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Maxwell's Equations and Plane Waves(12)Transmission Lines, Waveguides, Optical Fibers, and Antennas(13)

Maxwell's Equations and Plane Waves

12 Questions

GATE→2026→Electromagnetics→Maxwell's Equations and Plane Waves

Q1

MCQ[1 Mark]

The electric field of a monochromatic plane wave travelling in a lossless isotropic and homogenous medium is given by $\vec{E}(z,t)=E_{0}[\hat{x}cos(\omega t-kz)+\hat{y}sin(\omega t-kz)]$ in a right-handed orthogonal co-ordinate system. Which of the following is the correct polarization of the electromagnetic wave?

(A)

Right-handed circularly polarized

(B)

Left-handed circularly polarized

(C)

Linearly polarized

(D)

Linearly polarized with $-45^{\circ}$ angle to

Explanation

GATE→2025→Electromagnetics→Maxwell's Equations and Plane Waves

Q2

MCQ[2 Marks]

A square metal sheet of $4~m \times 4$ m is placed on the x-y plane as shown in the figure below. If the surface charge density (in $\mu C/m^2$) on the sheet is $\rho_s(x,y) = 4|y|$, then the total charge (in $\mu C$, rounded off to the nearest integer) on the sheet is

(A)

16

(B)

85

(C)

64

(D)

128

Explanation

GATE→2025→Electromagnetics→Maxwell's Equations and Plane Waves

Q3

MCQ[2 Marks]

An electric field of 0.01 V/m is applied along the length of a copper wire of circular cross-section with diameter 1 mm. Copper has a conductivity of $5.8 \times 10^7 S/m$. The current (in Amperes, rounded off to two decimal places) flowing through the wire is

(A)

0.46

(B)

1.82

(C)

0.58

(D)

1.12

Explanation

GATE→2025→Electromagnetics→Maxwell's Equations and Plane Waves

Q4

NAT[2 Marks]

Two resistors are connected in a circuit loop of area $5~m^2$, as shown in the figure below. The circuit loop is placed on the x-y plane. When a time-varying magnetic flux, with flux-density $B(t) = 0.5 t$ (in Tesla), is applied along the positive z-axis, the magnitude of current I (in Amperes, rounded off to two decimal places) in the loop is ______

Explanation

GATE→2024→Electromagnetics→Maxwell's Equations and Plane Waves

Q5

MCQ[1 Mark]

Let $\hat{i}$ and $\hat{j}$ be the unit vectors along x and y axes, respectively and let A be a positive constant. Which one of the following statements is true for the vector fields $\vec{F}_1 = A(\hat{i}y + \hat{j}x)$ and $\vec{F}_2 = A(\hat{i}y - \hat{j}x)$?

(A)

Both $\vec{F}_1$ and $\vec{F}_2$ are electrostatic fields.

(B)

Only $\vec{F}_1$ is an electrostatic field.

(C)

Only $\vec{F}_2$ is an electrostatic field.

(D)

Neither $\vec{F}_1$ nor $\vec{F}_2$ is an electrostatic field.

Explanation

GATE→2024→Electromagnetics→Maxwell's Equations and Plane Waves

Q6

MCQ[2 Marks]

A uniform plane wave with electric field $\vec{E}(x) = A_y \hat{a}_y e^{-j\frac{2\pi x}{3}} \text{ V/m}$ is travelling in the air in the +x direction. It is incident normally on an ideal electric conductor at $x = 0$. The position of the first null of the total magnetic field in the air (measured from $x = 0$ in metres) is

(A)

$-\frac{3}{4}$

(B)

$-\frac{3}{2}$

(C)

-6

(D)

-3

Explanation

GATE→2023→Electromagnetics→Maxwell's Equations and Plane Waves

Q7

MCQ[1 Mark]

Consider a narrow band signal, propagating in a lossless dielectric medium $(\epsilon_r = 4, \mu_r = 1)$, with phase velocity $v_p$ and group velocity $v_g$. Which of the following statement is true? (c is the velocity of light in vacuum.)

