GATE EC Electromagnetics questions

A mast antenna consisting of a $50$ meter long vertical conductor operates over a perfectly conducting ground plane. It is base-fed at a frequency of $600-\mathrm{kHz}$. The radiation resistance of the antenna in ohms is

Statement for Linked Answer Questions 84 and 85 A $30$-Volts battery with zero source resistance is connected to a coaxial line of characteristic impedance of $50$ Ohms at $t=0$ second and terminated in an unknown resistive load. The line length is such that it takes $400 \; \mu s$ for an electromagnetic wave to travel from source end to load end and …

Statement for Linked Answer Questions 84 and 85 A $30$-Volts battery with zero source resistance is connected to a coaxial line of characteristic impedance of $50$ Ohms at $t=0$ second and terminated in an unknown resistive load. The line length is such that it takes $400 \; \mu s$ for an electromagnetic wave to travel from source end to load end and …

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

Many circles are drawn in a Smith chart used for transmission line calculations. The circles shown in the figure represent

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.

Characteristic impedance of a transmission line is $50 \Omega$. Input impedance of the open-circuited line is $Z_{a^{-}}=100+j 150 \Omega$. When the transmission line is short- circuited, then value of the input impedance will be

Statement of Linked Answer Questions 84a and 84b: Voltage standing wave pattern in a lossless transmission line with characteristic impedance $50 \mathrm{~W}$ and a resistive load is shown in the figure. The value of the load resistance is

The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the $\mathrm{TE}_{10}$ mode is

Consider a lossless antenna with a directive gain of $+6 \mathrm{~dB}$. If $1 \mathrm{~mW}$ of power is fed to it the total power radiated to the antenna will be

A parallel plate air-filled capacitor has plate area of $10^{-1} \mathrm{~m}^{2}$ and plate separation of $10^{-3} \mathrm{~m}$. It is connected to a $0.5 \mathrm{~V}, 3.6 \; \mathrm{GHz}$ source. The magnitude of the displacement current is $\left(\varepsilon_{0}=1 / 36 \pi \times 10^{-9} \mathrm{~F} / \mathrm{m}\right)$

Consider a $300 \; \Omega$, quarter-wave long (at $1 \; \mathrm{GHz}$ ) transmission line as shown in the figure. It is connected to a $10 \mathrm{~V}, 50 \; \Omega$ source at one end and is left open circuited at the other end. The magnitude of the voltage at the open circuit end of the line is

If $\overrightarrow{\mathrm{E}}=\left(\hat{a}_{x}+j \vec{a}_{y}\right) e^{\beta a-k a t}$ and $\overrightarrow{\mathrm{H}}=\left(\frac{k}{\omega \mu}\right)\left(\hat{a}_{y}+j \hat{a}_{x}\right) e^{j u-\mu \mu 1}$, the time averaged Poynting 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 $\varepsilon>\varepsilon_{0}$. 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 …

A lossless transmission line is terminated in a load which reflects a part of the incident power. The measured VSWR is $2.$ The percentage of the power that is reflected back is

The unit of $\nabla \times \mathrm{H}$ is

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

Medium $1$ has the electrical permittivity $\varepsilon_{1}=1.5 \varepsilon_{0}$ farad $/ \mathrm{m}$ and occupies the region to the left of $x=0$ plane. Medium $2$ has the electrical permittivity $\varepsilon_{2}=2.5 \varepsilon_{0}$ farad $/ \mathrm{m}$ and occupies the region to the right of $x=0$ plane. If $\mathrm{E}_{1}$ in medium …

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