Class 12th Physics - Electromagnetic Waves Case Study Questions and Answers 2022 - 2023
QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 12th Physics Subject - Electromagnetic Waves, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.
QB365 - Question Bank Software
Electromagnetic Waves Case Study Questions With Answer Key
12th Standard CBSE
-
Reg.No. :
Physics
-
In an electromagnetic wave both the electric and magnetic fields are perpendicular to the direction of propagation, that is why electromagnetic waves are transverse in nature. Electromagnetic waves carry energy as they travel through space and this energy is shared equally by the electric and magnetic fields. Energy density of an electromagnetic waves is the energy in unit volume of the space through which the wave travels.
(i) The electromagnetic waves propagated perpendicular to both \(\vec{E} \text { and } \vec{B}\). The electromagnetic waves travel in the direction of\((a) \vec{E} \cdot \vec{B}\) \((b) \vec{E} \times \vec{B}\) \((c) \vec{B} \cdot \vec{E}\) \((d) \vec{B} \times \vec{E}\) (ii) Fundame tal particle in an electromagnetic wave is
(a) photon (b) electron (c) phonon (d) proton (iii) Electromagnetic waves are transverse in nature is evident by
(a) polarisation (b) interference (c) reflection (d) diffraction (iv) For a wave propagating in a medium, identify the property that is independent of the others.
(a) velocity (b) wavelength (c) frequency (d) all these depend on each other (v) The electric and magnetic fields of an electromagnetic waves are
(a) in opposite phase and perpendicular to each other (b) in opposite phase and parallel to each other (c) in phase and perpendicular to each other (d) in phase and parallel to each other. -
Maxwell showed that the speed of an electromagnetic wave depends on the permeability and permittivity of the medium through which it travels. The speed of an electromagnetic wave in free space is given by \(c=\frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}} .\)The fact led Maxwell to predict that light is an electromagnetic wave. The emergence of the speed of light from purely electromagnetic considerations is the crowning achievement of Maxwell's electromagnetic theory. The speed of an electromagnetic wave in any medium of permeability \(\mu\) and permittivity \(\varepsilon\) will be \(\frac{c}{\sqrt{K \mu_{r}}}\) where K is the dielectric constant of the medium and \(\mu_r\) is the relative permeability.
(i) The dimensions of \(\frac{1}{2} \varepsilon_{0} E^{2}\) (\(\varepsilon_o\) permittivity of free space; E = electric field) is\((a) \mathrm{MLT}^{-1}\) \((b) \mathrm{ML}^{2} \mathrm{~T}^{-2}\) \((c) \mathrm{ML}^{-1} \mathrm{~T}^{-2}\) \((d) M L^{2} T^{-1}\) (ii) Let [\(\varepsilon\)0] denote the dimensional formula of the permittivity of the vacuum. If M = mass, L = length, T = time and A = electric current, then
\((a) \left[\varepsilon_{0}\right]=\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{2} \mathrm{~A}\) \((b) \left[\varepsilon_{0}\right]=M^{-1} L^{-3} T^{4} A^{2}\) \((c) \left[\varepsilon_{0}\right]=\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\) \((d) \left[\varepsilon_{0}\right]=\mathrm{ML}^{2} \mathrm{~T}^{-1}\) (iii) An electromagnetic wave of frequency 3MHz passes from vacuum into a dielectric medium with permittivity \(\varepsilon\) = 4. Then
(a) wavelength and frequency both remain unchanged (b) wavelength is doubled and the frequency remains unchanged (c) wavelength is doubled and the frequency becomes half (d) wavelength is halved and the frequency remains unchanged. (iv) Which of the following are not electromagnetic waves?
(a) cosmic rays (b) \(\Upsilon\)-rays (c) \(\beta\)-rays (d) X-rays (v) The electromagnetic waves travel with
(a) the same speed in all media (b) the speed of light c = 3 x 108 m s-1 in free space (c) the speed oflight c = 3 x 108 m S-1 in solid medium (d) the speed of light c = 3 x 108 m s-1 in fluid medium -
An electromagnetic wave transports linear momentum as it travels through space. If an electromagnetic wave transfers a total energy U to a surface in time t, then total linear momentum delivered to the surface is \(p=\frac{U}{c}\) When an electromagnetic wave falls on a surface, it exerts pressure on the surface. In 1903, the American scientists Nichols and Hull succeeded in measuring radiation pressures of visible light where other had failed, by making a detailed empirical analysis of the ubiquitous gas heating and ballistic effects.
