Recent questions and answers in Plane waves and properties

The electric field of a monochromatic plane wave travelling in a lossless isotropic and homogenous medium is given by\[\vec{E}(z, t)=E_{0}[\hat{x} \cos (\omega t-k z)+\ha...

Consider a narrow band signal, propagating in a lossless dielectric medium $\left(\varepsilon_{r}=4, \mu_{r}=1\right)$, with phase velocity $v_{p}$ and group velocity $v_...

The electric field of a plane electromagnetic wave is$\boldsymbol{E}=\boldsymbol{a}_{x} C_{1 x} \cos (\omega t-\beta z)+\boldsymbol{a}_{y} C_{1 y} \cos (\omega t-\beta z+...

A transparent dielectric coating is applied to glass $\left(\varepsilon_r=4, \mu_r=1\right)$ to eliminate the reflection of red light $\left(\lambda_0=0.75 \; \mu \mathrm...

The skin depth at $10\; \mathrm{MHz}$ for a conductor is $1 \; \mathrm{cm}$. The phase velocity of an electromagnetic wave in the conductor at $1,000 \; \mathrm{MHz}$ is ...

(1) Wave tiltUnder-water propagation(2) Faraday RotationGround wave propagationSpace wave propagationIonospheric propagation

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 ...

A $\text{TEM}$ wave is incident normally upon a perfect conductor. The $\mathrm{E}$ and $\mathrm{H}$ fields at the boundary will be, respectively,minimum and minimummaxim...

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 i...

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 $\overr...

If a plane electromagnetic wave satisfies the equation $\frac{\partial^{2} \mathrm{E}_{\mathrm{x}}}{\partial \mathrm{z}^{2}}=\mathrm{c}^{2} \frac{\partial^{2} \mathrm{E}_...

The phase velocity of waves propagating in a hollow metal waveguide isgreater than the velocity of light in free space.less than the velocity of light in free space.equal...

The dominant mode in a rectangular waveguide is $\text{TE10,}$ because this mode hasno attenuationno cut-offno magnetic field componentthe highest cut-off wavelength

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 pow...

A medium has a breakdown strength of $16 \; \mathrm{KV} / \text{m r.m.s}$ its relative permeability is $1.0$ and relative permittivity is $4.0 \mathrm{~A}$ plane electrom...

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 islinearly polarizedcircularly polarizedell...

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 $...

A high-Q quartz crystal exhibits series resonance at the frequency $\omega_{s}$ and parallel resonance at the frequency $\omega_{p}$. Then$\omega_{s}$ is very close to, b...

The wavelength of a wave with propagation constant $(0.1 \pi+j 0.2 \pi) \mathrm{m}^{-1}$ is$\frac{2}{\sqrt{0.05}} \mathrm{~m}$$10 \mathrm{~m}$$20 \mathrm{~m}$$30 \mathrm{...

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

The polarisation of wave with electric field vector$\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \; e^{j(\hat{\rho}(\omega t+\beta z)}\left(\vec{a}_{x}+\vec{a}_{y}\right)$ ...

An antenna in free space receives $2 \; \mu \mathrm{W}$ of power when the incident electric field is $20 \mathrm{~m} \; \mathrm{V} / \mathrm{m} \; \mathrm{rms}$. The effe...

The far field of an antenna varies with distance $\mathrm{r}$ as$\frac{1}{r}$$\frac{1}{r^{2}}$$\frac{1}{r^{3}}$$\frac{1}{\sqrt{r}}$

A plane wave with $\overrightarrow{\mathrm{E}}=10 e^{j((\omega t-\beta z)} \overrightarrow{a_{y}}$ is incident normally on a thick plane conductor lying in the $x-y$ plan...

The electric field vector of a wave is given as\[\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} e^{t(\omega t +3x-4 y)} \frac{8 \vec{a}_{x}+6 \vec{a}_{y}+5 \vec{a}_{z}}{\sqr...

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 fo...

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 \t...

A rectangular metal wave guide filled with a dielectric material of relative permittivity $\varepsilon_{r}=4$ has the inside dimensions $3.0 \mathrm{~cm} \times 1.2 \math...

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_...

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}_{...