Consider a narrow band signal, propagating in a lossless dielectric medium , with phase velocity  and group velocity . Which of the following statement is true?

( is the velocity of light in vacuum.)

The electric field of a plane electromagnetic wave is

Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

Consider a rectangular coordinate system  with unit vectors  and . A plane wave traveling in the region  with electric field vector  is incident normally on the plane at , where  is the phase constant. The region  is in free space and the region  is filled with a lossless medium (permittivity , permeability , where  and  ). The value of the reflection coefficient is________.

The refractive indices of the core and cladding of an optical fibre are 1.50 and 1.48, respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fibre to achieve the total internal reflection, (rounded off to two decimal places) is ________degree.

For an infinitesimally small dipole in free space, the electric field  in the far field is proportional to , where . A vertical infinitesimally small electric dipole  is placed at a distance  above an infinite ideal conducting plane, as shown in the figure. The minimum value of , for which one of the maxima in the far field radiation pattern occurs at . Is

The magnetic field of a uniform plane wave in vacuum is given by

The value of  is ________.

The distance (in meters) a wave has to propagate in a medium having a skin depth of 0.1 in so that the amplitude of the wave attenuates by 20 dB, is

A uniform plane wave travelling in free space and having the electric field

 is incident on a dielectric medium (relative permittivity>1,

relative permeability = t) as shown in the figure and there is no reflected wave.

The relative permittivity (correct to two decimal places) of the dielectric medium is _______

The voltage of an electromagnetic wave propagating in a coaxial cable with uniform characteristic impedance is Volts, where l is the distance along the length of the cable in metres, is the complex propagation constant, and rad/s is the angular frequency. The absolute vale of the attenuation in the cable in dB/metre is ___________.

The expression for an electric field in free space is , where x, y, z represent the spatial coordinates, t represents time, and , k are constants. This electric field

An optical fiber is kept along the direction. The refractive indices for the electric fields along and directions in the fiber are respectively

(due to the imperfection in the fiber cross-section). The free space wavelength of a light wave propagating in the fiber is 1.5 µm. If the light wave is circularly polarized at the input of the fiber, the minimum propagation distance after which it becomes linearly polarized, in centimeters, is ______________.

The permittivity of water at optical frequencies is . It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5 m, as shown in the figure. The critical angle is

The value of d (in meter) is ___________

The electric field of a uniform plane wave travelling along the negative z direction is given by the following equation:

This wave is incident upon a receiving antenna placed at the origin and whose radiated electric field towards the incident wave is given by the following equation:

The polarization of the incident wave, the polarization of the antenna and losses due to the polarization mismatch are, respectively,

Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as , where the propagation constant β is a function of the angular frequency ω.  Assume that β(ω) and are known and are real. From the information available, which one of the following CANNOT be determined?

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

The electric field component of a plane wave travelling in a lossless dielectric medium is given by  V/m.

The wavelength (in m) for the wave is ___________.

The electric field intensity of a plane wave travelling in free space is given by the following expression  

In this field, consider a square area 10 cm x 10 cm on a plane x + y = 1. The total time-averaged power (in mW) passing through the square area is _______.

Consider a uniform plane wave with amplitude  of 10 V/m and 1.1 GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity  and permeability  as shown in the figure.

The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of 10 cm inside the dielectric region is _________.

The electric field of a uniform plane electromagnetic wave is        

 .

The polarization of the wave is

Which one of the following field patterns represents a TEM wave travelling in the positive 𝑥 direction?

If the electric field of a plane wave is

 ,

the polarization state of the plane wave is

Assume that a plane wave in air with an electric field   incident on a non-magnetic dielectric slab of relative permittivity 3 which covers the region z>0. The angle of transmission in the dielectric slab is ________ degrees.

The return of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and magnitude of reflection coefficient are respectively

A monochromatic plane wave of wavelength  is propagating in the direction as shown in the figure below.  denote incident, reflected, and transmitted electric field vectors associated with the wave.

The angle of incidence  and the expression for  are

A monochromatic plane wave of wavelength  is propagating in the direction as shown in the figure below.   denote incident, reflected, and transmitted electric field vectors associated with the wave.

The expression for   is

A plane wave propagating in air with   is incident on a perfectly conducting slab positioned at x≤ 0. The   field of the reflected wave is

The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction, is given by   . The frequency and polarization of the wave, respectively, are

Consider the following statements regarding the complex Poynting vector  for the power radiated by a point source in an infinite homogeneous and lossless medium. Re  denotes the real part of , S denotes a spherical surface whose centre is at the point source, and  denotes the unit surface normal on S. Which of the following statements is TRUE?

The electric and magnetic fields for a TEM wave of frequency 14 GHz in a homogenous medium of relative permittivity  and relative permeability  are given by

Assuming the speed of light in free space to be m/s, the intrinsic impedance of free space to be , the relative permittivity  and relative permeability  are given by

The electric field component of a time harmonic plane EM wave travelling in a nonmagnetic lossless dielectric medium has an amplitude of. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector  is

A plane wave having the electric field component  V/m and travelling in free space is incident normally on a lossless medium with  and  which occupies the region . The reflected magnetic field component is given by  

A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant). The magnitude of the reflection coefficient is

A plane wave of wavelength λ is travelling in a direction making an angle 30° with Positivex-axis and 90° with positive y-axis. The field of the plane wave can be represented as ( is a constant)

Thefield (in A/m) of a plane wave propagating in free space is given by

.

