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)

\text { Match the LIST-I with LIST-II }

Choose the correct answer from the options given below:

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)

$ \text { Match List - I with List - II. } $

Choose the correct answer from the options given below :

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 $\epsilon_{\mathrm{o}}=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ and $\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ )

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

$ E_y=69 \sin \left[0.6 \times 10^3 x-1.8 \times 10^{11} t\right] \mathrm{V} / \mathrm{m} . $

The expression for magnetic field associated with this electromagnetic wave is $\_\_\_\_$ T.

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

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L \mathrm{~m}$, measures the intensity as $I_{\mathrm{o}}$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as $45^{\circ}$. The measured intensity at new location will be $\_\_\_\_$ .

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 waves.

In the light of the above statements, choose the correct answer from the options given below :

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 $\alpha \times 10^6 \mathrm{~V} / \mathrm{s}$. The value of $\alpha$ is $\_\_\_\_$ .

A magnetic field vector in an electromagnetic wave is represented by $\vec{B}=B_0 \sin \left(2 \pi v t-\frac{2 \pi x}{\lambda}\right) \hat{j}$. Its associated electric field vector is $\_\_\_\_$ .

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

An electromagnetic wave travelling in x-direction is described by field equation

$E_y = 300 \sin \omega \left( t - \frac{x}{c} \right)$.

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 ______.

The unit of $\sqrt{\frac{2I}{\varepsilon_0 c}}$ is :

(I = intensity of an electromagnetic wave, c = speed of light)

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

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Electromagnetic waves carry energy but not momentum.

Reason (R) : Mass of a photon is zero.

In the light of the above statements, choose the most appropriate answer from the options given below :

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

The corresponding electric field in S.I. units is:

Due to presence of an em-wave whose electric component is given by $E=100 \sin (\omega t-k x) \mathrm{NC}^{-1}$ 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 one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

Arrange the following in the ascending order of wavelength $(\lambda)$ :

(A) Microwaves $\left(\lambda_1\right)$

(B) Ultraviolet rays $\left(\lambda_2\right)$

(C) Infrared rays $\left(\lambda_3\right)$

(D) X-rays $\left(\lambda_4\right)$

Choose the most appropriate answer from the options given below :

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 $\mathrm{E}_y=9.3 \mathrm{Vm}^{-1}$. Then, the magnetic field vector of the wave at that point is

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

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

A plane EM wave is propagating along $x$ direction. It has a wavelength of $4 \mathrm{~mm}$. If electric field is in $y$ direction with the maximum magnitude of $60 \mathrm{~Vm}^{-1}$, the equation for magnetic field is :

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:

In the given electromagnetic wave $\mathrm{E}_{\mathrm{y}}=600 \sin (\omega t-\mathrm{kx}) \mathrm{Vm}^{-1}$, intensity of the associated light beam is (in $\mathrm{W} / \mathrm{m}^2$ : (Given $\epsilon_0=9 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

Electromagnetic waves travel in a medium with speed of $1.5 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$. The relative permeability of the medium is 2.0. The relative permittivity will be:

Match List I with List II :

Choose the correct answer from the options given below :

Arrange the following in the ascending order of wavelength:

A. Gamma rays $\left(\lambda_1\right)$

B. $x$ - rays $\left(\lambda_2\right)$

C. Infrared waves $\left(\lambda_3\right)$

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 $\overrightarrow{\mathrm{E}}=\hat{i} 40 \cos \omega(\mathrm{t}-z / \mathrm{c}) \mathrm{NC}^{-1}$. The magnetic field induction of this wave is (in SI unit) :

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 the light of the above statements, choose the most appropriate answer from the options given below:

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 $\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$ ]

The electric field of an electromagnetic wave in free space is represented as $\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \cos (\omega \mathrm{t}-\mathrm{kz}) \hat{i}$. The corresponding magnetic induction vector will be :

A plane electromagnetic wave of frequency $35 \mathrm{~MHz}$ travels in free space along the $X$-direction. At a particular point (in space and time) $\vec{E}=9.6 \hat{j} \mathrm{~V} / \mathrm{m}$. The value of magnetic field at this point is :

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 $=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ) :

A plane electromagnetic wave propagating in $\mathrm{x}$-direction is described by

$E_y=\left(200 \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 t-0.05 x\right] \text {; }$

The intensity of the wave is :

(Use $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$)

In an electromagnetic wave, at an instant and at 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:

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions :

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

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.

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

The electric field in an electromagnetic wave is given as

$\overrightarrow{\mathrm{E}}=20 \sin \omega\left(\mathrm{t}-\frac{x}{\mathrm{c}}\right) \overrightarrow{\mathrm{j}} \mathrm{NC}^{-1}$

where $\omega$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5 \times 10^{-4} \mathrm{~m}^{3}$ will be

(Given $\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{Nm}^{2}$ )

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 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 :

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

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) :

Match List - I with List - II :

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 E_z = 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 :

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 :

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)