Electromagnetic Waves · JEE Main previous year questions

An electromagnetic wave travelling in $x$-direction is described by field equation ${\mathrm{E}}_y=300\sin \omega \left(t-\frac{x}{\mathrm{c}}\right)$. 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 ____.

1. A.200
2. B.150
3. C.400
4. D.300

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $\sigma =10mho/m$. The ratio of maximum conduction current density to maximum displacement current density is ____. $\left[\text{Take }\frac{1}{4\pi {ϵ}_0}=9\times 10^9\mathrm{N}{\mathrm{m}}^2/{\mathrm{C}}^2\right]$

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 :

1. A.${\lambda }_4<{\lambda }_3<{\lambda }_2<{\lambda }_1$
2. B.${\lambda }_4<{\lambda }_2<{\lambda }_3<{\lambda }_1$
3. C.${\lambda }_3<{\lambda }_4<{\lambda }_2<{\lambda }_1$
4. D.${\lambda }_4<{\lambda }_3<{\lambda }_1<{\lambda }_2$

Match List I with List II : $$\begin{array}{llll}& \text{LIST I}& & \text{LIST II}\\ & \text{EM-Wave}& & \text{Wavelength Range}\\ \text{A.}& \text{Infra-red}& \text{I.}& <10^{-3}\mathrm{nm}\\ \text{B.}& \text{Ultraviolet}& \text{II.}& 400\mathrm{nm}\text{ to }1\mathrm{nm}\\ \text{C.}& \text{X-rays}& \text{III.}& 1\mathrm{mm}\text{ to }700\mathrm{nm}\\ \text{D.}& \text{Gamma rays}& \text{IV.}& 1\mathrm{nm}\text{ to }10^{-3}\mathrm{nm}\end{array}$$ Choose the correct answer from the options given below :

1. A.(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
2. B.(A)-(III), (B)-(II), (C)-(IV), (D)-(I)
3. C.(A)-(IV), (B)-(III), (C)-(II), (D)-(I)
4. D.(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

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

1. A.${\lambda }_1<{\lambda }_2<{\lambda }_3<{\lambda }_4$
2. B.${\lambda }_2<{\lambda }_1<{\lambda }_4<{\lambda }_3$
3. C.${\lambda }_4<{\lambda }_3<{\lambda }_2<{\lambda }_1$
4. D.${\lambda }_4<{\lambda }_3<{\lambda }_1<{\lambda }_2$

A plane electromagnetic wave propagating in $x$-direction is described by $E_y=(200{\text{Vm}}^{-1})\sin \left[1.5\times 10^{7}t-0.05x\right]$; The intensity of the wave is : (Use ${ϵ}_0=8.85\times 10^{-12}{\text{C}}^2{\text{ N}}^{-1}{\text{ m}}^{-2}$)

1. A.$35.4{\text{ Wm}}^{-2}$
2. B.$53.1{\text{ Wm}}^{-2}$
3. C.$26.6{\text{ Wm}}^{-2}$
4. D.$106.2{\text{ Wm}}^{-2}$

Given below are two statements: Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface. Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light. In the light of above statements, choose the correct answer form the options given below

1. A.Both Statement I and Statement II are true
2. B.Statement I is true but statement II is false
3. C.Statement I is false but statement II is true
4. D.Both Statement I and Statement II are false

Given below are two statements: 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.

1. A.Both A and R are true but R is NOT the correct explanation of A
2. B.A is true but R is false
3. C.Both A and R are true and R is the correct explanation of A
4. D.A is false but R is true

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

1. A.$-2.2\times 10^{-8}\hat{i}\text{T}$
2. B.$2.2\times 10^{-8}\hat{i}\text{T}$
3. C.$2.2\times 10^{-8}\hat{k}\text{T}$
4. D.$-2.2\times 10^{-8}\hat{k}\text{T}$

For the plane electromagnetic wave given by $E=E_0\sin (\omega t-kx)$ and $B=B_0\sin (\omega t-kx)$, the ratio of average electric energy density to average magnetic energy density is

1. A.1
2. B.4
3. C.2
4. D.1/2

Match List I with List II | LIST I | LIST II | | :--- | :--- | | A. Microwaves | I. Physiotherapy | | B. UV rays | II. Treatment of cancer | | C. Infra-red light | III. Lasik eye surgery | | D. X-ray | IV. Aircraft navigation | Choose the correct answer from the options given below:

1. A.A - IV, B - III, C - I, D - II
2. B.A - II, B - IV, C - III, D - I
3. C.A - III, B - II, C - I, D - IV
4. D.A - IV, B - I, C - II, D - III

Match List - I with List - II : $$\begin{array}{llll}& \text{List - I}& & \text{List - II}\\ \text{(a)}& \text{UV rays}& \text{(i)}& \text{Diagnostic tool in medicine}\\ \text{(b)}& \text{X-rays}& \text{(ii)}& \text{Water purification}\\ \text{(c)}& \text{Microwave}& \text{(iii)}& \text{Communication, Radar}\\ \text{(d)}& \text{Infrared wave}& \text{(iv)}& \text{Improving visibility in foggy days}\end{array}$$ Choose the correct answer from the options given below :

