A current sheet $\vec j$= 10$\widehat u_y$A/m lies on the dielectric interface x = 0 between two dielectric media with $\epsilon_{r1}$= 5, $\mu_{r1}$ = 1 in Region - 1 (x 0). If the magnetic field in Region -1 at x = 0 - is $\vec H_1$ = 3$\widehat u_x$+ 30$\widehat u_y$A /m the magnetic field in Region -2 at x = 0 + is ![](https://i.imgur.com/adCXeQg.png)

$\vec H_2$ = 1.5$\widehat u_x$ + 30$\widehat u_y$ - 10$\widehat u_z$A/m

Advanced Electromagnetics for ECE

Question 1 Multiple Choice (Single Answer)

In a microwave test bench, why is the microwave signal amplitude modulated at 1 kHz?

To increase the sensitivity of measurement
To transmit the signal to a far-off place
To study amplitude modulations
Because crystal detector fails at microwave frequencies

Question 2 Multiple Choice (Single Answer)

Consider a 300 $\Omega$, quarter - wave long (at 1 GHz) transmission line as shown in figure. It is connected to a 10 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

10 V
5 V
60 V
60/7 V

Question 3 Multiple Choice (Single Answer)

If the electric field intensity is given by E = (xu_x + yu_y + zu_z) volt/m, the potential difference between X(20,0) and Y(1,2,3) is

+1 volt
-1 volt
+5 volt
+6 volt

Question 4 Multiple Choice (Single Answer)

A transmission line of characteristic impedance 50 Ω is terminated by a 50 Ωload.
When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm apart on the line is found to be $\dfrac{2\pi}{\lambda}$ radians. The phase velocity of the wave along the line is

0.8 x 10⁸ m/s
1.2 x 10⁸ m/s
1.6 x 10⁸ m/s
3 x 10⁸ m/s

Question 5 Multiple Choice (Single Answer)

A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm if filled with a dielectric of relative permittivity 10.89. Given $\mu_0 = 4\pi\times10^{-7}$H/m, $\epsilon_0$= $\dfrac{10^-9}{36 \pi}$F/m, the characteristic impedance of the cable is

330 $\Omega$
100 $\Omega$
143.3 $\Omega$
43.4$\Omega$

Question 6 Multiple Choice (Single Answer)

A transmission line is feeding 1 Watt of power to a horn antenna having a gain of 10 dB. The antenna is matched to the transmission line. The total power radiated by the horn antenna into the free-space is

10 Watts
1 Watt
0.1 Watt
0.01 Watt

Question 7 Multiple Choice (Single Answer)

For static electric and magnetic fields in an inhomogeneous source-free medium, which of the following represents the correct form of Maxwell`s equations?

$\nabla$. E = 0, $\nabla$ X B = 0
$\nabla$. E = 0,$\nabla$. B = 0
$\nabla$ X B = 0,$\nabla$ x B = 0
$\nabla$ x E = 0,$\nabla$. B = 0

Question 8 Multiple Choice (Single Answer)

A uniform plane wave in the free space is normally incident on an infinitely thick dielectric slab (dielectric constant $\epsilon$= 9). The magnitude of the reflection coefficient is

0
0.3
0.5
0.8

Question 9 Multiple Choice (Single Answer)

The electric and magnetic fields for a TEM wave of frequency 14 GHz in a homogeneous medium of relative permittivity $\epsilon_r$ and relative permeability $\mu_r$ = 1 are given by
$\vec E = E_p e^{j(\omega t - 280\pi \gamma)} \widehat U_z V/m
\qquad
\vec H = 3 e^{j(\omega t - 280\pi \gamma)} \widehat U_x A/m
$

Assuming the speed of light in free space to be 3 x 10⁸ m/s, the intrinsic impedance of free space to be 120$\pi$, the relative permittivity$\epsilon_r$of the medium and the electric field amplitude E_p are

$\epsilon_r$= 3, E_p = 120
$\epsilon_r$= 3, E_p = 360
$\epsilon_r$= 9, E_p = 360
$\epsilon_r$= 9, E_p = 120

Question 10 Multiple Choice (Single Answer)

A transmission line terminates in two branches, each of length $\dfrac{\lambda}{4}$, as shown.
The branches are terminated by 50 $\Omega$ loads. The lines are lossless and have the characteristic impedances shown. Determine the impedance Z_i as seen by the source.