(i) The pressure exerted by an electromagnetic wave of intensity I (W m-2) on a non-reflecting surface is (c is the velocity of light)(a) Ic (b) Ic2 (c) I/c (d) I/c2 (ii) Light with an energy flux of 18 W/cm2 falls on a non-reflecting surface at normal incidence. The pressure exerted on the surface is
(a) 2 N/m2 (b) 2 x 10-4 N/m2 (c) 6 N/m2 (d) 6 x 10-4 N/m2 (iii) Radiation of intensity 0.5 W m-2 are striking a metal plate. The pressure on the plate is
(a) 0.166 x 10-8 N m-2 (b) 0.212 x 10-8 N m-2 (c) 0.132 x 10-8 N m-2 (d) 0.083 x 10-8 N m-2 (iv) A point source of electromagnetic radiation has an average power output of 1500 W The maximum value of electric field at a distance of3 m from this source (in V m-1) is
(a) 500 (b) 100 \(\text { (c) } \frac{500}{3}\) \(\text { (c) } \frac{250}{3}\) (v) The radiation pressure of the visible light is of the order of
(a) 10-2 N m2 (b) 10-4N/m (c) 10-6 N/m2 (d) 10-8N -
All the known radiations from a big family of electromagnetic waves which stretch over a large range of wavelengths. Electromagnetic wave include radio waves, microwaves, visible light waves, infrared rays, UV rays, X-rays and gamma rays. The orderly distribution of the electromagnetic waves in accordance with their wavelength or frequency into distinct groups having widely differing properties is electromagnetic spectrum.
(i) Which wavelength of the Sun is used finally as electric energy?(a) radio waves (b) infrared waves (c) visible light (d) microwaves (ii) Which of the following electromagnetic radiations have the longest wavelength?
(a) X-rays (b) \(\Upsilon\)-rays (c) microwaves (d) radiowaves (iii) Which one of the following is not electromagnetic in nature?
(a) X-rays (b) gamma rays (c) cathode rays (d) infrared rays (iv) Which of the following has minimum wavelength?
(a) X-rays (b) ultraviolet rays (c) \(\Upsilon\)-rays (d) cosmic rays (v) The decreasing order of wavelength of infrared, microwave, ultraviolet and gamma rays is
(a) microwave, infrared, ultraviolet, gamma rays (b) gamma rays, ultraviolet, infrared, microwave (c) microwave, gamma rays, infrared, ultraviolet (d) infrared, microwave, ultraviolet, gamma rays -
Electrons oscillating in a circuit give rise to radiowaves. A transmitting antenna radiates most effectively the radiowaves of wavelength equal to the size of the antenna. The infrared waves incident on a substance set into oscillation all its electrons, atoms and molecules. This increases the internal energy and hence the temperature of the substance.
(i) If vg, vx and vm are the speeds of gamma rays, X-rays and microwaves respectively in vacuum, then(a) Vg > VX > Vm (b) Vg (c) Vg > VX > Vm (d) Vg= VX= Vm (ii) Which of the following will deflect in electric field?
(a) X-rays (b) \(\Upsilon\)-rays (c) cathode rays (d) ultraviolet rays (iii) \(\Upsilon\)-rays are detected by
(a) point contact diodes (b) thermopiles (c) ionization chamber (d) photocells (iv) The frequency of electromagnetic wave, which best suited to observe a particle of radius 3 x 10-4 cm is the order of
(a) 1015Hz (b) 1014Hz (c) 1013Hz (d) 1012Hz (v) We consider the radiation emitted by the human body. Which one of the following statements is true?
(a) The radiation emitted is in the infrared region. . (b) The radiation is emitted only during the day. (c) The radiation is emitted during the summers and absorbed during the winters (d) The radiation emitted lies in the ultraviolet region and hence it is not visible -
A stationary charge produces only an electrostatic field while a charge in uniform motion produces a magnetic field, that does not change with time. An oscillating charge is an example of accelerating charge. It produces an oscillating magnetic field, which in turruproduces an oscillating electric fields and so on. The oscillating electric and magnetic fields regenerate each other as a wave which propagates through space.
