Recent questions tagged plane-waves-and-properties

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 $...

Consider a parallel plate waveguide with plate separation $d$ as shown in the figure electric and magnetic fields for the TEM-mode are given by$\begin{array}{l}\mathrm{E}...

Consider a linear array of two half-wave dipoles $\mathrm{A}$ and $\text{B}$ as shown in the figure is. The dipoles are $\frac{\lambda}{4}$ apart and are excited in such ...

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$\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \; e^{j(\hat{\rho}(\omega t+\beta z)}\left(\vec{a}_{x}+\vec{a}_{y}\right)$ ...

The vector $\mathrm{H}$ in the far field of an antenna satisfies$\nabla \cdot \overrightarrow{\mathrm{H}}=0$ and $\nabla \times \overrightarrow{\mathrm{H}}=0$$\nabla \cdo...

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...

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 penetra...

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...

Two identical antennas are placed in the $\theta=\pi / 2$ plane as shown in the figure. The elements have equal amplitude excitation with $180^{\circ}$ polarity differenc...

The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the $\mathrm{TE}_{10}$ mode isequal to its group velocityless than...

If $\overrightarrow{\mathrm{E}}=\left(\hat{a}_{x}+j \vec{a}_{y}\right) e^{\beta a-k a t}$ and $\overrightarrow{\mathrm{H}}=\left(\frac{k}{\omega \mu}\right)\left(\hat{a}_...

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}_{...

Which one of the following does represent the electric field lines for the $\mathrm{TE}_{\mathrm{O}_{2}}$ mode in the cross-section of a hollow rectangular metallic waveg...

Two identical and parallel dipole antennas are kept apart by a distance of $\frac{\lambda}{4}$ in the H-plane. They are fed with equal currents but the right most antenna...

An antenna, when radiating, has a highly directional radiation pattern. When the antenna is receiving, its radiation patternis more directiveis less directiveis the samee...

A transverse electromagnetic wave with circular polarisation is received by a dipole antenna. Due to polarisation mismatch, the power transfer efficiency from the wave to...

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 ...

Some unknown material has a conductivity of $10^{6} \; \mathrm{mho} / \mathrm{m}$ and a permeability of $4 \pi \times 10^{-7} \; \mathrm{H} / \mathrm{m}$. The skin depth ...

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} \si...

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 o...

A medium is divided into regions I and II about $x=0$ plane, as shown in the figure below. An electromagnetic wave with electric field $\mathrm{E}_{1}=4 \hat{a}_{x}+3 \ha...

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$\...

A rectangular waveguide having $\mathrm{TE}_{10}$ mode as dominant mode is having a cutoff frequency of $18-\mathrm{GHz}$ for the $\mathrm{TE}_{w,}$ mode. The inner broad...