Electromagnetic Waves
The energy density associated with electric field $\vec{E}$ and magnetic field $\vec{B}$ of an electromagnetic wave in free space is given by $\left(\epsilon_{0}-\right.$ permittivity of free space, $\mu_{0}-$ permeability of free space)
For the plane electromagnetic wave given by $E=E_{0} \sin (\omega t-k x)$ and $B=B_{0} \sin (\omega t-k x)$, the ratio of average electric energy density to average magnetic energy density is
The ratio of average electric energy density and total average energy density of electromagnetic wave is :
Match List I with List II :
| List I | List II | ||
|---|---|---|---|
| A. | Microwaves | I. | Radio active decay of the nucleus |
| B. | Gamma rays | II. | Rapid acceleration and deceleration of electron in aerials |
| C. | Radio waves | III. | Inner shell electrons |
| D. | X-rays | IV. | Klystron valve |
Choose the correct answer from the options given below :
| 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:
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 ${E_0} = \sqrt {{{{\mu _0}} \over {{\varepsilon _0}}}} {B_0}$.
In the light of the above statements, choose the correct answer from the options given below :
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 is 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 medium is independent of intensity.
Choose the correct answer from the options given below:
Match List I with List II
| List I | List II | ||
|---|---|---|---|
| A. | Gauss's Law in Electrostatics | I. | $\oint {\overrightarrow E \,.\,d\overrightarrow l = - {{d{\phi _B}} \over {dt}}} $ |
| B. | Faraday's Law | II. | $\oint {\overrightarrow B \,.\,d\overrightarrow A = 0} $ |
| C. | Gauss's Law in Magnetism | III. | $\oint {\overrightarrow B \,.\,d\overrightarrow l = {\mu _0}{i_c} + {\mu _0}{ \in _0}{{d{\phi _E}} \over {dt}}} $ |
| D. | Ampere-Maxwell Law | IV. | $\oint {\overrightarrow E \,.\,d\overrightarrow s = {q \over {{ \in _0}}}} $ |
Choose the correct answer from the options given below :
An 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?
The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by
$\mathrm{{E_x} = {E_o}\sin (kz - \omega t)}$
$\mathrm{{B_y} = {B_o}\sin (kz - \omega t)}$
Then the correct relation between E$_0$ and B$_0$ is given by
In $\overrightarrow E $ and $\overrightarrow K $ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by :
($\omega$ - angular frequency) :
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 $=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$ and for the given medium $\mu_{\mathrm{r}}=1$)
Explanation:
Putting the values:
$0.2 c=\frac{c}{\sqrt{\varepsilon_{r}}}$
$\Rightarrow \sqrt{\varepsilon_{r}}=5$
$\Rightarrow$ Required ratio $=\frac{\varepsilon_{r}}{n}=\frac{\varepsilon_{r}}{\sqrt{\varepsilon_{r}}}=\sqrt{\varepsilon_{r}}=5$
$\Rightarrow x=5$
A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of $24 \mathrm{~W}$. The radius of curvature of hemisphere is $10 \mathrm{~cm}$ and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is ____________ $\times~10^{-8} \mathrm{~N}$.
Explanation:
$ \begin{aligned} & \text { Force }=\int P d A \cos \theta \\\\ & =\frac{2 \mathrm{I}}{\mathrm{C}} \int \mathrm{dA} \cos \theta=\frac{2 \mathrm{I}}{\mathrm{C}} \pi \mathrm{R}^2=2 \frac{\mathrm{p}_0}{4 \pi \mathrm{R}^2} \cdot \frac{\pi \mathrm{R}^2}{\mathrm{C}} \\\\ & =\frac{\mathrm{p}_0}{2 \mathrm{C}}=\frac{24}{2 \times 3 \times 10^8}=4 \times 10^{-8} \mathrm{~N} \end{aligned} $
Match List - I with List - II :
| List - I | List - II | ||
|---|---|---|---|
| (a) | UV rays | (i) | Diagnostic tool in medicine |
| (b) | X-rays | (ii) | Water purification |
| (c) | Microwave | (iii) | Communication, Radar |
| (d) | Infrared wave | (iv) | Improving visibility in foggy days |
Choose the correct answer from the options given below :
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
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 field or magnetic field.
(B) The energy in electromagnetic wave is divided equally between electric and magnetic fields.
(C) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.
