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A plane electromagnetic wave propagating in \( x \)-direction is described by \( E_{y} = (200 \, \mathrm{V \, m^{-1}})\sin[1.5 \times 10^{7} t - 0.05 \, x] \);
The intensity of the wave is : (Use \( \varepsilon_{0} = 8.85 \times 10^{-12} \, \mathrm{C^{2} \, N^{-1} \, m^{-2}} \) )

A point light source emits E.M. waves in free space. A detector, placed at a distance of \( L \, \text{m} \), measure the intensity as \( I_0 \). 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 ______.

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

If the total energy transferred to a surface in time \( t \) is \( 6.48\times10^{5}\, \text{J} \), then the magnitude of the total momentum delivered to this surface for complete absorption will be:

Match List I with List II:

Choose the correct answer from the options given below:

A parallel plate capacitor has a capacitance \( C = 200 \, \text{pF} \). It is connected to \( 230 \, \text{V} \) ac supply with an angular frequency \( 300 \, \text{rad}/\text{s} \). The rms value of conduction current in the circuit and displacement current in the capacitor respectively are:

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by, \( E_y = 20 \sin(3 \times 10^6 x - 4.5 \times 10^{14} t) \, \text{V} / \text{m} \) (where \( x \), \( t \) and other values have S.I units). The dielectric constant of the medium is _______. (speed of light in free space is \( 3 \times 10^8 \, \text{m} / \text{s} \))

Match List I with List II.

Choose the correct answer from the options given below:

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

A square shaped coil of area \( 70 \,\text{cm}^{2} \) having \( 600 \) turns rotates in a magnetic field of \( 0.4 \,\text{wb m}^{-2} \), about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes \( 500 \) revolution in a minute, the instantaneous emf when the plane of the coil is inclined at \( 60^{\circ} \) with the field, will be _______ \( \text{V} \). (Take : \( \pi = \frac{22}{7} \) )

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of \( M^{P}L^{Q}T^{R}A^{S} \), where value of 'Q' and 'R' are:

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.
I. The electron will experience magnetic force along the axis of the solenoid
II. The electron will not experience magnetic force
III. The electron will continue to move along the axis of the solenoid
IV. The electron will be accelerated along the axis of the solenoid
V. The electron will follow parabolic path inside the solenoid
Choose the correct answer from the options given below :

Electric field of a plane electromagnetic wave propagating through a non-magnetic medium is given by \( E = 20 \, \sec(2 \times 10^{10}(t - 200x)) \, \text{V}/\text{m} \). The dielectric constant of the medium is equal to: (Take \( \mu_r = 1 \))

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of \( 5 \times 10^{10} \, \text{Hz} \) and an amplitude of \( 50 \, \text{V m}^{-1} \). The total average energy density of the electromagnetic field of the wave is:
[Use \( \varepsilon_0 = 8.58 \times 10^{-12} \, \text{C}^2 /\text{N m}^2 \)]

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:

The electric field in a plane electromagnetic wave is given by
$\vec{E} = 200 \cos \left[ \left( \frac{0.5 \times 10^3}{\text{m}} \right) x - \left( 1.5 \times 10^{11} \frac{\text{rad}}{\text{s}} \times t \right) \right] \frac{\text{V}}{\text{m}} \hat{j}$
If this wave falls normally on a perfectly reflecting surface having an area of $100 \text{ cm}^2$. If the radiation pressure exerted by the E.M. wave on the surface during a $10 \text{ minute}$ exposure is $\frac{x}{10^9} \frac{\text{N}}{\text{m}^2}$. Find the value of $x$.

The electric field of an electromagnetic wave in free space is represented as \( \vec{E} = E_{0} \cos(\omega t - kz) \, \hat{i} \). The corresponding magnetic induction vector will be:

The intensity of the light from a bulb incident on a surface is \( 0.22 \, \text{W/ m}^{2} \). The amplitude of the magnetic field in this light-wave is __________ \( \times 10^{-9} \, \text{T} \).
(Given : Permittivity of vacuum \( \varepsilon_{0} = 8.85 \times 10^{-12} \, \text{C}^{2}\, \text{N}^{-1}\, \text{m}^{-2} \) , speed of light in vacuum \( c = 3 \times 10^{8} \, \text{m s}^{-1} \) )

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

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 \( 3 \times 10^{7} \, \text{ms}^{-1} \). What is the maximum magnetic force exerted on the electron?

