Electromagnetics Test 2

Question 1
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Consider \(\vec D = (10x{\hat a_y} - 4y{\hat a_y} + kz{\hat a_z}~)\frac{{\mu C}}{{{m^2}}}\) and \(\vec B = 2{\hat a_y}~mT\). To satisfy the Maxwell’s equation for region σ = 0 and ρ_v = 0, the value of k will be

A
– 8 μC/m³

B
– 6 μC/ m3

C
– 4 μC/ m³

D
– 2 μC/ m³

Question 2
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It is required to match a 200 Ω load to a 300 Ω transmission line to reduce the SWR along the line to 1. If it is connected directly to the load, the characteristic impedance of the quarter-wave transformer used for this purpose will be

A
275 Ω

B
260 Ω

C
245 Ω

D
230 Ω

Question 3
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A magnetic field in the air is measured as
\(\vec H = {H_0}\left( {\frac{{7x}}{{{y^2}}}\;\hat x - \frac{{8y}}{{{x^2}}}\hat y} \right)\;A/m\)
The magnitude of current distribution at (1,1,0) that caused this field is?

A
30 H₀

B
50 H₀

C
-30 H₀

D
10 H₀

Question 4
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Electric field intensity of linearly polarized plane wave in free space is given by:
E = (5a_y – 6a_x) cos (ωt – 50z) V / m
The phasor form of magnetic field intensity of the wave will be

A
–η₀(5a_x + 6a_y)e^-j50z V / m

B
\(\left( {5{a_x} - 6{a_z}} \right)\frac{{{e^{ - j50z}}}}{{{\eta _0}}}V/m\)

C
\(\left( {5{a_x} - 6{a_y}} \right)\frac{{{e^{ - j50z}}}}{{{\eta _0}}}\;V/m\)

D
\( - \left( {5{a_x} + 6{a_y}} \right)\frac{{{e^{ - j50z}}}}{{{\eta _0}}}V/m\)

Question 5
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A transmission line having characteristic impedance ‘Z₁’ of varying length in series with a load impedance ‘Z_L’ appears in a Smith Chart on

A
Constant Resistance Circle

B
Constant VSWR circle

C
Constant Reactance Circle

D
All of the above

Question 6
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The skin depth of an EM wave in two dissipative media A and B is δ and 2δ respectively. If the velocity of the wave in medium A is ν, the velocity of wave in medium B is

A
ν/n

B
ν/2

C
v

D
2ν

Question 7
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For a wave propagating in an air-filled rectangular waveguide.

A
The guided wavelength is always less than the free-space wavelength.

B
The phase velocity is linear function of the operating frequency

C
The ratio of the transverse magnetic field to the transverse electric field is called waveguide impedance

D
The wave impedance can be less than or greater than the free space impedance

Question 8
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At Ultra-high frequencies, short-circuited lossless transmission lines can be used to provide appropriate values of impedance. Match List I with List-II and select the correct answer using the code given below the lists:
List I
List II
a.
l < λ / 4
1.
Capacitive
b.
λ / 4 < l < λ / 2
2.
Inductive
c.
l = λ / 4
3.
0
d.
L = λ / 2
4.
∞

A
a-2, b-1, c-4, d-3

B
a-3, b-1, c-4, d-2

C
a-2, b-4, c-1, d-3

D
a-3, b-4, c-1, d-2

Question 9
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The angle (in degree) with which the wave should be incident on polystyrene with ϵ_r = 2.7 such that the reflected wave is linearly polarised is __________.

A
58.67°

B
31.32°

C
37.486°

D
None of the above

Question 10
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Which of the following statements is/are true?

A
The principle of fiber optical communication is frequency modulation.

B
Optical fibers experience less attenuation as compared to coaxial cables.

C
A rectangular waveguide cannot support TEM mode of transmission.

D
For a wave propagating in an air-filled rectangular waveguide propagation constant is always a real quantity.

