Electromagnetic Waves

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 :

The intensity of the light from a bulb incident on a surface is 0.22 W/m$^2$. The amplitude of the magnetic field in this light-wave is ______ $\times10^{-9}$ T.

(Given : Permittivity of vacuum $\epsilon_0=8.85\times10^{-12}$ C$^2$ N$^{-1}$-m$^{-2}$, speed of light in vacuum $c=3\times10^8$ms$^{-1}$)

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 $10^6$ Vs$^{-1}$. The area of each plate of the capacitor is 40 cm$^2$. The distance between each plate of the capacitor is $x\times10^{-3}$m. The value of $x$ is ______

(Permittivity of free space, $E_0=8.85\times10^{-12}$ C$^2$ N$^{-1}$ m$^{-2}$)

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$^{-1}$)

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

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 :

As shown in the figure, after passing through the medium 1. The speed of light $v_2$ in medium 2 will be :

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

Match List - I with List - II :

Choose the correct answer from the options given below :

Nearly 10% of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is $a\times10^{-2}$ W/m$^2$. The value of 'a' will be _______.

A plane electromagnetic wave propagating in free space has amplitude of electric field of 900 N/C. The amplitude of magnetic field will be : _______

A physical quantity $\vec S$ is defined as $\vec S = (\vec E \times \vec B)/\mu_0$, where $\vec E$ is electric field, $\vec B$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec S$ are the same as the dimensions of which of the following quantity(ies)?

An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is _______ $\times10^7$ m/s.

Sunlight of intensity $1.3\ \mathrm{kW\,m^{-2}}$ is incident normally on a thin convex lens of focal length 20 cm. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in $\mathrm{kW\,m^{-2}}$, at a distance 22 cm from the lens on the other side is ______.

The relation between $[E]$ and $[B]$ is