(A)

$v_p > c$, $v_g > c$

(B)

$v_p < c$, $v_g > c$

(C)

$v_p > c$, $v_g < c$

(D)

$v_p < c$, $v_g < c$

Explanation

GATE→2023→Electromagnetics→Maxwell's Equations and Plane Waves

Q8

MCQ[2 Marks]

A uniform plane wave with electric field $\vec{E}(x) = A_y \hat{a}_y e^{-j\frac{2\pi x}{3}} \text{ V/m}$ is travelling in the air. It is incident normally on an ideal electric conductor at $x = 0$. The position of the first null of the total magnetic field in the air (measured from $x = 0$ in metres) is

(A)

$-\frac{3}{4}$

(B)

$-\frac{3}{2}$

(C)

-6

(D)

-3

Explanation

GATE→2023→Electromagnetics→Maxwell's Equations and Plane Waves

Q9

MSQ[2 Marks]

The electric field of a plane electromagnetic wave is $E = a_x C_{1x} \cos(\omega t - \beta z) + a_y C_{1y} \cos(\omega t - \beta z + \theta)$ V/m. Which of the following combination(s) will give rise to a left handed elliptically polarized (LHEP) wave?

(A)

$C_{1x} = 1$, $C_{1y} = 1$, $\theta = \pi/4$

(B)

$C_{1x} = 2$, $C_{1y} = 1$, $\theta = \pi/2$

(C)

$C_{1x} = 1$, $C_{1y} = 2$, $\theta = 3\pi/2$

(D)

$C_{1x} = 2$, $C_{1y} = 1$, $\theta = 3\pi/4$

Explanation

GATE→2022→Electromagnetics→Maxwell's Equations and Plane Waves

Q10

MCQ[1 Mark]

In a circuit, there is a series connection of an ideal resistor and an ideal capacitor. The conduction current (in Amperes) through the resistor is $2 \sin(t + \pi/2)$. The displacement current (in Amperes) through the capacitor is

(A)

$2 \sin(t)$

(B)

$2 \sin(t + \pi)$

(C)

$2 \sin(t + \pi/2)$

(D)

0

Explanation

GATE→2022→Electromagnetics→Maxwell's Equations and Plane Waves

Q11

MSQ[1 Mark]

Consider the following wave equation, $\frac{\partial^2 f(x,t)}{\partial t^2} = 10000 \frac{\partial^2 f(x,t)}{\partial x^2}$. Which of the given options is/are solution(s) to the given wave equation?

(A)

$f(x,t) = e^{-(x-100t)^2} + e^{-(x+100t)^2}$

(B)

$f(x,t) = e^{-(x-100t)} + 0.5 e^{-(x+1000t)}$

(C)

$f(x,t) = e^{-(x-100t)} + \sin(x+100t)$

(D)

$f(x,t) = e^{j100\pi(-100x+t)} + e^{j100\pi(100x+t)}$

Explanation

GATE→2022→Electromagnetics→Maxwell's Equations and Plane Waves

Q12

NAT[2 Marks]

In an electrostatic field, the electric displacement density vector, $\vec{D}$, is given by $\vec{D}(x,y,z) = (x^3\vec{i} + y^3\vec{j} + xy^2\vec{k})~\text{C/m}^2$... The electric charge enclosed within R is _______ C (rounded off to two decimal places).

Explanation

Transmission Lines, Waveguides, Optical Fibers, and Antennas

13 Questions

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q13

MCQ[1 Mark]

Consider the Friis' transmission equation $P_{R}=(P_{T}G_{T}G_{R}\lambda^{2})/(4\pi D)^{2}$, where $P_{R}$ and $P_{T}$ are the received and the transmitted powers, respectively. $G_{T}$ and $G_{R}$ are the gain of transmitting and receiving antennas, respectively, D is the distance between the transmitting and receiving antennas, and $\lambda$ is the wavelength in free space. Given: $G_{T}=G_{R}=1.0$, $\lambda=0.30$ m and $P_{T}=+10$ dBm. Choose the distance (D), in km, from the following options at which the received power, $P_{R}=-90$ dBm?

(A)

$\frac{15}{4\pi}$

(B)

$\frac{15}{2\pi}$

(C)

$\frac{75}{2\pi}$

(D)

$\frac{3}{4\pi}$

Explanation

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q14

MSQ[1 Mark]

Which option(s) represents/ represent the dielectric loss tangent of a substrate?

(A)

Ratio of the real to imaginary parts of the total displacement current

(B)

$(\omega\epsilon^{\prime\prime}+\sigma)/(\omega\epsilon^{\prime})$

(C)

Ratio of the electric susceptibility to permittivity

(D)

Ratio of the polarization vector $\vec{P}$ to the displacement vector $\vec{D}$

Explanation

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q15

NAT[1 Mark]

The cutoff frequency (in GHz) for the dominant $TE_{10}$ mode of an air-filled rectangular waveguide of inner dimension $0.28~inch\times0.14$ inch is ______ (rounded off to two decimal places).