Question 11
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An 18 GHz common-carrier microwave communications link uses a tower-mounted antenna with a gain of 36 dB and a transmitter power of 10 W. The power density at a distance of 20 m from the antenna is _______ Watt / m²

A
7.8-8.2

B
7.84-8.21

C
7.87-8.26

D
7.89-8.22

Question 12
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A TE wave propagating in a lossless dielectric filled waveguide of unknown permittivity has dimensions. a = 5 cm, b = 3 cm. the x-component of the electric field is
\({E_x} = - 36\cos \left( {40\pi x} \right)\sin \left( {100\pi y} \right)\left[ {\sin 2.4\pi \times {{10}^{10}}t - 52.9\pi z} \right]V/m\)
the cutoff frequency of the wave guide for the mode is _______ GHz

A
9-11

B
94-111

C
97-116

D
99-112

Question 13
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A uniform plane wave in region 1 is normally incident on the planner boundary separating regions 1 and 2. Both region are lossless and ε_r1 = μ³_r1, ε_r2 = μ³_r2. If 20% of the energy in the incident wave is reflected at the boundary, the possible value of the ratio ε_r2 / ε_r1 is/are:

A
1.48

B
17.9

C
0.056

D
58.3

Question 14
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Given \(\vec J = \frac{{50}}{\rho }{\hat a_\rho } + \frac{{40}}{{{\rho ^2} + 4}}{\hat a_z}\;A/{m^2}\), then the total current crossing the plate z = 0.2 in the a_z direction, for ρ varying as 0 < ρ < 16 is ____ in (A)

A
524-525

B
5244-5251

C
5247-5256

D
5249-5252

Question 15
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In a telecommunication trans-receive system, the transmitting antenna with an antenna aperture of 1m is fed with 1W of power at 10 GHz. The receiver antenna with antenna aperture of 0.5m located at 1km away receives ‘x’ mW of power. If the transmitting frequency changes to 20 GHz, what will happen to receive power ?

A
Increase by 3dB

B
Increase by 6dB

C
Decrease by 3dB

D
Decrease by 6dB

Question 16
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Medium 1 comprising the region z > 0 is a magnetic material with permeability μ₁ = 4μ₀ whereas the medium 2, comprising the region z < 0 is a magnetic material with permeability μ₂ = 2μ₀. Magnetic flux density is medium 1 is given by:
B₁ = (0.4 a_x + 0.8 a_y + a_z) Wb/m²
If the boundary z = 0 between the two media carries a surface current of density K given by:
\(K = \frac{1}{{{\mu _0}}}\left( {0.2\;{a_x} - 0.4\;{a_y}} \right)A/m\)
The magnetic flux density in medium 2 will be:

A
(0.8 a_x + a_y + a_z) Wb/m²

B
(-a_x + 0.8 a_y - a_z) Wb/m²

C
(a_x + 0.8 a_y + a_z) Wb/m²

D
(a_x + 0.8 a_y) Wb/m²

Question 17
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The reflection coefficient on a 500 m long transmission line has a phase angle of -150°. If the operating wavelength is 150 m. The number of voltage maxima on line are:

A
2

B
3

C
6

D
7

Question 18
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A 3 GHz 10 V/m amplitude wave in incident at air soil boundary. Ignoring reflection if the wet soil medium is characterised by μ_r = 1, ϵ_r = 9 and conductivity σ = 5 × 10^-4 S/m. Then the depth at which the Amplitude of incident wave be down to 1 mV/m is ___________ meters (upto 2 decimal places)

A
290-300

B
2904-3001

C
2907-3006

D
2909-3002

Question 19
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A 45 m long lossless transmission line with Z₀ = 50 Ω operating 2 MHz is terminated with a load, Z_L = (60 + j40) Ω. If the phase velocity on the line is 0.6 times the velocity of light, the input impedance is:

A
60 + j40

B
60 – j40

C
50

D
50 + j30

Question 20
2 / -0.33

A 4-port network has the scattering matrix as shown
\(\left[ S \right]=\left[ \begin{matrix} 0.1\angle 90{}^\circ & 0.8\angle -45 & 0.3\angle -45 & a \\ 0.8\angle -45{}^\circ & 0 & 0 & 0.4\angle 45{}^\circ \\ 0.3\angle -45{}^\circ & 0 & 0 & 0.6\angle -45{}^\circ \\ a & 0.4\angle 45{}^\circ & 0.4\angle -45{}^\circ & 0 \\\end{matrix} \right]\)
For the network to be lossless the value of |a| is _________.

