Electromagnetic Fields Test - 1 - PDF Flipbook
Electromagnetic Fields Test - 1
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GATE
EEE
Electro
MagneticFields
Test-01Solutions
ELECTROMAGNETIC FIELDS
1. Which one of the following statements is correct? When an
electromagnetic wave strikes the air-dielectric interface at an
angle
a) The normal electric field components have the same value.
b) The tangential magnetic field components are continuous.
c) The electromagnetic wave is reflected back according to
Snell's law.
d) The electromagnetic wave is diffracted.
Answer: (c)
Solution:
EM wave reflected as per Snell's law where Angle of incidence
= Angle of reflection.
2. In a uniform electric field, field lines and equi-potentials
a) are parallel to one another
b) intersect at 45o
c) intersect at 30o
d) are orthogonal
Answer: (d)
Solution:
Field lines i.e., direction of � ⃗ fields are orthogonal or normal to
the equipotential surface and are in the direction of decreasing
potentials.
1
3. If a very flexible wire is laid out in the shape of a hairpin with
its two ends secured, what shape will the wire tend to assume if
a current is passed through it?
a) Parabolic
b) Straight line
c) Circle
d) Ellipse
Answer: (b)
Solution:
Direction of current is opposite so repulsion force will be
present till the wire become straight.
4. The far-zone electric field Eθ, and magnetic field Hϕ of a
Hertzian dipole differ in time phase by
a) 00
b) 900
c) 1200
d) 1800
Answer: (a)
Solution:
For far zone field, = 0 sin � � −
4
= 0 sin � � −
4
So, and are in same time phase, phase difference = 0
2
5. Consider the following:
Lorentz force ⃗ = � ⃗ × � ⃗ �
where e, ⃗ and � ⃗ are respectively the charge of the particle,
velocity of the particle and flux density of uniform magnetic
field
Which one of the following statements is not correct?
a) Acceleration is normal to the plane containing the particle
path and � ⃗ .
b) If the direction of the particle path is normal to � ⃗ , the
acceleration is maximum.
c) If the particle is at rest, the field will deflect the particle.
d) If the particle path is in the same direction of � ⃗ , there will be
no acceleration.
Answer: (c)
Solution:
⃗ = � ⃗ × � ⃗ �
⃗ acceleration will be in the direction of force
and ⃗ = � ⃗ × � ⃗ � = | ⃗ |� � ⃗ � sin �
→ angle between ⃗ and � ⃗ , � normal vector perpendicular to
both ⃗ and � ⃗ .
So, when = 900 as sin = 1 maximum when = 0
⇒ a = 0 i.e., minimum
When | ⃗ | = 0 ⇒ = 0
So no deflection to the charge particle.
3
6. A circular loop placed perpendicular to a uniform sinusoidal
magnetic field of frequency ω1 is revolved about an axis through
its diameter at an angular velocity ω2 rad/sec (ω2 < ω1 ) as shown
in the figure below. What are the frequencies for the e.m.f.
induced in the loop?
a) ω1 and ω2
b) ω1, ω1 + ω2 and ω2
c) ω2, ω1 – ω2 and ω2
d) ω1 – ω2 and ω1 + ω2
Answer: (a)
Solution:
Since magnetic field has frequency ω1 and induced emf due to
varying field assuming loop is at rest i.e., transformer emf = −
has frequency ω1 because differential doesn’t change frequency.
And due to motion of loop assuming B to be constant we have
induced emf having frequency = ω2 (frequency of rotation) so
overall induced emf has frequency component at ω1 and ω2.
4
7. By which one of the following modes the rectangular cavity
resonator cannot be excited?
a) TE011
b) TE101
c) TM110
d) TE110
Answer: (d)
Solution:
For TE mode,
= 0 cos � � cos � � sin � � 110
For p = 0, = 0
So, cannot exists. Cavity can’t be excited in
mode.