(D) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.
(E) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.
Choose the most appropriate answer from the options given below :
A beam of light travelling along $X$-axis is described by the electric field $E_{y}=900 \sin \omega(\mathrm{t}-x / c)$. The ratio of electric force to magnetic force on a charge $\mathrm{q}$ moving along $Y$-axis with a speed of $3 \times 10^{7} \mathrm{~ms}^{-1}$ will be :
(Given speed of light $=3 \times 10^{8} \mathrm{~ms}^{-1}$)
The oscillating magnetic field in a plane electromagnetic wave is given by
$B_{y}=5 \times 10^{-6} \sin 1000 \pi\left(5 x-4 \times 10^{8} t\right) T$. The amplitude of electric field will be :
A velocity selector consists of electric field $\vec{E}=E \,\hat{k}$ and magnetic field $\vec{B}=B \,\hat{j}$ with $B=12 \,m T$. The value of $E$ required for an electron of energy $728 \,\mathrm{e} V$ moving along the positive $x$-axis to pass undeflected is :
(Given, mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$ )
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} x+1.5 \times 10^{11} \mathrm{t}\right) \,\hat{j} \mathrm{~T}$.
The amplitude of the electric field would be :
Light wave travelling in air along x-direction is given by ${E_y} = 540\sin \pi \times {10^4}(x - ct)\,V{m^{ - 1}}$. Then, the peak value of magnetic field of wave will be (Given c = 3 $\times$ 108 ms$-$1)
The rms value of conduction current in a parallel plate capacitor is $6.9 \,\mu \mathrm{A}$. The capacity of this capacitor, if it is connected to $230 \mathrm{~V}$ ac supply with an angular frequency of $600 \,\mathrm{rad} / \mathrm{s}$, will be :
An expression for oscillating electric field in a plane electromagnetic wave is given as Ez = 300 sin(5$\pi$ $\times$ 103x $-$ 3$\pi$ $\times$ 1011t) Vm$-$1
Then, the value of magnetic field amplitude will be :
(Given : speed of light in Vacuum c = 3 $\times$ 108 ms$-$1)
An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm$-$1. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :
${E_y} = 60\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat j\,\,V{m^{ - 1}}$
${B_z} = 2\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat k\,\,T$
${E_y} = 60\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat j\,\,V{m^{ - 1}}$
${B_z} = 2 \times {10^{ - 7}}\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat k\,\,T$
${E_y} = 2 \times {10^{ - 7}}\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat j\,\,V{m^{ - 1}}$
${B_z} = 60\sin \left[ {{\pi \over 4} \times {{10}^3}(x - 3 \times {{10}^8}t)} \right]\widehat k\,\,T$
${E_y} = 2 \times {10^{ - 7}}\sin \left[ {{\pi \over 4} \times {{10}^4}(x - 4 \times {{10}^8}t)} \right]\widehat j\,\,V{m^{ - 1}}$
${B_z} = 60\sin \left[ {{\pi \over 4} \times {{10}^4}(x - 4 \times {{10}^8}t)} \right]\widehat k\,\,T$
A radar sends an electromagnetic signal of electric field (E0) = 2.25 V/m and magnetic field (B0) = 1.5 $\times$ 10$-$8 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 back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar?
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 $v = {1 \over {\sqrt {{\mu _0}{ \in _0}} }}$. In the light of the above statements, choose the correct answer from the options given below.
Match List-I with List-II :
| List - I | List - II | ||
|---|---|---|---|
| (a) | Ultraviolet rays | (i) | Study crystal structure |
| (b) | Microwaves | (ii) | Greenhouse effect |
| (c) | Infrared rays | (iii) | Sterilizing surgical instrument |
| (d) | X-rays | (iv) | Radar system |
Choose the correct answer from the options given below :
Which is the correct ascending order of wavelengths?
If Electric field intensity of a uniform plane electromagnetic wave is given as $E = - 301.6\sin (kz - \omega t){\widehat a_x} + 452.4\sin (kz - \omega t){\widehat a_y}{V \over m}$. Then magnetic intensity 'H' of this wave in Am$-$1 will be :
[Given : Speed of light in vacuum $c = 3 \times {10^8}$ ms$-$1, Permeability of vacuum ${\mu _0} = 4\pi \times {10^{ - 7}}$ NA$-$2]
In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size ${\lambda \over {100}}$, where $\lambda$ is the wavelength of the wave in free space. The phenomenon, which happens there will be :
The electromagnetic waves travel in a medium at a speed of 2.0 $\times$ 108 m/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 E = 56.5 sin $\omega$(t $-$ x/c) NC$-$1. Find the intensity of the wave if it is propagating along x-axis in the free space.
