GATE EC Plane Waves and Properties questions

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

If the electric field of a plane wave is $$\overrightarrow{E}(z,t)= \hat{x}3 \cos(\omega t-kz+30^{\circ}) – \hat{y} 4 \sin(\omega t – kz+45^{\circ}) (mV/m),$$ the polarization state of the plane wave is

The phase response of a passband waveform at the receiver is given by $$\varphi (f)= -2\pi \alpha (f-f_{c})-2\pi \beta f_{c}$$ where $f_{c}$ is the centre frequency, and $\alpha$ and $\beta$ are positive constants. The actual signal propagation delay from the transmitter to receiver is

Assume that a plane wave in air with an electric field $\overrightarrow{E}= 10\cos ( \omega t-3x-\sqrt{3}z )\hat{a_{y}}V/m$ is 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.

A plane wave propagating in air with $\overrightarrow{E}=(8\hat{a}_x+6\hat{a}_y+5\hat{a}_z)e^{j(\omega t+3x-4y)}\:V/m$ is incident on a perfectly conducting slab positioned at $x\le0$ . The $\overrightarrow{E}$ 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 $\overrightarrow{E}=10(\hat{a}_y+j\hat{a}_z)e^{-j\:25x}$. The frequency and polarization of the wave, respectively, are

The electric field of an electomagnetic wave propagating in the positive $z$-direction is given by $$\left.\text{E}=\hat{a_x} \sin (\omega t-\beta z\right)+\hat{a_y} \sin \left(\omega t-\beta z+\frac{\pi}{2}\right)$$ The wave is

A medium of relative permittivity $\varepsilon_{r 2}=2$ forms an interface with free-space. A point source of electronagnetic 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 …

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

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

A plane electromagnetic wave propagating in free space in incident normally on a large slab of loss-less, non magnetic, dielectric material with $\varepsilon>\varepsilon_{0}$. 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 …

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

A uniform plane wave travelling 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 travelling in a perfect dielectric medium is given by $E(z, t)=10 \cos \left(2 \pi \times 10^{7} t=0.1 \pi z\right)$ volt $/ \mathrm{m}$, then the velocity of the travelling wave is

Distilled water at $25^{\circ} \mathrm{C}$ is characterized by $\sigma=1.7 \times 10^{-1} \mathrm{mho} / \mathrm{m}$ and $\epsilon=78 \; \epsilon_{0}$ at a frequency of $3 \; \mathrm{GHz}.$ Its loss tangent $\tan\delta$ is $\left(\epsilon=10^{-9} /(36 \pi) \mathrm{F} / \mathrm{m}\right)$

A plane wave is characterized by $\overline{\mathrm{E}}=\left(0.5 \hat{x}+\hat{y} e^{jz} / 2 \right)e^{jzet – jkz}.$ This wave is

A uniform plane electromagnetic wave incident normally on a plane surface of a dielectric material is reflected with a VSWR of $3.$ What is the percentage of incident power that is reflected?

A uniform plane wave in air impinges at $45^{\circ}$ angle on a lossless dielectric material with dielectric constant $\varepsilon_{r}$. The transmitted wave propagates in a $30^{\circ}$ direction with respect to the normal. The value of $\varepsilon_{r}$ is

A plane wave propagating through a medium $\left[\varepsilon_{\mathrm{r}}=8, v_{\mathrm{r}}=2\right.$, and $\left.\sigma=0\right]$ has its electric field given by $\overrightarrow{\mathrm{E}}=0.5 \hat{\mathrm{X}} \mathrm{e}^{-(z / 3)} \sin \left(10^{8} t-\beta z\right) \mathrm{V} / \mathrm{m}$. The wave impedance, in ohms is