(i) Magnetic field in a plane electromagnetic wave is given by \(\vec{B}=B_{0} \sin (k x+\omega t) \hat{j} \mathrm{~T}\) Expression for corresponding electric field will be (Where C is speed of light.)\((a) \vec{E}=-B_{0} c \sin (k x+\omega t) \hat{k} \mathrm{~V} / \mathrm{m}\) \((b) \vec{E}=B_{0} c \sin (k x-\omega t) \hat{k} \mathrm{~V} / \mathrm{m}\) \((c) \vec{E}=\frac{B_{0}}{c} \sin (k x+\omega t) \hat{k} \mathrm{~V} / \mathrm{m}\) \((d) \vec{E}=B_{0} c \sin (k x+\omega t) \hat{k} \mathrm{~V} / \mathrm{m}\) (ii) The electric field component of a monochromatic radiation is given by \(\vec{E}=2 E_{0} \hat{i} \cos k z \cos \omega t\) .Its magnetic field \(\vec{B}\) is then given by
\((a) \frac{2 E_{0}}{c} \hat{j} \cos k z \cos \omega t\) \((b) \frac{2 E_{0}}{c} \hat{j} \sin k z \cos \omega t\) \((c) \frac{2 E_{0}}{c} \hat{j} \sin k z \sin \omega t\) \((d) -\frac{2 E_{0}}{c} \hat{j} \sin k z \sin \omega t\) (iii) A plane em wave of frequency 25 MHz travels in a free space along x-direction. At a particular point in space and time, \(E=(6.3 \hat{j}) \mathrm{V} / \mathrm{m}\) What is magnetic field at that time?
\((a) 0.095 \mu \mathrm{T}\) \((b) 0.124 \mu \mathrm{T}\) \((c) 0.089 \mu \mathrm{T}\) \((d) 0.021 \mu \mathrm{T}\) (iv) A plane electromagnetic wave travelling along the x-direction has a wavelength of 3 mm. The variation in the electric field occurs in the y-direction with an amplitude 66 V m-1. The equations for the electric and magnetic fields as a function of x and t are respectively
\((a) E_{y}=33 \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right), B_{z}=1.1 \times 10^{-7} \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right)\) \((b) E_{y}=11 \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right), \quad B_{y}=11 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right)\) \((c) E_{x}=33 \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right), \quad B_{x}=11 \times 10^{-7} \cos \pi \times 10^{11}\left(t-\frac{x}{c}\right)\) \((d) E_{y}=66 \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right), \quad B_{z}=2.2 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right)\) (v) A plane electromagnetic wave travels in free space along x-axis. At a particular point in space, the electric field along y-axis is 9.3 V m-1. The magnetic induction (B) along z-axis is
(a) 3.1 x 10-8 T (b) 3 x 10-5 T (c) 3 x 10-6 T (d) 9.3 x 10-6 T -
Radio waves are produced by the accelerated motion of charges in conducting wires. Microwaves are produced by special vacuum tubes. Infrared waves are produced by hot bodies and molecules also known as heat waves. UV rays are produced by special lamps and very hot bodies like Sun.
(i) Solar radiation is(a) transverse electromagnetic wave (b) longitudinal electromagnetic waves (c) both longitudinal and transverse electromagnetic waves (d) none of these. (ii) What is the cause of greenhouse effect?
(a) Infrared rays (b) Ultraviolet rays (c) X-rays (d) Radiowaves (iii) Biological importance of ozone layer is
(a) it stops ultraviolet rays (b) It layer reduces greenhouse effect (c) it reflects radiowaves (d) none of these (iv) Ozone is found in
(a) stratosphere (b) ionosphere (c) mesosphere (d) troposphere (v) Earth's atmosphere is richest in
(a) ultraviolet (b) infrared (c) X-rays (d) microwaves -
Figure below shows the parts of the electromagnetic spectrum.
(i) Name one type of radiation that has
(a) a higher frequency than ultraviolet.
(b) used in luggage security checks at airports
(c) Which part of spectrum is missing in the given figure? Write one use of this part.
