GATE EC Electromagnetics questions

If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be

Faraday’s law of electromagnetic induction is mathematically described by which one of the following equations?

Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. At $10 \:GHz$ operating frequency, the value of the propagation constant (per meter) of the corresponding propagation mode is _______

Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. The increasing order of the cut-off frequencies for different modes is

A radar operating at $5\:GHz$ uses a common antenna for transmission and reception. The antenna has a gain of $150$ and is aligned for maximum directional radiation and reception to a target $1\:km$ away having radar cross-section of $3\:m^2$. If it transmits $100\:kW$, then the received power (in $\mu W)$ is _______

Consider the charge profile shown in the figure. The resultant potential distribution is best described by

The polar plot of the transfer function $G(s) = \frac{10(s+1)}{s+10}$ for $0 \leq \omega < \infty$ will be in the

The electric field component of a plane wave traveling in a lossless dielectric medium is given by $\overrightarrow{E}(z,t) = \hat{a}_y 2 \cos \bigg( 10^st-\frac{z}{\sqrt{2}} \bigg) \: V/m$. The wavelength (in m) for the wave is ___________.

All the logic gates shown in the figure have a propagation delay of $20$ ns. Let $A=C=0$ and $B=1$ until time $t=0$. At $t=0$, all the inputs flip (i.e., $A=C=1$ and $B=0$) and remain in that state. For $t>0$, output $Z=1$ for a duration (in ns) of ________.

The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression $$H_z (x,y,z,t) = 0.1 \: cos(25 \pi x) \: \: \cos(30.3 \: \pi y) \: \: \cos(12 \pi \times 10^9 t- \beta z) \: \: (A/m)$$ The cross-sectional dimensions of the waveguide are give as …

In a source free region in vacuum, if the electrostatic potential $\varphi = 2x^{2} + y^{2} + cz^{2},$ the value of constant ܿ$c$ must be _______.

The electric field of a uniform plane electromagnetic wave is $$\overrightarrow{E} = \left(\overrightarrow{a}_{x} + j 4 \overrightarrow{a}_{y}\right) \text{exp }[j(2\pi \times 10^{7}t – 0.2z)].$$ The polarization of the wave is

An air-filled rectangular waveguide of internal dimensions $a\: cm \times b\: cm\:(a>b)$ has a cutoff frequency of $6\:GHz$ for the dominant $TE_{10}$ mode. For the same waveguide, if the cutoff frequency of the $TM_{11}$mode is $15\: GHz,$ the cutoff frequency of the $TE_{01}$ mode in $GHz$ is __________.

The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following expression $$\text{E}(z,t) = \textbf{a}_{x} 5 \cos(2\pi \times 10^{9}t + \beta z) + \textbf{a}_{y} 3 \cos\left(2\pi \times 10^{9} t + \beta z – \frac{\pi}{2}\right)$$ The type of the polarization is

The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements

A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon $(\varepsilon_{r} = 2.1, \tan \delta = 0).$ Which one of the following circuits can represent the lumped element model of a small piece of this cable having length $\Delta z$?

Consider the $3\:m$ long lossless air-filled transmission line shown in the figure. It has a characteristic impedance of $120\pi\: \Omega,$ is terminated by a short circuit, and is excited with a frequency of $37.5\: MHz.$ What is the nature of the input impedance $(Z_{in})?$

For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance $Z_{1}$ of the first section to the input impedance $Z_{2}$ of the second section is

A good current buffer has

The force on a point charge $+q$ kept at a distance $d$ from the surface of an infinite grounded metal plate in a medium of permittivity $\epsilon\:$ is