Uniform Plane Waves Practice Questions

The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\vec{E}=10(\hat{a}_{y}+j\hat{a}_{z})e^{-j25x}$ . The frequency and polarization of the wave, respectively, are

The electric and magnetic fields for a TEM wave of frequency 14 GHz in a homogeneous medium of relative permittivity er and relative permeability $\mu _{r}$ =1 are given by $\vec{E}=E_{p}e^{j(\omega t-280\pi t)}\hat{u}_{z} V/m$ $\vec{H}=3e^{j(\omega t-280\pi y)}\hat{u}_{x} V/m$ Assuming the speed of light in free space to be $3 \times 10^{8}$ m/s, the intrinsic impedance of free space to be 120 $\pi$ , the relative permittivity $\varepsilon_{r}$ of the medium and the electric field amplitude $E_{p}$ are

A plane wave having the electric field components $\vec{E}_{i}=24 \cos (3 \times 10^{8}t-\beta y)\hat{a}_{z} V/m$ and traveling in free space is incident normally on a lossless medium with $\mu =\mu_{0}$ and $\varepsilon =9\varepsilon_{0}$ which occupies the region $y\geq 0$ . The reflected magnetic field component is given by

The electric field component of a time harmonic plane EM wave traveling in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector (in W/ $m^{2}$ ) is

A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant $\varepsilon_{r}$ =9). The magnitude of the reflection coefficient is

A right circularly polarized (RCP) plane wave is incident at an angle $60^{\circ}$ to the normal, on an air-dielectric interface. If the reflected wave is linearly polarized, the relative dielectric constant $\varepsilon_{r2}$ is.

The $\vec{H}$ field (in A/m) of a plane wave propagating in free space is given by $\vec{H}=\hat{x}\frac{5\sqrt{3}}{\eta _{0}}cos(\omega t-\beta z)+\hat{y}\frac{5}{\eta _{0}}sin(\omega t-\beta z+\frac{\pi }{2})$ . The time average power flow density in Watts is

A plane wave of wavelength $\lambda$ is traveling in a direction making an angle $30^{\circ}$ with positive x-axis and $90^{\circ}$ with positive y-axis. The $\vec{E}$ field of the plane wave can be represented as ( $E_0$ is constant)

When a planes wave traveling in free-space is incident normally on a medium having $\varepsilon_{r}=4.0$ , the fraction of power transmitted into the medium is given by

A medium of relative permittivity $\varepsilon _{r2}=2$ 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 crosssection at the interface is given by

The electric field of an electromagnetic wave propagation in the positive direction is given by $E=\hat{a}_{x}sin(\omega t-\beta z)+\hat{a}_{y}sin(\omega t-\beta z+\pi /2)$ . The wave is

The magnetic field intensity vector of a plane wave is given by $\bar{H}(x,y,z,t)=10sin(50000t+0.004x+30)\hat{a}_{y}$ where $\hat{a}_{y}$ , 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 frequency of $10^{14}$ Hz in glass. Assume velocity of light is 3 × $10^{8}$ m/s in vacuum

A parallel plate air-filled capacitor has plate area of $10^{-4} m^{2}$ and plate separation of $10^{-3}$ m. It is connected to a 0.5V, 3.6 GHz source. The magnitude of the displacement current is ( $\varepsilon =\frac{1}{36\pi}10^{-9} F/m$ )

If $\vec{E}=(\hat{a}_{x}+j\hat{a}_{y})e^{jkz-k\omega t}$ and $\vec{H}=(k/\omega \mu )(\hat{a}_{y}+j\hat{a}_{x})e^{jkz-j\omega t}$ , the time-averaged Poynting vector is

A uniform plane wave traveling in air is incident on the plane boundary between air and another dielectric medium with $\varepsilon _{r}$ = 4. The reflection coefficient for the normal incidence, is

If the electric field intensity associated with a uniform plane electromagnetic wave traveling in a perfect dielectric medium is given by $E(z,t)=10\cos (2\pi 10^{7}t-0.1\pi z)$ V/m, then the velocity of the traveling wave is

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

Distilled water at 25 $^{\circ}$ C is characterized by $\sigma$ = 1.7 × $10^{-4}$ mho/m and $\epsilon =78\epsilon_{0}$ at a frequency of 3 GHz. Its loss tangent $tan\delta$ is ( $\epsilon=10^{-9} /(36\pi)$ F/m)