A
0.48-0.52

B
0.484-0.521

C
0.487-0.526

D
0.489-0.522

Question 21
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Light pulses propagate through a fiber cable with an attenuation of 0.3 dB/km. The fiber has core diameter of 100 μm. The core and cladding refractive indices are 1.6 and 1.57 respectively.
Which of the following statements is/are true?

A
The maximum angle over which light rays entering the fiber will be trapped in its core is 17.96°

B
The maximum angle over which light rays entering the fiber will be trapped in its core is 78.8°

C
The number of modes that the fiber can propagate at a wavelength of 1 μm is 500

D
The power of pulses is reduced by 50% at a distance of 10 km

Submit Test

List I		List II
a.	l < λ / 4	1.	Capacitive
b.	λ / 4 < l < λ / 2	2.	Inductive
c.	l = λ / 4	3.	0
d.	L = λ / 2	4.	∞

Electromagnetic...

Question 1

– 8 μC/m3

– 6 μC/ m3

– 4 μC/ m3

– 2 μC/ m3

Question 2

275 Ω

260 Ω

245 Ω

230 Ω

Question 3

30 H0

50 H0

-30 H0

10 H0

Question 4

–η0 (5ax + 6ay)e-j50z V / m

\(\left( {5{a_x} - 6{a_z}} \right)\frac{{{e^{ - j50z}}}}{{{\eta _0}}}V/m\)

\(\left( {5{a_x} - 6{a_y}} \right)\frac{{{e^{ - j50z}}}}{{{\eta _0}}}\;V/m\)

\( - \left( {5{a_x} + 6{a_y}} \right)\frac{{{e^{ - j50z}}}}{{{\eta _0}}}V/m\)

Question 5

Constant Resistance Circle

Constant VSWR circle

Constant Reactance Circle

All of the above

Question 6

ν/n

ν/2

v

2ν

Question 7

The guided wavelength is always less than the free-space wavelength.

The phase velocity is linear function of the operating frequency

The ratio of the transverse magnetic field to the transverse electric field is called waveguide impedance

The wave impedance can be less than or greater than the free space impedance

Question 8

a-2, b-1, c-4, d-3

a-3, b-1, c-4, d-2

a-2, b-4, c-1, d-3

a-3, b-4, c-1, d-2

Question 9

58.67°

31.32°

37.486°

None of the above

Question 10

The principle of fiber optical communication is frequency modulation.

Optical fibers experience less attenuation as compared to coaxial cables.

A rectangular waveguide cannot support TEM mode of transmission.

For a wave propagating in an air-filled rectangular waveguide propagation constant is always a real quantity.

Question 11

7.8-8.2

7.84-8.21

7.87-8.26

7.89-8.22

Question 12

9-11

94-111

97-116

99-112

Question 13

1.48

17.9

0.056

58.3

Question 14

524-525

5244-5251

5247-5256

5249-5252

Question 15

Increase by 3dB

Increase by 6dB

Decrease by 3dB

Decrease by 6dB

Question 16

(0.8 ax + ay + az) Wb/m2

(-ax + 0.8 ay - az) Wb/m2

(ax + 0.8 ay + az) Wb/m2

– 8 μC/m³

– 4 μC/ m³

– 2 μC/ m³

30 H₀

50 H₀

-30 H₀

10 H₀

–η₀(5a_x + 6a_y)e^-j50z V / m

(0.8 a_x + a_y + a_z) Wb/m²

(-a_x + 0.8 a_y - a_z) Wb/m²

(a_x + 0.8 a_y + a_z) Wb/m²

(a_x + 0.8 a_y) Wb/m²