(ii) Some \(\gamma\)-rays emitted from a radioactive source has a speed in air of 3.0 x 108 m/s and a wavelength of 1.0 x 10- 12 m.
Calculate the frequency of the \(\gamma\)-rays.
Case Study
*****************************************
Answers
Electromagnetic Waves Case Study Questions With Answer Key Answer Keys
-
(i) (b): Electromagnetic waves propagate in the direction of \((b) \vec{E} \times \vec{B}\)
(ii) (a): Photon is the fundamental particle in an electromagnetic wave.
(iii) (a): Polarisation establishes the wave nature of electromagnetic waves.
(iv) (c): Frequency D remains unchanged when a wave propagates from one medium to another. Both wavelength and velocity get changed.
(v) (c): The electric and magnetic fields of an electromagnetic wave are in phase and perpendicular to each other. -
(i) (c) : \(\frac{1}{2} \varepsilon_{0} E^{2}=\text { energy density }=\frac{\text { Energy }}{\text { Volume }}\)
\(\therefore\left[\frac{1}{2} \varepsilon_{0} E^{2}\right]=\frac{\mathrm{ML}^{2} \mathrm{~T}^{-2}}{\mathrm{~L}^{3}}=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]\)
(ii) (b): \(\text { As } \varepsilon_{0}=\frac{q_{1} q_{2}}{4 \pi F R^{2}}(\text { from Coulomb's law) }\)
\(\varepsilon_{0}=\frac{C^{2}}{N m^{2}} \frac{[A T]^{2}}{M L T^{-2} L^{2}}=M^{-1} L^{-3} T^{4} A^{2}\)
(iii) (d): The frequency of the electromagnetic wave remains same when it passes from one medium to another. Refractive index of the medium \(n=\sqrt{\frac{\varepsilon}{\varepsilon_{0}}}=\sqrt{\frac{4}{1}}=2\)
Wavelength of the electromagnetic wave in the medium, \(\lambda_{\mathrm{med}}-\frac{\lambda}{n}-\frac{\lambda}{2}\)
(iv) (b): \(\beta\)-rays consists of electrons which are not electromagnetic in nature.
(v) (b): The velocity of electromagnetic waves in free space (vacuum) is equal to velocity of light in vacuum (i.e., 3 x 108m S-1).
-
(i) (c): Pressure exerted by an electromagnetic radiation, \(P=\frac{I}{c}\)
(ii) (d): \(P_{\mathrm{rad}}=\frac{\text { Energy flux }}{\text { Speed of light }}=\frac{18 \mathrm{~W} / \mathrm{cm}^{2}}{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}\)
\(=\frac{18 \times 10^{4} \mathrm{~W} / \mathrm{m}^{2}}{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}=6 \times 10^{-4} \mathrm{~N} / \mathrm{m}^{2}\)
(iii) (a): \(P=\frac{I}{c}=\frac{0.5}{3 \times 10^{8}}=0.166 \times 10^{-8} \mathrm{~N} \mathrm{~m}^{-2}\)
(iv) (b): Intensity of EM wave is given by \(I=\frac{P}{4 \pi R^{2}}\)
\(V_{a v}=\frac{1}{2} \varepsilon_{0} E_{0}^{2} \times c\)
\(\Rightarrow E_{0}=\sqrt{\frac{P}{2 \pi R^{2} \varepsilon_{0} c}}=\sqrt{\frac{1500}{2 \times 3.14(3)^{2} \times 8.85 \times 10^{-12} \times 3 \times 10^{8}}}\)
\(=\sqrt{10,000}=100 \mathrm{Vm}^{-1}\)
(v) (c): The radiation pressure of visible light
= 7 x 10-6 N/m2 -
(i) (b): Infrared rays can be converted into electric energy as in solar cell.
(ii) (d): Radiowaves have longest wavelength.
(iii) (c) : Cathode rays are invisible fast moving streams of electrons emitted by the cathode of a discharge tube which is maintained at a pressure of about 0.01 mm of mercury.
(iv) (c): \(\Upsilon\)-rays have minimum wavelength
(v) (a): \(\lambda_{\text {micro }}>\lambda_{\text {infra }}>\lambda_{\text {ultra }}>\lambda_{\text {gamma }}\) -
(i) (d): All electromagnetic waves travel in vacuum with the same speed.
