in vacuum is dependent on the direction of propagation.
(B) Speed of light in a medium in independent of the wavelength of light.
(C) The speed of light is independent of the motion of the source.
(D) The speed of light in a med …

If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be :
Given : Earth's radius $=6.4\times 10^6\mathrm{m}$.

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 …

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 :

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of 24 W. The radius of curvature of hemisphere is 10 cm and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is …

In a medium the speed of light wave decreases to 0.2 times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x:1$. The value of x is _____.
(Given speed of light in free space $=3\times 10^8$ m s${}^{-1}$ and for the given med …

Match List-I with List-II.

List-I:
A. Microwaves
B. UV rays
C. Infra-red rays
D. X-rays

List-II:
I. Physiotherapy
II. Treatment of cancer
III. Lasik eye surgery
IV. Aircraft navigation

Choose the correct answer from the option given below:

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

Sun light falls normally on a surface of area $36{\mathrm{cm}}^2$ and exerts an average force of $7.2\times 10^{-9}\mathrm{N}$ within a time period of 20 minutes. Considering a case of complete absorption, the energy flux of incident light is

A beam of light travelling along X-axis is described by the electric field ${\mathrm{E}}_{\mathrm{y}}=900\sin \omega (\mathrm{t}-\mathrm{x}/\mathrm{c})$. The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of …

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to

The oscillating magnetic field in a plane electromagnetic wave is given by ${\mathrm{B}}_{\mathrm{y}}=5\times 10^{-6}\sin 1000\pi \left(5\mathrm{x}-4\times 10^8\mathrm{t}\right)$ T. The amplitude of electric field will be:

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 f …

Light wave traveling in air along x -direction is given by ${\mathrm{E}}_{\mathrm{y}}=540\sin \pi \times 10^4(\mathrm{x}-\mathrm{ct}){\mathrm{Vm}}^{-1}$. Then, the peak value of magnetic field of wave will be (Given $\mathrm{c}=3\times 10^8{\mathrm{ms}}^{-1}$ )

The magnetic field of a plane electromagnetic wave is given by
$\overrightarrow{\mathrm{B}}=2\times 10^{-8}\sin \left(0.5\times 10^3\mathrm{x}+1.5\times 10^{11}\mathrm{t}\right)\hat{\mathrm{j}}\mathrm{T}$
The amplitude of the electric field would be

An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of $60{\mathrm{Vm}}^{-1}$. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum:

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 …

We do not transmit low frequency signal to long distances because
(a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength.
(b) Effective power radiated by a long wavelength baseband signal would be high.
(c) …

A radar sends an electromagnetic signal of electric field $(E_0)=2.25\mathrm{V}/\mathrm{m}$ and magnetic field $(B_0)=1.5\times 10^{-8}\mathrm{T}$ which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects ba …

Which is the correct ascending order of wavelengths?

The intensity of the light from a bulb incident on a surface is $0.22\mathrm{W}/{\mathrm{m}}^2$. The amplitude of the magnetic field in this light-wave is ______ $\times 10^{-9}\mathrm{T}$.
(Given : Permittivity of vacuum …

If electric field intensity of a uniform plane electro magnetic wave is given as $\mathrm{E}=-301.6\sin (\mathrm{kz}-\omega \mathrm{t}){\hat{\mathrm{a}}}_{\mathrm{x}}+452.4\sin (\mathrm{kz}-\omega \mathrm{t}){\hat{a}}_y\frac{V}{m}$

Then, magnetic intensity H of this wave in …

The height of a transmitting antenna at the top of a tower is 25 m and that of receiving antenna is 49 m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is $K\sqrt{5}\times 10^2$ m. The value of $K$ is ______.
[Assume radius of Ea …

A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is $4.5\times 10^{-2}{\mathrm{Am}}^{-1}$ at a point, what will be the approximate magnitude of electric field intensity at that point? …

A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal ?

An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced by the radiations coming from this bulb? Consider this bulb as a point source with $3.5\%$ efficiency.

An antenna is placed in a dielectric medium of dielectric constant 6.25. If the maximum size of that antenna is 5.0 mm, it can radiate a signal of minimum frequency of ______ GHz.
(Given ${\mu }_{\mathrm{r}}=1$ for dielectric medium)

The electromagnetic waves travel in a medium at a speed of $2.0\times 10^8\mathrm{m}/\mathrm{s}$. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be:

The electric field in an electromagnetic wave is given by $\mathrm{E}=56.5\sin \omega (\mathrm{t}-\mathrm{x}/\mathrm{c}){\mathrm{NC}}^{-1}$. Find the intensity of the wave if it is propagating along $x$-axis in the free space. (Given …

A signal of 100 THz frequency can be transmitted with maximum efficiency by:

The electric field in a plane electromagnetic wave is given by …

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 ______ × $10^7$ m/s.

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 $3\times 10^7{\mathrm{ms}}^{-1}$. What is the maximum magnetic force exerted on the electron?

A transmitting antenna at top of a tower has a height of 50 m and the height of receiving antenna is 80 m. What is the range of communication for Line of Sight (LoS) mode? [use radius of earth = 6400 km]

Match List - I with List -II

List - I
(a) Source of microwave frequency
(b) Source of infrared frequency
(c) Source of Gamma Rays
(d) Source of X- rays

List - II
(i) Radioactive decay of nucleus
(ii) Magnetron
(iii) Inner shell electrons
(iv) Vibration of atoms and molecules
(v …

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 ____ $\times 10^{-2}\mathrm{cm}$.

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.

An antenna is mounted on a 400 m tall building. What will be the wavelength of signal that can be radiated effectively by the transmission tower upto a range of 44 km?

A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is $6\mathrm{V}/\mathrm{m}$. The magnetic field at this point will be $x\times 10^{-8}\mathrm{T}$. The value of $x$ is ____.

Intensity of sunlight is observed as $0.092{\mathrm{Wm}}^{-2}$ at a point in free space. What will be the peak value of magnetic field at that point? $\left({\epsilon }_0=8.85\times 10^{-12}{\mathrm{C}}^2{\mathrm{N}}^{-1}{\mathrm{m}}^{-2}\right)$

What should be the height of transmitting antenna and the population covered if the television telecast is to cover a radius of 150 km ? The average population density around the tower is $200/{\mathrm{km}}^2$ and the value of $R_e=6.5\times 10^6\mathrm{m}$.