Electromagnetic Waves

The electric field associated with an electromagnetic wave travelling in vacuum is given by $E_0\sin(3y+4z+\omega t)\hat\imath$, where $\omega$ is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are:
[Given: speed of light in vacuum $c=3\times10^8$ ms$^{-1}$.]

An electromagnetic wave travelling in $x$-direction is described by field equation $E_y=300\sin\omega\left(t-\dfrac xc\right)$. If the electron is restricted to move in $y$-direction only with speed of $1.5\times10^6$ m/s then ratio of maximum electric and magnetic forces acting on the electron is ________.

An electromagnetic wave travels in free space along the $x$-direction. At a particular point in space and time, $\vec B=2\times10^{-7}\hat j$ T is associated with this wave. The value of corresponding electric field $\vec E$ at this point is ________ V/m.

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

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

A displacement current of 4.0 A can be set up in the space between two parallel plates of 6 μF capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha\times10^6$ V/s. The value of $\alpha$ 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 :

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L$ m, measures the intensity as $I_o$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as 45°. The measured intensity at new location will be ________.

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 monochromatic source of light operating at 15 kW emits $2.5\times10^{22}$ photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ________.

(Take $h=6.6\times10^{-34}$ J.s and $c=3\times10^8$ m/s).

A cube of unit volume contains $35\times10^7$ photons of frequency $10^{15}$ Hz. If the energy of all the photons is viewed as the average energy being contained in the electromagnetic waves within the same volume, then the amplitude of the magnetic field is $\alpha\times10^{-9}$ T. Taking permeability of free space $\mu_0 = 4\pi\times10^{-7}$ Tm/A, Planck's constant $h = 6\times10^{-34}$ Js and $\pi = \dfrac{22}{7}$, the value of $\alpha$ is _____.

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec E = 30(2\hat x + \hat y)\sin\left[2\pi\left(5\times10^{14}\,t - \frac{10^7}{3}z\right)\right]\ \mathrm{V\,m^{-1}}$. Which of the following option(s) is(are) correct?

[Given: The speed of light in vacuum, $c = 3\times10^8\ \mathrm{m\,s^{-1}}$]

A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is $4.5\times10^{-2}\ \mathrm{Am^{-1}}$ at a point, what will be the approximate magnitude of electric field intensity at that point ?

(Given : Permeability of free space $\mu_0=4\pi\times10^{-7}\ \mathrm{NA^{-2}}$, speed of light in vacuum $c=3\times10^8\ \mathrm{ms^{-1}}$)

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.

The electric field in an electromagnetic wave is given by $E=56.5\sin\omega(t-x/c)\ \mathrm{NC^{-1}}$. Find the intensity of the wave if it is propagating along $x$-axis in the free space.

(Given $\varepsilon_0=8.85\times10^{-12}\ \mathrm{C^2N^{-1}m^{-2}}$)

A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be :

(Given : relative permeability of medium $\mu_r=1$)

The electromagnetic waves travel in a medium at a speed of $2.0\times10^8$ m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :

If Electric field intensity of a uniform plane electro magnetic wave is given as
$$E=-301.6\sin(kz-\omega t)\,\hat a_x+452.4\sin(kz-\omega t)\,\hat a_y\ \frac{\mathrm V}{\mathrm m}.$$
Then, magnetic intensity 'H' of this wave in A m$^{-1}$ will be :

[Given : Speed of light in vacuum $c=3\times10^8\ \mathrm{ms^{-1}}$, Permeability of vacuum $\mu_0=4\pi\times10^{-7}\ \mathrm{NA^{-2}}$]

Which is the correct ascending order of wavelengths ?

Match List - I with List - II :

Choose the correct answer from the options given below :