(Given : $\varepsilon $0 = 8.85 $\times$ 10$-$12C2N$-$1m$-$2)
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.
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$-$2 Am$-$1 at a point, what will be the approximate magnitude of electric field intensity at that point?
(Given : Permeability of free space $\mu$0 = 4$\pi$ $\times$ 10$-$7 NA$-$2, speed of light in vacuum c = 3 $\times$ 108 ms$-$1)
Nearly 10% of the power of a $110 \mathrm{~W}$ light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of $1 \mathrm{~m}$ from the bulb to a distance of $5 \mathrm{~m}$ is $a \times 10^{-2} \mathrm{~W} / \mathrm{m}^{2}$. The value of 'a' will be _________.
Explanation:
$=\frac{10}{100} \times 110 \mathrm{~W}$
$=11 \mathrm{~W}$
$\mathrm{I}_1-\mathrm{I}_2=\frac{\mathrm{P}^{\prime}}{4 \pi \mathrm{r}_1^2}-\frac{\mathrm{P}^{\prime}}{4 \pi \mathrm{r}_2^2}$
$=\frac{11}{4 \pi}\left[\frac{1}{1}-\frac{1}{25}\right]$
$=\frac{11}{4 \pi} \times \frac{24}{25}$
$=\frac{264}{\pi} \times 10^{-2}=84 \times 10^{-2} \mathrm{~W} / \mathrm{m}^2$
The displacement current of 4.425 $\mu$A is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 106 Vs$-$1. The area of each plate of the capacitor is 40 cm2. The distance between each plate of the capacitor is x $\times$ 10$-$3 m. The value of x is __________.
(Permittivity of free space, E0 = 8.85 $\times$ 10$-$12 C2 N$-$1 m$-$2).
Explanation:
$4.425\,\mu A = {{{E_0}A} \over d} \times {{dV} \over {dt}}$
$ \Rightarrow d = {{8.85 \times {{10}^{ - 12}} \times 40 \times {{10}^{ - 4}}} \over {4.425 \times {{10}^{ - 6}}}} \times {10^6}$
$ \Rightarrow d = 8 \times {10^{ - 3}}$ m
$ \Rightarrow x = 8$
The intensity of the light from a bulb incident on a surface is 0.22 W/m2. The amplitude of the magnetic field in this light-wave is ______________ $\times$ 10$-$9 T.
(Given : Permittivity of vacuum $\in$0 = 8.85 $\times$ 10$-$12 C2 N$-$1-m$-$2, speed of light in vacuum c = 3 $\times$ 108 ms$-$1)
Explanation:
$I = {1 \over 2}{\varepsilon _0}E_0^2\,.\,c = {1 \over 2}{\varepsilon _0}{(c{B_0})^2}c$
$ \Rightarrow I = {1 \over 2}{\varepsilon _0}{c^3}B_0^2$
$ \Rightarrow 0.22 = {1 \over 2}\left( {8.85 \times {{10}^{ - 12}}} \right){\left( {3 \times {{10}^8}} \right)^3}B_0^2$
$ \Rightarrow {B_0} \simeq 43 \times {10^{ - 9}}$ T
E = 20cos(2 $\times$ 1010 t $-$ 200x) V/m. The dielectric constant of the medium is equal to : (Take $\mu$r = 1)
(Given C = speed of light in vacuum)
(Given $\mu$r = 1)
$E = 3.1\cos \left[ {(1.8)z - (5.4 \times {{10}^6})t} \right]\widehat iN/C$
is incident normally on a perfectly reflecting wall at z = a. Choose the correct option
(${\varepsilon _0} = 8.85 \times {10^{ - 12}}{C^2}{N^{ - 1}}{m^{ - 2}}$)
$\overrightarrow B $ = 8.0 $\times$ 10$-$8 $\widehat z$T. The value of electric field at this point is :
(speed of light = 3 $\times$ 108 ms$-$1)
$\widehat x$, $\widehat y$, $\widehat z$ are unit vectors along x, y and z directions.