8. Match List-I with List-II and select the correct answer using the
code given below the lists:
List-I
A. Work
B. Electric field strength
C. Magnetic flux
D. Magnetic field strength
List-II
1. Ampere per meter
2. Weber
3. Volt per meter
5
4. Joule
Codes:
ABC D
a) 4 3 2 1
b) 1 3 2 4
c) 4 2 3 1
d) 1 2 3 4
Answer: (a)
Solution:
Work → Joule, A → 4
Electric field strength → V/m, B → 3
Magnetic flux → Weber, C → 2
Magnetic field strength → A/m, D → 1
9. For electromechanical energy conversion, a magnetic field is
employed as the medium rather than electric field because
a) the stored energy density for practicable field strength is low
in the electric field.
b) the electric field presents insulation problem
c) the specific magnetic loss is more than the specific dielectric
loss
d) None of the above
Answer: (a)
6
10. A parallel plate capacitor consisting two dielectric materials is
shown in the figure. The middle dielectric slab is placed
symmetrically with respect to the plates.
If the potential difference between one of the plates and the
nearest surface of dielectric interface is 2 Volt, then the ratio ε1:
ε2 is
a) 1:4
b) 2:3
c) 3:2
d) 4:1
Answer: (c)
Solution:
Voltage ratio is 4: 6
2: 3
Voltage is inversely proportional to 'C' and 'C' is proportional
to .
∴ 1: 2 = 3: 2
7
11. Match List-I (Type of field denoted by � � ⃗ ) with List-II
(Behaviour) and select the correct answer using the codes given
below:
List-I List-II
A. A static electric field 1. ∇. ⃗ = 0
in a charge free region ∇ × ⃗ ≠ 0
B. A static electric field 2. ∇. ⃗ ≠ 0
in a charged region ∇ × ⃗ = 0
C. A steady magnetic field in a 3. ∇. ⃗ ≠ 0
current carrying conductor ∇ × ⃗ ≠ 0
D. A time-varying electric field 4. ∇. ⃗ = 0
in a charged medium with time- ∇ × ⃗ = 0
varying magnetic field
Codes:
ABC D
a) 4 2 3 1
b) 4 2 1 3
c) 2 4 3 1
d) 2 4 1 3
Answer: (b)
Solution:
• Curl of static electric field is always zero i.e. it is
conservative
8
• Div of steady magnetic field is always zero. No monopole
can exist.
• Curl of time-varying electric field is never zero.
12. Which one of the following is correct?
A particular mode in a cavity resonator can be excited by
introducing a probe inside the cavity at a location where
a) The electric field is a maximum.
b) The electric field is a minimum.
c) The magnetic field is a maximum.
d) The magnetic field is a minimum
Answer: (a)
Solution:
Cavity can be excited or a mode can be produced by a small
loop at a position where magnetic field is minimum or by a
probe where electric field is maximum.
13. Assertion (A): Knowing magnetic vector potential ⃗ at a
point, the flux density � ⃗ at that point can be obtained.
Reason (R): �∇⃗. ⃗ = 0
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is not the correct explanation of
A.
c) A is true but R is false.
d) A is false but R is true.
Answer: (b)
9
Solution:
Since magnetic vector potential is defined as
∇�⃗. ⃗ = � ⃗
So knowledge of ⃗ will be useful in determining � ⃗ so A is
correct.
∇. ⃗ = 0
It is also true but not the reason for A
14. Smith's charts are used to obtain the impedance relations along
a
a) Lossless transmission line for different load conditions.
b) Lossy transmission line for different load conditions.
c) Lossy transmission line terminated at a load equal to line
characteristic impedance.
d) Lossless transmission line terminated at a load equal to line
characteristic impedance.
Answer: (a)
Solution:
Smith chart are obtained for lossless transmission line for
different line loading.
15. Maxwell equations
1. are extension of the works of Gauss, Faraday and Ampere.
2. help studying the application of electrostatic fields only.
3. can be written in integral form and point form.
4. need not be modified depending upon the media involved in
the problem.