A point source of \( 100 \, \mathrm{W} \) emits light with \( 5\% \) efficiency. At a distance of \( 5 \, \mathrm{m} \) from the source, the intensity produced by the electric field component is:

Match List -I with List -II:

Choose the correct answer from the options given below:

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

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

The expression for magnetic field associated with this electromagnetic wave is ________.

A plane electromagnetic wave travels in a medium of relative permeability \( 1.61 \) and relative permittivity \( 6.44 \). If magnitude of magnetic intensity is \( 4.5 \times 10^{-2} \, \mathrm{A \, m^{-1}} \) at a point, what will be the approximate magnitude of electric field intensity at the point?
(Given: Permeability of free space \( \mu_{0} = 4 \pi \times 10^{-7} \, \mathrm{N \, A^{-2}} \) , speed of light in vacuum \( c = 3 \times 10^{8} \, \mathrm{m \, s^{-1}} \) )

In an electromagnetic wave, at an instant and at a 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 :

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

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by:

$E_x = E_0 \sin (kz - \omega t)$
$B_y = B_0 \sin (kz - \omega t)$
Then the correct relation between $E_0$ and $B_0$ is given by:

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

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

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:

An alternating voltage of amplitude \( 40 \, \text{V} \) and frequency \( 4 \, \text{kHz} \) is applied directly across the capacitor of \( 12 \, \mu \text{F} \). The maximum displacement current between the plates of the capacitor is nearly:

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:

Electric field in a plane electromagnetic wave is given by
\( E = 50 \sin(500x - 10 \times 10^{10} t) \ \text{V}/\text{m} \)
The velocity of electromagnetic wave in this medium is: (Given \( C \) = Speed of light in vacuum)

The electric field in an electromagnetic wave is given by \( \vec{E} = \hat{\imath} \, 40 \cos \omega \!\left( t - \frac{z}{c} \right) \, \text{N C}^{-1} \). The magnetic field induction of this wave is (in SI unit):

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

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

The electric field in an electromagnetic wave is given
\( E = (50 \, \text{N C}^{-1}) \sin \omega (t - x / c) \)
The energy contained in a cylinder of volume \( V \) is \( 5.5 \times 10^{-12} \, \text{J} \), The value of \( V \) is ________ \( \text{cm}^{3} \).
(given \( \varepsilon_{0} = 8.8 \times 10^{-12} \, \text{C}^{2} \text{N}^{-1} \text{m}^{-2} \))

The magnetic field vector of an electromagnetic wave is given by \( \vec{B_0} = B_0 \dfrac{\hat{i} + \hat{j}}{\sqrt{2}} \cos(k z - \omega t) \); where \( \hat{i}, \hat{j} \) represents unit vector along \( x \) and \( y \)-axis respectively. At \( t = 0 \, \text{s} \), two electric charges \( q_1 \) of \( 4\pi \) coulomb and \( q_2 \) of \( 2\pi \) coulomb located at \( \left(0, 0, \dfrac{\pi}{k}\right) \) and \( \left(0, 0, \dfrac{3\pi}{k}\right) \), respectively, have the same velocity of \( 0.5\,c\,\hat{i} \), (where \( c \) is the velocity of light). The ratio of the force acting on charge \( q_1 \) to \( q_2 \) is:

A light wave is propagating with plane wave fronts of the type \( x+y+z=\text{constant} \). The angle made by the direction of wave propagation with the x-axis is:

The relative permittivity of distilled water is \( 81 \). The velocity of light in it will be: (Given \( \mu_r = 1 \))

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

Choose the correct answer from the options given below:

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:

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

Due to presence of an em-wave whose electric component is given by \( E = 100 \sin (\omega t - k x) \, \mathrm{N\,C}^{-1} \), a cylinder of length \( 200 \, \text{cm} \) 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:
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:

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

The rms value of conduction current in a parallel plate capacitor is \( 6.9\,\mu\text{A} \). The capacity of this capacitor, if it is connected to \( 230\,\text{V} \) ac supply with an angular frequency of \( 600\,\text{rad/s} \), will be:

If \( \varepsilon_0 \) denotes the permittivity of free space and \( \phi_E \) is the flux of the electric field through the area bounded by the closed surface, then dimensions of \( \left( \varepsilon_0 \, \frac{d\phi_E}{dt} \right) \) are that of:

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

An electromagnetic wave of frequency \( 3 \, \text{GHz} \) enters a dielectric medium of relative electric permittivity \( 2.25 \) from vacuum. The wavelength of this wave in that medium will be ________ \( \times 10^{-2} \, \text{cm} \).

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 in an electromagnetic wave is given as \( \vec{E} = 20\sin \omega \left( t - \dfrac{x}{c} \right) \vec{j} \; \text{N C}^{-1} \) where \( \omega \) and \( c \) are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of \( 5\times10^{-4} \; \text{m}^{3} \) will be:
(Given \( \varepsilon_{0}=8.85\times10^{-12} \; \text{C}^{2}/\text{N m}^{2} \))

A radar sends an electromagnetic signal of electric field \( (E_{0}) = 2.25 \, \text{V/m} \) and magnetic field \( (B_{0}) = 1.5 \times 10^{-8} \, \text{T} \) which strikes a target on line of sight at a distance of \( 3 \, \text{km} \) 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 as transmitted at time \( t = 0 \) from radar, then after how much time echo will reach to the transmitted at time \( t = 0 \) from radar, then after how much time echo will echo to the radar?

A plane electromagnetic wave propagating along \( y -\)direction can have the following pair of electric field \( (\vec{E}) \) and magnetic field \( (\vec{B}) \) components.

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

Given below are two statements:
Statement I : Electromagnetic waves are not defected by electric and magnetic field.
Statement II : The amplitude of electric field and the magnetic field in electromagnetic waves are released to each other as \( E_{0} = \sqrt{\frac{\mu_{0}}{\varepsilon_{0}}} \, B_{0} \).
In the light of the above statement, choose the correct answer from options given below:

Match List-I with List-II

Choose the correct answer from the options given below:

If electric field intensity of a uniform plane electro magnetic wave is given as

$E = -301.6 \sin(kz - \omega t)\hat{a}_x + 452.4 \sin(kz - \omega t)\hat{a}_y \, \frac{\text{V}}{\text{m}}$

Then, magnetic intensity '$\text{H}$' of this wave in $\text{Am}^{-1}$ will be:
[Given: speed of light in vacuum $c = 3 \times 10^8 \, \text{ms}^{-1}$, Permeability of vacuum $\mu_0 = 4\pi \times 10^{-7} \, \text{NA}^{-2}$]

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:

The electric field in an electromagnetic wave is given by \( E = 56.5 \sin \omega (t - x/c) \, \mathrm{N\,C^{-1}} \). Find the intensity of the wave if it is propagating along \( x \)-axis in the free space.
(Given \( \varepsilon_0 = 8.85 \times 10^{-12} \, \mathrm{C^2 N^{-1} m^{-2}} \))

In \( \vec{E} \) & \( \vec{K} \) represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: ( \( \omega \) - angular frequency)

A plane electromagnetic wave of frequency \( 100 \, \text{MHz} \) is travelling in vacuum along the \( x \)-direction. At a particular point in space and time, \( \vec{B} = 2.0 \times 10^{-8} \, \hat{k} \, \text{T} \). (where, \( \hat{k} \) is unit vector along \( z \)-direction) what is \( \vec{E} \) at this point?
(speed of light \( c = 3 \times 10^{8} \, \text{m/s} \))

The amplitude of magnetic field in an electromagnetic wave propagating along \( y \)-axis is \( 6.0 \times 10^{-7} \, \text{T} \). The maximum value of electric field in the electromagnetic wave is:

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:

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JEE Main 2023 24th Jan Morning Shift

In \( \vec{E} \) & \( \vec{K} \) represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: ( \( \omega \) - angular frequency)