Properties of EM 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 ________.

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 :

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 $c=3\times10^8\ \mathrm{ms^{-1}}$)

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 $\mu_0=4\pi\times10^{-7}\ \mathrm{NA^{-2}}$]

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 $v=\dfrac1{\sqrt{\mu_0\varepsilon_0}}$.

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

A radar sends an electromagnetic signal of electric field $(E_0)=2.25$ V/m and magnetic field $(B_0)=1.5\times10^{-8}$ 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?

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 :

An expression for oscillating electric field in a plane electromagnetic wave is given as $E_z=300\sin\left(5\pi\times10^3x-3\pi\times10^{11}t\right)$ Vm$^{-1}$. Then, the value of magnetic field amplitude will be :

(Given : speed of light in Vacuum $c=3\times10^8$ ms$^{-1}$)

Light wave traveling in air along x-direction is given by $E_y=540\sin\pi\times10^4(x-ct)$ Vm$^{-1}$. Then, the peak value of magnetic field of wave will be (Given $c=3\times10^8$ ms$^{-1}$)

The magnetic field of a plane electromagnetic wave is given by :

$$\vec B=2\times10^{-8}\sin\left(0.5\times10^3x+1.5\times10^{11}t\right)\hat j\ \text{T}.$$

The amplitude of the electric field would be :

The oscillating magnetic field in a plane electromagnetic wave is given by $B_y=5\times10^{-6}\sin1000\pi\left(5x-4\times10^8t\right)$ T. The amplitude of electric field will be :

A beam of light travelling along X-axis is described by the electric field $E_y=900\sin\omega(t-x/c)$. The ratio of electric force to magnetic force on a charge q moving along Y-axis with a speed of $3\times10^7$ ms$^{-1}$ will be :

(Given speed of light = $3\times10^8$ ms$^{-1}$)

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 :