Explanation

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q16

NAT[1 Mark]

For a lossless passive two-port network, $|S_{11}|$ and $|S_{21}|$ intersect at -3 dB. For a lossy passive two-port network, $|S_{11}|$ and $|S_{21}|$ intersect at -4 dB. The percentage of power dissipated in the lossy network at the intersection frequency is ______ (rounded off to two decimal places)

Explanation

GATE→2026→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q17

MCQ[2 Marks]

A complex load (in $\Omega$) is represented as $\Gamma_{L}=0.5\angle30^{\circ}$ on the Smith chart. A co-axial cable with a characteristic impedance of $50~\Omega$ is connected to the load. The new input impedance of the load now moves to a diametrically opposite point on the same VSWR circle on the Smith chart. Which option is the nearest input impedance of the cable connected load (in Ω)?

(A)

$20.7-j5.1$

(B)

$17.7-j11.8$

(C)

$97.5-j65.0$

(D)

$97.5+j65.0$

Explanation

GATE→2025→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q18

NAT[2 Marks]

A $50~\Omega$ lossless transmission line is terminated with a load $Z_L$ of $(50 - j75)~\Omega$. If the average incident power on the line is 10 mW, then the average power delivered to the load (in mW, rounded off to one decimal place) is ______

Explanation

GATE→2024→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q19

MCQ[1 Mark]

Consider a lossless transmission line terminated with a short circuit. As one moves towards the generator from the load, the normalized impedances at intervals of $\lambda/8$ are evaluated.

(A)

$Z_{inA} = +1j~\Omega$, $Z_{inB} = \infty$, $Z_{inC} = -1j~\Omega$, $Z_{inD} = 0$

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q20

NAT[2 Marks]

A lossless transmission line with characteristic impedance $Z_0 = 50~\Omega$ is terminated with an unknown load. The magnitude of the reflection co-efficient is $|\Gamma| = 0.6$. As one moves towards the generator from the load, the maximum value of the input impedance magnitude looking towards the load (in $\Omega$) is

Explanation

GATE→2023→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q21

MCQ[2 Marks]

The S-parameters of a two port network is given as $[S] = \begin{bmatrix} S_{11} & S_{12} \\ S_{21} & S_{22} \end{bmatrix}$ with reference to $Z_0$. Two lossless transmission line sections of electrical lengths $\theta_1 = \beta l_1$ and $\theta_2 = \beta l_2$ are added to the input and output ports. The S-parameters $[S']$ of the resultant two port network is

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2023→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q22

MSQ[2 Marks]

The standing wave ratio on a $50~\Omega$ lossless transmission line terminated in an unknown load impedance is found to be 2.0. The distance between successive voltage minima is 30 cm and the first minimum is located at 10 cm from the load. $Z_L$ can be replaced by an equivalent length $l_m$ and terminating resistance $R_m$ of the same line. The value of $R_m$ and $l_m$, respectively, are

(A)

$R_m = 100~\Omega$, $l_m = 20$ cm

(B)

$R_m = 25~\Omega$, $l_m = 20$ cm

(C)

$R_m = 100~\Omega$, $l_m = 5$ cm

(D)

$R_m = 25~\Omega$, $l_m = 5$ cm

Explanation

GATE→2023→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q23

MSQ[2 Marks]

The following circuit(s) representing a lumped element equivalent of an infinitesimal section of a transmission line is/are

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2023→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q24

NAT[2 Marks]

A transparent dielectric coating is applied to glass $(\epsilon_r = 4, \mu_r = 1)$ to eliminate the reflection of red light $(\lambda_0 = 0.75~\mu\text{m})$. The minimum thickness of the dielectric coating, in $\mu\text{m}$, that can be used is _______ (rounded off to two decimal places).

Explanation

GATE→2022→Electromagnetics→Transmission Lines, Waveguides, Optical Fibers, and Antennas

Q25

MSQ[2 Marks]

A waveguide consists of two infinite parallel plates (perfect conductors) at a separation of $10^{-4}$ cm, with air as the dielectric. Assume the speed of light in air to be $3 \times 10^8$ m/s. The frequency/frequencies of TM waves which can propagate in this waveguide is/are

(A)

$6 \times 10^{15}$ Hz

(B)

$0.5 \times 10^{12}$ Hz

(C)

$8 \times 10^{14}$ Hz

(D)

$1 \times 10^{13}$ Hz

Explanation