1. A.(a)-(iii), (b)-(ii), (c)-(i), (d)-(iv)
2. B.(a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
3. C.(a)-(ii), (b)-(iv), (c)-(iii), (d)-(i)
4. D.(a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)

Match List-I with List-II : $$\begin{array}{llll}& \text{List - I}& & \text{List - II}\\ \text{(a)}& \text{Ultraviolet rays}& \text{(i)}& \text{Study crystal structure}\\ \text{(b)}& \text{Microwaves}& \text{(ii)}& \text{Greenhouse effect}\\ \text{(c)}& \text{Infrared rays}& \text{(iii)}& \text{Sterilizing surgical instrument}\\ \text{(d)}& \text{X-rays}& \text{(iv)}& \text{Radar system}\end{array}$$ Choose the correct answer from the options given below :

1. A.(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)
2. B.(a)-(iii), (b)-(i), (c)-(ii), (d)-(iv)
3. C.(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
4. D.(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)

In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size $\frac{\lambda }{100}$, where $\lambda$ is the wavelength of the wave in free space. The phenomenon, which happens there will be :

1. A.Reflection
2. B.Refraction
3. C.Diffraction
4. D.Scattering

A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the x-direction. At a particular point in space and time, $\vec{B}=2.0\times 10^{-8}\hat{k}T$. (where, $\hat{k}$ is unit vector along z-direction) What is $\vec{E}$ at this point?

1. A.$0.6\hat{j}\text{ V/m}$
2. B.$6.0\hat{k}\text{ V/m}$
3. C.$6.0\hat{j}\text{ V/m}$
4. D.$0.6\hat{k}\text{ V/m}$

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (${\mathrm{U}}_{\mathrm{e}}$) and magnetic (${\mathrm{U}}_{\mathrm{m}}$) fields is :

1. A.${\mathrm{U}}_{\mathrm{e}}={\mathrm{U}}_{\mathrm{m}}$
2. B.${\mathrm{U}}_{\mathrm{e}}\ne {\mathrm{U}}_{\mathrm{m}}$
3. C.${\mathrm{U}}_{\mathrm{e}}<{\mathrm{U}}_{\mathrm{m}}$
4. D.${\mathrm{U}}_{\mathrm{e}}>{\mathrm{U}}_{\mathrm{m}}$

Given below in the the left column are different modes of communication using the kinds of waves given the right column. | A | Optical Fibre communication | P | Ultrasound | |---|---|---|---| | B | Radar | Q | Infrared Light | | C | Sonar | R | Microwaves | | D | Mobile Phones | S | Radio Waves |

1. A.A-Q, B-S, C-R, D-P
2. B.A-Q, B-S, C-P, D-R
3. C.A-S, B-Q, C-R, D-P
4. D.A-R, B-P, C-S, D-Q

During the propagation of electromagnetic waves in a medium :

1. A.Electric energy density is double of the magnetic energy density.
2. B.Electric energy density is half of the magnetic energy density.
3. C.Electric energy density is equal to the magnetic energy density.
4. D.Both electric and magnetic energy of densities are zero.

Match List - 1 (Electromagnetic wave type ) with List - 2 (Its association/application) and select the correct option from the choices given below the lists: | List 1 | List 2 | | :--- | :--- | | 1. Infrared waves | (i) To treat muscular strain | | 2. Radio waves | (ii) For broadcasting | | 3. X-rays | (iii) To detect fracture of bones | | 4. Ultraviolet rays | (iv) Absorbed by the ozone layer of the atmosphere |

1. A.$1-iv,2-iii,3-ii,4-i$
2. B.$1-i,2-ii,3-iv,4-iii$
3. C.$1-iii,2-ii,3-i,4-iv$
4. D.$1-i,2-ii,3-iii,4-iv$

The frequency of $X$-rays; $\gamma$-rays and ultraviolet rays are respectively $a,b$ and $c$ then

1. A.$a<b;b>c$
2. B.$a>b;b>c$
3. C.$a<b<c$
4. D.$a=b=c$

A $10\mathrm{kW}$ transmitter emits radio waves of wavelength $500\mathrm{m}$. The number of photons emitted per second by the transmitter is of the order of

1. A.$10^{37}$
2. B.$10^{31}$
3. C.$10^{25}$
4. D.$10^{43}$

The transition from the state $n=4$ to $n=3$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from :

1. A.$3\to 2$
2. B.$4\to 2$
3. C.$5\to 4$
4. D.$2\to 1$

Electromagnetic waves are transverse in nature is evident by

1. A.polarization
2. B.interference
3. C.reflection
4. D.diffraction

Which of the following are not electromagnetic waves?

1. A.cosmic rays
2. B.gamma rays
3. C.$\beta$-rays
4. D.$X$-rays