(ii) (c): Cathode rays (beam of electrons) get deflected in an electric field.
(iii) (c) : \(\Upsilon\)-rays are detected by ionization chamber.
(iv) (b): Size of particle \(=\lambda=\frac{c}{v}\)
\(v=\frac{c}{\lambda}=\frac{3 \times 10^{10} \mathrm{~cm} \mathrm{~s}^{-1}}{3 \times 10^{-4} \mathrm{~cm}}=3 \times 10^{14} \mathrm{~Hz}\)
(v) (a): Every body at a temperature T > 0 K emits radiation in the infrared region. -
(i) (d): Given \(\vec{B}=B_{0} \sin (k x+\omega t) \hat{j} \mathrm{~T}\)
The relation between electric and magnetic field is,
\(c-\frac{E}{B} \text { or } E-c B\)
The electric field component is perpendicular to the direction of propagation and the direction of magnetic field. Therefore, the electric field component along z-axis is obtained as
\(\vec{E}=c B_{0} \sin (k x+\omega t) \hat{k} \mathrm{~V} / \mathrm{m}\)
(ii) (c): \(\frac{d E}{d z}=-\frac{d B}{d t}\)
\(\frac{d E}{d z}=-2 E_{0} k \sin k z \cos \omega t=-\frac{d B}{d t} \)
\(d B=+2 E_{0} k \sin k z \cos \omega t d t \)
\(B=+2 E_{0} k \sin k z \int \cos \omega t d t=+2 E_{0} \frac{k}{\omega} \sin k z \sin \omega t \)
\(\frac{E_{0}}{B_{0}}=\frac{\omega}{k}=c \)
\(B=\frac{2 E_{0}}{c} \sin k z \sin \omega t \ \therefore \ \vec{B}=\frac{2 E_{0}}{c} \sin k z \sin \omega t \hat{j}\)
E is along y-direction and the wave propagates along x-axis,
\(\therefore\) B should be in a direction perpendicular to both x-and y-axis
(iii) (d): Here, \(E=6.3 \hat{j} ; c=3 \times 10^{8} \mathrm{~m} / \mathrm{s}\)
The magnitude of B is
\(B_{z}=\frac{E}{c}=\frac{6.3}{3 \times 10^{8}}=2.1 \times 10^{-8} \mathrm{~T}=0.021 \mu \mathrm{T}\)
(iv) (d): Here, \(E_{0}=66 \mathrm{Vm}^{-1}, E_{y}=66 \cos \omega\left(t-\frac{x}{c}\right)\)
\(\lambda=3 \mathrm{~mm}=3 \times 10^{-3} \mathrm{~m}, k=\frac{2 \pi}{\lambda} \)
\(\frac{\omega}{k}=c \Rightarrow \omega=c k=3 \times 10^{8} \times \frac{2 \pi}{3 \times 10^{-3}} \)
\(\text {or } \ \omega=2 \pi \times 10^{11} \)
\(\therefore \quad E_{y}=66 \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right) \)
\(B_{z}=\frac{E_{y}}{c}=\left(\frac{66}{3 \times 10^{8}}\right) \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right) \)
\(=2.2 \times 10^{-7} \cos 2 \pi \times 10^{11}\left(t-\frac{x}{c}\right)\)
(v) (a): At a particular point, E = 9.3 V m-1
\(\therefore\) Magnetic iel at the same point \(=\frac{9.3}{3 \times 10^{8}}\)
= 3.1 x 10-8 T -
(i) (a)
(ii) (a): Greenhouse effect is due to infrared rays.
(iii) (a): Ozone layer absorbs the harmful ultraviolet radiations coming from the sun.
(iv) (a): Ozone layer lies in stratosphere.
(v) (b): The atmosphere of earth is richest in infrared radiation. -
(i) (a) x-rays or y-rays
(b) x-rays
(c) Microwaves: Microwaves are used in RADAR for aircraft navigation/cooking food in microwave oven/knowing the speed of vehicles on road.
(ii) c = 3.0 x 10 8 m/s
\(\lambda\) = 1.0 x 10- 12 m
\(\therefore \quad v=\frac{c}{\lambda}=\frac{3 \times 10^{8}}{10^{-12}}=3 \times 10^{20} \mathrm{~Hz}\)