The time average power flow density in Watts is

A right circularly polarized (RCP) plane wave is incident at an angle of 60° to the normal, on an air-dielectric interface. If the reflected wave is linearly polarized, the relative dielectric constants,   is

The electric field of an electromagnetic wave propagating in the positive z-direction is given by

The wave is

A medium of relative permittivity forms an interface with free-space. A point source of electromagnetic energy is located in the medium at a depth of 1 meter from the interface. Due to the total internal reflection, the transmitted beam has a circular cross-section over the interface. The area of the beam cross-section at the interface is given by

When a plane wave travelling in free-space is incident normally on a medium having , the fraction of power transmitted into the medium is given by

The magnetic field intensity vector of a plane wave is given by  Where denotes the unit vector in y direction. The wave is propagating with a phase velocity

Refractive index of glass is 1.5. Find the wavelength of a beam of light with a frequency of  Hz in glass. Assume velocity of light is  in vacuum.

If  and ,

the time averaged pointing vector is

A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non-magnetic, dielectric material with . Maxima and minima are observed when the electric field is measured in front of the slab. The maximum electric field is found to be 5 times the minimum field. The intrinsic impedance of the medium should be

The depth of penetration of electromagnetic wave in a medium having conductivity σ at a frequency of 1 MHz is 25 cm. The depth of penetration at a frequency of 4MHz will be

A uniform plane wave travelling in air is incident on the plane boundary between air and another dielectric medium with. The reflection coefficient for the normal incidence, is

The VSWR can have any value between

A plane wave is characterized by  . This wave is

A TEM wave is incident normally upon a perfect conductor. The E and H fields at the boundary will be, respectively.

A uniform plane wave in air impinges at  angle on a lossless dielectric material with dielectric constant. The transmitted wave propagates in a  direction with respect to the normal. The value of  is

The three regions shown in figure are all lossless and non-magnetic.

Find

(a) Wave impedance in mediums 2 and 3.

(b) Find d such that medium 2 acts as a quarter wave  transformer.

(c) Reflection coefficient  and voltage standing wave ratio (VSWR) at the interface of the medium 1 and 2, when

Identify which one of the following will NOT satisfy the wave equation.

A plane wave propagating through a medium  has its electric field given by .

The wave impedance, in ohms is

A plane wave in free space with

, where  and  are unit vectors in the x-y directions, respectively, is incident normally on a semi-infinite block of ice as shown in figure.

For ice, , , .

(a) Calculate the average power density associated with the incident wave.

(b) Calculate the skin depth in ice.

(c) Estimate the average power density at a distance of 5 times the skins depth in the ice block, measured from the interface.

The intrinsic impedance of copper at high frequencies is

The time averages Poynting vector, in , for a wave with  in free space is

The wavelength of a wave with propagation constant  is

The depth of penetration of wave in a lossy dielectric increases with increasing

The polarization of wave with electric field vector  is

The radiation resistance of a circular loop of one turn is . The radiation resistance of five turns of such a loop will be

A plane wave with  is incident normally on a thick plane conductor lying in the x-y plane. Its conductivity is  and surface impedance is . Determine the propagation constant and the skin depth in the conductor.

The electric field vector of a wave is given as

.

Its frequency is 10 GHz.

(i) Investigate if this wave is a plane wave.

(ii) Determine its propagation constant, and

(iii) Calculate the phase velocity in y-direction.

The skin depth at 10 MHz for a conductor is 1 cm. The phase velocity of an electromagnetic wave in the conductor at 1,000 MHz is about

A uniform plane wave is normally incident from air on an infinitely thick magnetic material with relative permeability 100 and relative permittivity 4 see the figure is. The wave has an electric field of 1V, meter (RMS).

Find the average pointing vector inside the material.

A uniform plane wave in air is normally incident on infinitely thick slab. If the refractive index of the glass slab is 1.5, then the percentage of incident power that is reflected from the air-glass interface is

Some unknown material has a conductivity of  and a permeability of.

The skin depth for the material at 1 GHz is

The intrinsic impedance of a lossy dielectric medium is given by

Copper behaves as a

A plane electromagnetic wave travelling along +z – directions, has its electric field given by  and .

The wave is

A plane electromagnetic wave of the form

Where  is a constant and y is the unit vector along y-direction) represents a wave propagating along

A material is described by the following electrical parameters as a frequency of 10 GHz, , , . The material at this frequency is considered to be

A plane wave is incident normally on a perfect conductor as shown in figure. Here  and  are electric field, magnetic field and poynting vector respectively, for the incident wave. The reflected wave should be

A uniform plane wave travelling in free space along the +z direction and having its electric field along the x-direction, is normally incident on a thick brass sheet, infinite in extent along the x-and y-directions). The electric field intensity of the wave is given by

 volts/metre.

Calculate the power per square metre that causes heating of the brass sheet taking,  and  mhos/ metre for brass.

The electric field component of a uniform plane electromagnetic wave propagating in the Y-direction in a lossless medium will satisfy the equation.

A uniform plane electromagnetic wave travelling in free space enters into a lossless medium at normal incidence. In the medium its velocity reduces by 50% and in free space sets up a standing wave having a reflection coefficient of -0.125. Calculate the permeability and the permeability of the medium.