200 $\Omega$
100 $\Omega$
50 $\Omega$
25 $\Omega$

Question 11 Multiple Choice (Single Answer)

The radiation pattern of an antenna in spherical co - ordinates is given by
F ($\theta$) = cos^4$\theta$; 0$\le$$\theta$$\le$$\pi$/2
The directivity of the antenna is

10 dB
12.6 dB
11.5 dB
18 dB

Question 12 Multiple Choice (Single Answer)

The parallel branches of a 2-wire transmission line are terminated in 100 $\Omega$ and 200 $\Omega$ resistors as shown in the figure. The characteristic impedance of the line is Z₀ = 50 $\Omega$ and each section has a length of $\dfrac{\lambda}{4}$. The voltage reflection coefficient at the input is

- j $\dfrac{7}{5}$
$\dfrac{-5}{7}$
j$\dfrac{5}{7}$
$\dfrac{5}{7}$

Question 13 Multiple Choice (Single Answer)

A uniform plane wave travelling in air is incident on the plane boundary between air and another dielectric medium with $\epsilon_r$= 4. The reflection coefficient for the normal incidence, is

zero
0.5$\angle$180�
0.333$\angle$0�
0.333$\angle$180�

Question 14 Multiple Choice (Single Answer)

Which of the following statements is true regarding the fundamental mode of the metallic waveguides shown?

Only P has no cutoff-frequency
Only Q has no cutoff-frequency
Only R has no cutoff-frequency
All three have cutoff-frequencies

Question 15 Multiple Choice (Single Answer)

The depth of penetration of electromagnetic wave in a medium having conductivity $\sigma$ at a frequency of 1 MHz is 25 cm. The depth of penetration at a frequency of 4 MHz will be

6.25 cm
12.50 cm
50.00 cm
100.00 cm

Question 16 Multiple Choice (Single Answer)

The modes in a rectangular waveguide are denoted by where m and n are the eigen numbers along the larger and smaller dimensions of the waveguide respectively. Which one of the following statements is TRUE?

The TM₁₀ mode of the wave does not exist
The TE₁₀ mode of the wave does not exist
The TM₁₀ and the TE₁₀ modes both exist and have the same cut-off frequencies
The TM₁₀ and TM₀₁ modes both exist and have the same cut-off frequencies

Question 17 Multiple Choice (Single Answer)

Refractive index of glass is 1.5. Find the wavelength of a beam of light with a frequency of 10¹⁴ Hz in glass. Assume velocity of light is 3 × 10⁸ m/s in vacuum.

3 $\mu$m
3 mm
2 $\mu$m
1 m

Question 18 Multiple Choice (Single Answer)

A plane wave of wavelength ^$\lambda$ is travelling in a direction making an angle 30° with positive x-axis and 90° with positive y-axis. The ^{$\vec E$} field of the plane wave can be represented as (E₀ is constant)

^{$\vec E$}= ^{$\widehat Y$}E₀ e^j ^{$\left( \omega t + \dfrac{\pi}{\lambda}x \times \dfrac{\sqrt 3 \pi}{\gamma} z \right)$}
^{$\vec E$}= ^{$\widehat Y$}E₀ e^j^{$\left( \omega t - \dfrac{\pi}{\lambda} \times \dfrac{\sqrt 3 \pi}{\gamma} z \right)$}
^{$\vec E$}= ^{$\widehat Y$}E₀ e^j ^{$\left( \omega t + \dfrac{\sqrt 3 \pi}{\gamma} \times \dfrac{\pi}{\lambda} z \right)$}
^{$\vec E$}= ^{$\widehat Y$} E₀ e^j ^{$\left( \omega t - \dfrac{\pi}{\lambda} x + \dfrac{\sqrt 3 \pi}{\gamma} z \right)$}

Question 19 Multiple Choice (Single Answer)

The magnetic field along the propagation direction inside a rectangular waveguide with the cross section shown in the figure is
H_z = 3 Cos(2.094 x 10²x) cos(2.618 x 10² y) cos (6.283 x 10¹⁰ t -$\beta z$

The phase velocity V_p of the wave inside the wave guide satisfies

v_p > c
v_p = c
o < v_p < c
v_p = 0

Question 20 Multiple Choice (Single Answer)

A current sheet $\vec j$= 10$\widehat u_y$A/m lies on the dielectric interface x = 0 between two dielectric media with $\epsilon_{r1}$= 5, $\mu_{r1}$ = 1 in Region - 1 (x < 0) and $\epsilon_{r2}$ = 5, $\mu_{r2}$ = 2 in Region - 2 (x > 0). If the magnetic field in Region -1 at x = 0^- is $\vec H_1$ = 3$\widehat u_x$+ 30$\widehat u_y$A /m the magnetic field in Region -2 at x = 0 + is

$\vec H_2$ = 1.5$\widehat u_x$ + 30$\widehat u_y$ - 10$\widehat u_z$A/m
$\vec H_2$ = 3$\widehat u_x$ + 30$\widehat u_y$ - 10$\widehat u_z$A/M
$\vec H_2$ = 1.5$\widehat u_x$ + 40$\widehat u_y$A/M
$\vec H_2$ = 3$\widehat u_x$ + 30$\widehat u_y$ + 10$\widehat u_z$A/M

Advanced Electromagnetics for ECE

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