10
Which of the above statements are correct?
a) 1 and 3
b) 1 and 4
c) 2 and 3
d) 3 and 4
Answer: (a)
Solution:
Maxwell's equations comprise of Gauss's, Faraday's and
Ampere's equations which help studying the application of
electromagnetic field to any medium. These equations can be
represented in point as well as integral form.
16. Which of the following values of alternating voltage should in
insulation absolutely with stand?
a) The effective value
b) The arithmetical average value
c) Half the effective value
d) The peak value
Answer: (d)
17. A structure consisting of two loss-less lines, each λ/4 long and
terminated in a resistance R, is shown in the figure given below.
The lines have characteristic impedances of 2Z0 and Z0
respectively as shown. What is the impedance measured at the
end XX?
11
a) R
b) 4R
c) Z02/R
d) 4Z02/R
Answer: (b)
Solution:
2 = 0 � 0 ++ 0 tan �
tan
2 = λ
4
⇒ 2 = � = 2λ �
2
So, 2 = 0 � 0++ 0 tan //22�
tan
= 02 = 1
Line 1, 1 = λ , 1 =
4 2
1 = 2 0 � 2 10++2 01 tan �
tan
= (2 0) � 20 + 2 0 �tan 2
2 0+ 02 tan 2
1 = 4 02 = 4
02
12
18. What is the value of total electric flux coming out of a closed
surface?
a) Zero
b) Equal to volume charge density
c) Equal to the total charge enclosed by the surface
d) Equal to the surface charge density
Answer: (c)
19. Two parallel wires separated by a distance 'd' are carrying a
current 'I' in the same direction. The magnetic field along a line
running parallel to these wires at midway between them
a) depends upon 'I'
b) is zero
c) depends upon 'd'
d) depends upon the permeability of medium between the wires.
Answer: (b)
Solution:
In fig;
13
By using Ampere’s law; we can find that at any point the z-axis,
� due to (1) = (− ) / and � due to (2) =
2 ( /2)
( ) / . Net � = 0 at any point on this line
2 ( /2)
20. A plane slab of dielectric having dielectric constant 5, placed
normal to a uniform field with a flux density of 2 c/m2 is
uniformly polarized. The polarization of the slab is
a) 0.4 c/m2
b) 1.6 c/m2
c) 2.0 c/m2
d) 6.4 c/m2
Answer: (b)
21. Match List-I (Parameters) with List-II (Range of values)
and select the correct answer using the code given below the
lists:
List-I
A. Reflection coefficient at input
B. VSWR
C. Input impedance
D. Phase shift magnitude
List-II
1. 0 to ∞
2. 1 to ∞
3. -1 to +1
4. 0 to 2π
14
Codes:
ABC D
a) 1 2 3 4
b) 1 4 3 2
c) 3 1 4 2
d) 3 2 1 4
Answer: (d)
Solution:
Reflection coefficient = − 0
+ 0
For = 0, Γ = −1
For = 0, Γ = 0
For = ∞, Γ = +1
−1 ≤ Γ ≤ 1
= 1+|Γ |
1−|Γ |
For |Γ | = 0 = 1
|Γ | = 1 = ∞
1 ≤ ≤ ∞ … . . (2)
= 0 � ++ 0 tan � … … (1)
tan
For = 0 tan = 0
⇒ =
=
2
If = 0, = 0
= ∞, = ∞
15
0 ≤ ≤ ∞
Phase shift 0 to 2
22. The force with which the plates of a parallel plate capacitor
having charge Q and area of each plate, A attract each other is
1. directly proportional to Q
2. directly proportional to Q2
3. inversely proportional to A
a) 1 and 2 only
b) 2 and 3 only
c) 1 and 3 only
d) 1, 2 and 3
Answer: (b)
23. Which one of the following statement is correct?
The condition which does not guarantee distortion less
transmission is
a) at low frequencies, R >> ωL and G >> ωC
b) at high frequencies, R
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